# Refutation of Stable Thermal Equilibrium Lapse Rates

Guest post by Robert G. Brown
Duke University Physics Department

### The Problem

In 2003 a paper was published in Energy & Environment by Hans Jelbring that asserted that a gravitationally bound, adiabatically isolated shell of ideal gas would exhibit a thermodynamically stable adiabatic lapse rate. No plausible explanation was offered for this state being thermodynamically stable – indeed, the explanation involved a moving air parcel:

An adiabatically moving air parcel has no energy loss or gain to the surroundings. For example, when an air parcel ascends the temperature has to decrease because of internal energy exchange due to the work against the gravity field.

This argument was not unique to Jelbring (in spite of his assertion otherwise):

The theoretically deducible influence of gravity on GE has rarely been acknowledged by climate change scientists for unknown reasons.

The adiabatic lapse rate was and is a standard feature in nearly every textbook on physical climatology. It is equally well known there that it is a dynamical consequence of the atmosphere being an open system. Those same textbooks carefully demonstrate that there is no lapse rate in an ideal gas in a gravitational field in thermal equilibrium because, as is well known, thermal equilibrium is an isothermal state; nothing as simple as gravity can function like a “Maxwell’s Demon” to cause the spontaneous stable equilibrium separation of gas molecules into hotter and colder reservoirs.

Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics. It is a direct, literal violation of the refrigerator statement of the second law of thermodynamics as it causes and maintains such a separation without the input of external work. As is usually the case, violation of the refrigeration statement allows heat engines to be constructed that do nothing but convert heat into work – violating the “no perfectly efficient heat engine” statement as well.

The proposed adiabatic thermal lapse rate in EEJ is:

where g is the gravitational acceleration (presumed approximately constant throughout the spherical shell) and cp  is the heat capacity per kilogram of the particular “ideal” gas at constant pressure. The details of the arguments for an adiabatic lapse rate in open systems is unimportant, nor does it matter what cp is as long as it is not zero or infinity.

What matters is that EEJ asserts that   in stable thermodynamic equilibrium.

The purpose of this short paper is to demonstrate that such a system is not, in fact, in thermal equilibrium and that the correct static equilibrium distribution of gas in the system is the usual isothermal distribution.

### The Failure of Equilibrium

In figure 1 above, an adiabatically isolated column of an ideal gas is illustrated. According to EEJ, this gas spontaneously equilibrates into a state where the temperature at the bottom of the column Tb is strictly greater than the temperature Tt at the top of the column. The magnitude of the difference, and the mechanism proposed for this separation are irrelevant, save to note that the internal conductivity of the ideal gas is completely neglected. It is assumed that the only mechanism for achieving equilibrium is physical (adiabatic) mixing of the air, mixing that in some fundamental sense does not allow for the fact that even an ideal gas conducts heat.

Note well the implication of stability. If additional heat is added to or removed from this container, it will always distribute itself in such a way as to maintain the lapse rate, which is a constant independent of absolute temperature. If the distribution of energy in the container is changed, then gravity will cause a flow of heat that will return the distribution of energy to one with Tb > Tt . For an ideal gas in an adiabatic container in a gravitational field, one will always observe the gas in this state once equilibrium is established, and while the time required to achieve equilibrium is not given in EEJ, it is presumably commensurate with convective mixing times of ordinary gases within the container and hence not terribly long.

Now imagine that the bottom of the container and top of the container are connected with a solid conductive material, e.g. a silver wire (adiabatically insulated except where it is in good thermal contact with the gas at the top and bottom of the container) of length  L . Such a wire admits the thermally driven conduction of heat according to Fourier’s Law:

where λ  is the thermal conductivity of silver, A is the cross-sectional area of the wire, and ΔT=Tb-Tt . This is an empirical law, and in no way depends on whether or not the wire is oriented horizontally or vertically (although there is a small correction for the bends in the wire above if one actually solves the heat equation for the particular geometry – this correction is completely irrelevant to the argument, however).

As one can see in figure 2, there can be no question that heat will flow in this silver wire. Its two ends are maintained at different temperatures. It will therefore systematically transfer heat energy from the bottom of the air column to the top via thermal conduction through the silver as long as the temperature difference is maintained.

One now has a choice:

• If EEJ is correct, the heat added to the top will redistribute itself to maintain the adiabatic lapse rate. How rapidly it does so compared to the rate of heat flow through the silver is irrelevant. The inescapable point is that in order to do so, there has to be net heat transfer from the top of the gas column to the bottom whenever the temperature of the top and bottom deviate from the adiabatic lapse rate if it is indeed a thermal equilibrium state.
• Otherwise, heat will flow from the bottom to the top until they are at the same temperature. At this point the top and the bottom are indeed in thermal equilibrium.

It is hopefully clear that the first of these statements is impossible. Heat will flow in this system forever; it will never reach thermal equilibrium. Thermal equilibrium for the silver no longer means the same thing as thermal equilibrium for the gas – heat only fails to flow in the silver when it is isothermal, but heat only fails to flow in the gas when it exhibits an adiabatic lapse in temperature that leaves it explicitly not isothermal. The combined system can literally never reach thermal equilibrium.

Of course this is nonsense. Any such system would quickly reach thermal equilibrium – one where the top and bottom of the gas are at an equal temperature. Nor does one require a silver wire to accomplish this. The gas is perfectly capable of conducting heat from the bottom of the container to the top all by itself!

One is then left with an uncomfortable picture of the gas moving constantly – heat must be adiabatically convected downward to the bottom of the container in figure 1 in ongoing opposition to the upward directed flow of heat due to the fact that Fourier’s Law applies to the ideal gas in such a way that equilibrium is never reached!

Of course, this will not happen. The gas in the container will quickly reach equilibrium. What will that equilibrium look like? The answer is contained in almost any introductory physics textbook. Take an ideal gas in thermal equilibrium:

where N is the number of molecules in the volume V, k is Boltzmann’s constant, and T is the temperature in degrees Kelvin. n is the number of moles of gas in question and R is the ideal gas constant. If we assume a constant temperature in the adiabatically isolated container, one gets the following formula for the density of an ideal gas:

where M is the molar mass, the number of kilograms of the gas per mole.

The formula for that describes the static equilibrium of a fluid is unchanged by the compressibility (or lack thereof) of the fluid – for the fluid to be in force balance the variation of the pressure must be:

(so that the pressure decreases with height, assuming a non-negative density). If we multiply both sides by dz and integrate, now we get:

Exponentiating both sides of this expression, we get the usual exponential isothermal lapse in the pressure, and by extension the density:

where P0 is the pressure at z=0 (the bottom of the container).

This describes a gas that is manifestly:

1. In static force equilibrium. There is no bulk transport of the gas as buoyancy and gravity are in perfect balance throughout.
2. In thermal equilibrium. There is no thermal gradient in the gas to drive the conduction of heat.

If this system is perturbed away from equilibrium, it will quickly return to this combination of static and thermal equilibrium, as both are stable. Even in the case of a gas with an adiabatic lapse rate (e.g. the atmosphere) remarkably small deviations are observed from the predicted P(z) one gets treating the atmosphere as an ideal gas. An adiabatically isolated gas initially prepared in a state with an adiabatic lapse rate will thermally equilibrate due to the internal conduction of heat within the gas by all mechanisms and relax to precisely this state.

### Conclusion

As we can see, it is an introductory physics textbook exercise to demonstrate that an adiabatically isolated column of gas in a gravitational field cannot have a thermal gradient maintained by gravity. The same can readily be demonstrated by correctly using thermodynamics at a higher level or by using statistical mechanics, but it is not really necessary. The elementary argument already suffices to show violation of both the zeroth and second laws of thermodynamics by the assertion itself.

In nature, the dry adiabatic lapse rate of air in the atmosphere is maintained because the system is differentially heated from below causing parcels of air to constantly move up and down. Reverse that to a cooling, like those observed during the winter in the air above Antarctica, and the lapse rate readily inverts. Follow the air column up above the troposphere and the lapse rate fails to be observed in the stratosphere, precisely where vertical convection stops dominating heat transport. The EEJ assertion, that the dry adiabatic lapse rate alone explains the bulk of so-called “greenhouse warming” of the atmosphere as a stable feature of a bulk equilibrium gas, is incorrect.

## 1,011 thoughts on “Refutation of Stable Thermal Equilibrium Lapse Rates”

1. DanSanto says:

Do people really have to have stuff like this demonstrated? I saw, but didn’t read, the previous post on this topic. I thought it was a weird thing to have on a climate blog, though since it did deal with a gas and our climate is a gas, I didn’t think too much of it.

Now, I’ve gone back and read that previous post and glanced through the LONG bunch of comments, a disturbing number of which actually supported the impossible idea. This is basic physics, Second Law of Thermodynamics sort of stuff – you can’t get perpetual-anything.

I thought everyone realized you can’t magically use gravity or magnets to generate perpetual energy machines. It blows my mind that there are actually people who think a thermally graded column would result. It’s nothing but a variation on a perpetual energy machine.

Kudos to WUWT for spending some time debunking this sort of nonsense. It’s sad that there are apparently so many people who swallow this sort of nonsense in the first place.

2. steveta_uk says:

There seem to be a lot of people who think that a lapse rate is a proprty of the matter itself, rather than a convenient description of the behaviour of the gas.

I’m not sure that Dr Brown will convince them otherwise.

But maybe Hans Jelbring can convince us all that the heat in figure 2 cannot rise up the silver bar because graivity is holding it down!

3. Sometimes something like this comes along that refutes a common idea so well and simply that it just makes a guy go ‘holy crap!’. Thanks for this excellent post as for me it was a revelation.

4. ‘what goes up, has to come down,spinning wheel has to go round’ blood sweat and tears. it’s a bit warm !

5. Alan Robertson says:

“If this system is perturbed away from equilibrium, it will quickly return to this combination of static and thermal equilibrium, as both are stable.
_______________________
This is also perfectly expressed by Le Chatelier’s Principle.

6. Bryan says:

What would complement this theoretical explanation is if an experiment backed it up.
So far as I know no experiment has ever been carried out.
All suggested proposals seem to run into problems when real components and physically accurate numbers are used.

7. Joules Verne says:

“Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics. It is a direct, literal violation of the refrigerator statement of the second law of thermodynamics as it causes and maintains such a separation without the input of external work.”

No, Robert. The second law requires that no energy gradient can be maintained without input of work. It requires the reservoir of gas to be isoenergetic not isothermal. A horizontal layer may be a different temperature than another if the cooler layer has its lesser kinetic energy balanced by greater gravitational energy. This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer. Thus the second law actually demands a temperature difference of equal and opposite polarity to compensate for the difference in gravitational energy. An isothermal atmosphere in a gravity field is the one that violates the second law.

My name is Joules because I know how to find and count them no matter how they try to hide.

Thanks for playing.

8. Richard says:

Hmmm. Temperature is the integral of the number and energy of particles seen at the measuring surface. Less particles equal lower temperature given equal velocity profiles of the particles. Less particles also equals lower pressure. Temperature and pressure are thus directly linked. Hence the dry lapse rate. Gravity and pressure are also directly linked. Hence the dry lapse rate.

9. Alan Millar says:

Well thanks for taking the time to post Doc.

I gave up trying to convince Tallbloke in the other thread as he is clearly in ‘La La La’ mode.

His reply as to what was going to stop heat flow in a system with a temperature gradient was that at the interface between hotter and colder the actual temperature was the same and therefore no heat would flow!

Lets see, take a rod with a temperature gradient and cut it into the thinnest possible slices allowed in physics and apparently adjoining slices are the same temperature!

However, that would mean the rod was actually the same temperature all the way through as not only are those two touching slices (call them a & b) the same temperature, then obviously, the two slices c & d touching them are also at the same temperature and the two slices e & f touching c & d are the same as c & d and a & b also. Well you get the picture.

Anyway I am sure he will be along soon to show that gravity has some magical quality that allows work to be done indefinitly in a closed system.

Alan

10. kdk33 says:

The dry adiabatic lapse rate is derived several ways, each of which assumes an isentropic atmosphere.

Example 1. A packet of dry air rises. Let’s first assert that it is adiabatic (hopefully not controversial), as it rises it expands and does work on it’s environemnt. But that work is reversible. Thus the process is adiabatic and reversible, hence isentropic. By definition.

Example 2. We know from calculus that dx/dy(w)*dy/dw(x)*dw/dx(y) = -1. Let us apply this identity to dT/dp(s), the temperature pressure relationship at constant entropy. We will find that dT/dp=-dS/dP * dT/ds. the second RHS term is Cp/T by the definitoin of entropy. The first RHS term is, by a Maxwell relationship, -dV/dT, which for an ideal gas is R/P (you can google Maxwell relationship). Making the substitutions: dT/dp = RT/PCp = V/Cp for an ideal gas. Lastly we recognize that the gravity imposed pressure gradient is dP/dz = rho*g, but rho is 1/V, so when we multiply: dT/dp * dp/dz = V/Cp * g/V = g/Cp.

Example 3. The state of an ideal gas is fully specified when two variables are specified. We shall choose T and p. The total entropy differential is: dS = dS/dT * dT + dS/dp * dp. at constant entropy, dS=0, then dT/dp = dS/dp * dT/dS and we proceed as above.

So, it seems quite clear to me that the near surface atmosphere is isentropic.

The moist adiabatic lapse rate MALR differs from the DALR because it must account for the latent heat release as water condenses. This extra heat slows the rate of cooling of a rising air packet, so the MALR is less than the DALR – but it is still isentropic as it satisfies all the condition of my example 1, but the math is kinda nasty.

The adiabatic lapse rate need not be an equilibrium critereia, but instead a steady state condition if heat transfer in the near surface atmosphere is dominated by convection.

Let’s set moisture aside for the moment and set up a simple dry ideal gas atmosphere. Incoming radiation heats the planet surface. Air at the surface is heated and begins to rise, thus convection begins. Convection is attempting to return the atmospheric temperature gradient to zero, but as it rises it experiences an isentropic expansion, which causes it to cool (the reverse also occurs). If convection is the dominate mode of heat transfer (conduction negligible), it cannot drive the temperature gradient to zero, but only to the DALR.

Thus, I think the DALR is a steady state condition that arises because, in the near surface atmosphere, convection is the dominate heat transfer mode and it is a compressible fluid with a gravity imposed pressure gradient, hence convection is constrained by the DALR.

Lastly, if I assume the entire atmosphere is isentropic – all the way to the tippy top – then T1/T2 = P1/P2^0.4. If I solve for T2 letting T1 and P1 be the conditions at the tippy top of the atmosphere, I calculate an enormous value for T2, the surface temperature. Clearly the atmosphere cannot be isentropic all the way up. At some point it becomes non-isentropic.

I think the isentropic condition breaks down when convection ceases to be the dominant mode of heat transfer. As you rise, the atmosphere becomes less dense, convection less effective, until eventually heat transfer is dominated by radiative heat transfer. Radiative heat transfer is not constrained by the DALR and can drive the temperature gradient to zero. Hence the planet surface temperature is not enormous.

So, the non-radiative atmospheric thermal effect becomes an exercise in identifying at what point in the atmosphere does convection cease to dominate, which is also the point where the isentropic assumption breaks down. If that point is known (yes I know it won’t be a sharpt break between convection and radiation, but let’s keep it simple), then the equation above can be used to find the increase in surface temperature resulting from an isentropic near surface atmosphere.

Now, I could very well be wrong, or have made mistakes along the way (I do that sometimes – maybe even more than sometimes). But please don’t wave your hands at me and tell me to “check the meaning of entropy” – I find that frustrating. I think I’ve shown sufficient work…

Show me my mistake. Anybody. I won’t be offended.

T = temperature
p = pressure
V = olume
R = ideal gas constant
Cp = ideal gas heat capacity = 5/2R
g = gravitational constant
rho = density = 1/V
z = vertical spatical coordinate.

11. John Marshall says:

Very interesting but really irrelevant given that our atmosphere is not an ideal gas in a cylinder. Gas, ideal or otherwise, is a very poor heat conductor compared to Silver so perhaps your example above is not very good and enrtopy will still increase. It can be demonstrated by observation that convecting gas does rise, due to the density difference between the rising gas and that of the surroundings. If we consider real air it can be saturated with water vapour and rise to form clouds. The rising air will cool adiabatically at the SALR (4c/1000m rise) but will descend, as it must as dried air having the water vapour removed in the cloud formation, and warm at the DALR (9.8C/1000m) and end up with more heat than it started with. Rather like a Foehne Wind in a vertical loop. Katabatic winds are warmer at the bottom of their descent than the cold mountain start. The atmosphere is never in equilibrium because the planet rotates, there is a non-uniform surface and moving clouds which alter the solar energy falling on the surface. It is the lack of atmospheric equilibrium that gives us weather.

I am not being obtuse here but there is so much wrong with the GHG theory, cooling planet and rising GHG’s, lack of the predicted tropospheric heat, and the violation of 2nd law with this heat transfer from a cool troposphere to the warmer surface. If you could do that you really would have a PMM. So an alternative mechanism must be found to explain the BB heat anomaly, assuming that this is correct.

12. Ed Caryl says:

“In nature, the dry adiabatic lapse rate of air in the atmosphere is maintained because the system is differentially heated from below causing parcels of air to constantly move up and down.”

I live half-way up a mountain at 6100 feet. The valley below is at 4500 feet. The temperature difference is nearly always the dry lapse rate 8 degrees F, whether it is calm or windy. Only if it is raining or snowing will it be different. It then goes to the moist lapse rate. Most of the time it is sunny, heating the ground equally, both in my back yard and in the valley below. What maintains the lapse rate temperature difference?

13. Bryan says:

In the real atmosphere the Earth surface is heated and radiation cools at top of atmosphere.
Convection is the major method of heat transfer.
Is convection always present?
The answer according to textbooks is no.
We can have the interesting situation where there is little or no convection, still air in other words.
This condition is called the Neutral Atmosphere.
This atmospheric condition is known as the neutral atmosphere and can be stable particularly at night.
See the near Neutral RESIDUAL LAYER page 31
What happens then?

Robert Brown says
“What maintains the adiabatic lapse rate is convection”
Nick Stokes and Joel Shore would agree.

So if convection is absent presumably the lapse rate disappears!
Well not in the real world.
If the air is dry, the lapse rate is at its maximum of g/Cp = – 9.8K/km

Climate Science define convection as an UNSTABLE vigorous vertical exchange of air. .
See bottom of page 13.

The stable condition (hydrostatic approximation) is used to derive the DALR. See page 12
This condition holds for still air and air parcels moving up and down at constant speed (no unbalanced force) will track the DALR.
These air parcels are assumed not to exchange heat with their surroundings.
On going up expansion work PdV is stored by the surroundings(temperature dropping by 9.8K/km)
At TOA there will be a loss of heat by radiation to space causing the down phase
On going down the surroundings do work on the parcel (PdV) (temperature increasing by 9.8K/km)
Stationary parcels will not change temperature.

These two idealised adiabatic processes (like the adiabatic stages in the Carnot Cycle) will result in the parcel returning to Earth with nearly the same temperature as leaving (the slight drop being accounted for by radiation at TOA).

http://www-as.harvard.edu/education/brasseur_jacob/ch2_brasseurjacob_Jan11.pdf

14. Wayne2 says:

@Joules Verne: “This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer.” Does the fact that the air in a higher layer also has fewer molecules matter? That is, are we talking individual molecules or rather volumes of molecules here?

15. Douglas Hoyt says:

Two points:

1) If the atmosphere were isothermal, then a unit mass of atmosphere would have greater total energy (thermal + potential) the higher it is located and the further it is away from the surface heating source. That is not a stable situation.

2) The silver wire will transport heat from warmer region to the cooler region, but in so doing it short circuits the transport of heat by convection. So with the wire present, convection will be less, but the net transport of heat will remain the same.

16. Trick says:

This head post now makes me want to more fully question all the textbooks to which I’ve ever been exposed.

Consider this simplest and no simpler demonstration:

Robert Brown’s wire is U shaped. This sudden U-turn enables the wire to enter a 2nd thermal energy reservoir (another control volume that happens to be a gray colored one). The wire, in Robert’s example in his words, is: “adiabatically insulated except where it is in good thermal contact with the gas at the top and bottom of the container”.

Thus the wire is adiabatically insulated from the temperature field of the gas in the white colored area. Heat will indeed flow until the gray reservoir is in thermal equilibrium with the white reservoir. This just shows why there are no perfect insulators – Perpetuum Mobiles could be constructed in gas in a gravity field. This IS textbook stuff.

Why did Robert Brown have to go to the trouble of constructing a second gray reservoir with the U-turn? Robert Brown needed a second thermal body.

Trick’s view is Robert Brown should run this analysis again with the wire not leaving thermal contact w/white colored control volume gas and report back with only one thermal body or one energy reservoir or one thermodynamic system. Call it what you will.

Meaning Robert Brown is allowed only one heat reservoir to demonstrate his proposed isothermal gas column where the wire stays in thermal contact with the white colored gas everywhere – no U-turns as here to a 2nd thermal reservoir. Trick’s view is Robert will be unable to do so – the gas column will not be isothermal – there will be a temperature lapse rate.

Trick’s view remains that Robert Brown’s proper application 0th, 1st,2nd Thermo Laws will enable Robert Brown to eventually see the one thermodynamic system GHG-free gas column w/gravity is not isothermal in theory since Robert Brown is smart and the thermo grand masters are right.

NB: I am posting here b/c I have had a miserable head cold last few days and was looking for a way to pass the time. It has been interesting & fun to re-learn about thermo. I have to thank Robert Brown (and Willis) for a more enjoyable few days than I would have had otherwise .

17. Joules Verne says:

steveta_uk says:
January 24, 2012 at 6:42 am

“I’m not sure that Dr Brown will convince them otherwise.”

Brown won’t convince him this way.

“But maybe Hans Jelbring can convince us all that the heat in figure 2 cannot rise up the silver bar because graivity is holding it down!”

The device in figure 2 doesn’t work because it’s a closed system and the work extracted will reduce the total energy of the column until eventually there’s no more energy to extract at which point the gas reaches a temperature of absolute zero and has presumably vanished from this universe being totally converted to kinetic energy in the extracted useful work. In the real world the gas will collapse to the surface as a liquid before it gets to absolute zero and this will shut off further extraction of energy because the cold side of the thermocouple no longer has any cold gas to cool it.

18. Eilert says:

When doing thought experiments it is wise to think about what might have been assumed.

I see two assumptions above:
1. It does not matter what the density of the gas is. It will equally conduct heat at the bottom into silver wire, as the wire will be able to conduct its heat into the gas at the top, even though the density at the bottom and top is different, due to the gravitational effect on the gas.
2. The cross-section of the wire will stay the same, which means the ability of the wire to conduct the heat, which depends on its cross-section, is the same at the bottom and top.
The gravitational field will actually pull down a considerable part of the mass to the bottom, making it far wider at the bottom then the top (depending on the length of the wire and its tensile strength), deforming it more into a tear drop shape.

With your setup you may be able to change the lapse rate, but I doubt that you achieve an isothermal state in this way.

19. The iceman cometh says:

I find the analysis quite reasonable – but it is so idealized as to be useless. A more interesting thought experiment has a spherical planet heated by a remote star, rotating on an axis roughly normal to the line to the star, with an atmosphere of non-greenhouse gases. The equator would be warmer than the poles, so there would be Hadley-type circulation that would cool the equator and warm the poles. Would there then be a vertical thermal gradient? I think there would be, but I’m sure someone would like to argue to the contrary.

20. Archonix says:

I see a lot of people talking about heat and temperature as if they’re the same thing here, then basing their arguments on that false premise.

21. pat says:

Isn’t that, for the most part. why we have variable wind? And the reason there is not a pocket of ‘missing’ heat 800 meters below the oceans surface, as is commonly conjectured by Hansen, et al.

22. Marc77 says:

It clearly shows that without an already present differential of temperatures, gravity cannot create one. But the atmosphere is a different problem. It is heated at the bottom and it loses its heat in altitude. So the question is, what can impede the flow of heat from the warmer ground to the cooler “layer of emissions”. It seems to me that both greenhouse gases and gravity would enhance the lapse rate or impede the flow of heat between those 2 layers.

I often hear people say that nights would not be as warm if IRs were not coming from the atmosphere, but what about gas particles falling and hitting them all of the time?

23. Genghis says:

This is funny : ) Almost everyone is right.

Take a single gas molecule and put it at the top of the tube. It has zero kinetic energy and zero temperature. Let it fall and just before it hits the bottom it will have a lot of kinetic energy and heat. That is the lapse rate and it isn’t in equilibrium by definition.

Now place the atom at the bottom of the tube, it is now in isothermic equilibrium, its kinetic energy and temperature is zero.

If we let the atom bounce up and down in the tube, and don’t allow any energy to be extracted, it will stay in perpetual motion (and gravity will be continuously accelerating it) and will have a lapse rate (as long as the lapse rate isn’t measured).

24. Joules Verne says:

Wayne2 says:
January 24, 2012 at 7:39 am

“@Joules Verne: “This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer.” Does the fact that the air in a higher layer also has fewer molecules matter? That is, are we talking individual molecules or rather volumes of molecules here?”

No. The fewer molecules must have sufficient gravitational energy that, if it were converted to kinetic energy, would be able to raise the temperature of a larger number of molecules in the lower layer the temperature in that lower layer. It MUST be isoenergetic to satisfy the second law. It need not be isothermal. In politics they say to follow the money to arrive at the truth. In physics you want to follow the jewels joules.

25. markus says:

“Follow the air column up above the troposphere and the lapse rate fails to be observed in the stratosphere, precisely where vertical convection stops dominating heat transport. The EEJ assertion, that the dry adiabatic lapse rate alone explains the bulk of so-called “greenhouse warming” of the atmosphere as a stable feature of a bulk equilibrium gas, is incorrect”.

So your wonderful assertion, is that the radiative forcing of Co2, occur after its entry into the thermostats of the tropopause, and that extra radiative forcing, causes that missing hot spot, increasing the temperature back through the stratosphere and down again through the thermostat of the tropopause.

Been there, done that.

26. My name is Joules because I know how to find and count them no matter how they try to hide.

Well then, by all means go patent your perpetual motion machine of the second kind or explain heat flow in the second diagram, Joules.

And I’m ever so sorry, but in an ideal gas the temperature is not determined by the total energy. That’s an absurd idea, given that one can perform a gauge transformation — change the zero of the total energy — without changing any of the physics. What matters is the distribution of energy in degrees of freedom. The number of degrees of freedom in an ideal gas does not depend on whether or not the air is in a gravitational field. Take a sealed jar full of air at temperature T and gently carry it upstairs, and it is still at T.

But all of this is too difficult for you, so stick with explaining why figure 2 — based on absolutely trivial physical principles would not occur as described, given a thermal lapse rate in the gas. Is there something miraculously interesting in the thermal contact between silver and air that keeps heat from being conducted from hot to cold — in just this one special circumstance? I’m all ears.

rgb

27. Marc77 says:

Also, a constant temperature with altitude means that particles at the top of the atmosphere have more momentum than particles at the bottom. Can you show that this sorting will happen at the molecular level? Or can this sorting happen only by convection of masses of air?

28. Joe Born says:

That Dr. Brown has it wrong is readily demonstrated by a thought experiment nearly any layman can perform.

If an ideal monatomic gas subjected to gravity in a thermally isolated container consists of only a single molecule, its kinetic energy K–and thus the mean translational kinetic energy–at any altitude z is given by K = mg(z_max -z), where m is molecular mass, g is the acceleration of gravity, and mgz_max is the total (kinetic + potential) energy of the gas. This is true no matter how long you’ve allowed the gas to “equilibrate.” In other words, temperature depends on altitude at equilibrium: there’s a non-zero temperature lapse rate.

Extending this result to any number N of moleculles yields

K = 3 mg(5N-2)(1-z/z_max),

an equation that I’ve adapted from Equation 8 of the Velasco et al. paper, to which I was introduced here: http://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/. Note that temperature still depends on altitude.

As a practical matter, this result differs only negligibly from the isothermality for which Dr. Brown argues if the number of molecules is large. As Dr. Brown states, though, “[t]he magnitude of the [temperature difference, and the mechanism proposed for this separation are irrelevant,” to his attempted refutation. So the fact that there is any non-zero lapse rate at all at equilibrium establishes that Dr. Brown’s attempted refutation is invalid.

I hasten to add that the lapse rate that does prevail at equilibrium is much smaller than that for which Jelbring contends, so Jelbring is still wrong. .

I should also state that I was not able to follow each and every step of Velasco et al. and the Román et al. paper on which it relies. But its result is consistent with the thought experiment above, whereas Dr. Brown’s isothermality theory is not. Moreover, the Román et al. paper starts from a statistical-mechanics basis,, i.e., from first principles, rather than being based based on blindly accepting equations as received truth without double-checking their ranges of applicability.

I would welcome the assistance of any true physicists out there in examining those papers’ equations further.

29. kdk33 says:

says: These two idealised adiabatic processes (like the adiabatic stages in the Carnot Cycle) will result in the parcel returning to Earth with nearly the same temperature as leaving (the slight drop being accounted for by radiation at TOA).

Carnot cycles are ISENTROPIC. By definition. Isentropic means adiabatic AND reversible.

30. Hmmm. Temperature is the integral of the number and energy of particles seen at the measuring surface. Less particles equal lower temperature given equal velocity profiles of the particles. Less particles also equals lower pressure. Temperature and pressure are thus directly linked. Hence the dry lapse rate. Gravity and pressure are also directly linked. Hence the dry lapse rate.

Sure, sure, sure. But no. I provide the explicit algebra that shows that an isothermal gas is perfectly happy supporting itself. If you want to discuss the temperature of the gas, learn what microscopic temperature is, because it does not depend on the number of particles. 10^18 particles of gas in a container can have any temperature you like. So can 10^23. If those two containers have the same temperature, they have the same average kinetic energy per particle (for a monatomic gas). This doesn’t even depend on the mass of the particles.

However, the reason I drew the pictures is so you could all stop pretending that you can do stat mech computations in your head without even knowing what molecular temperature actually is, and concentrate on easier stuff, like heat flow. If the stable thermal equilibrium of the gas in figure 2 has a lapse rate, heat has to be resorted by gravity from the top to the bottom order to maintain the lapse rate as heat flows in the silver! Heat will definitely flow in the silver, right? It’s just a chunk of metal that’s an excellent conductor of heat. Put it in good thermal contact in between gases at two different temperatures, heat will flow because there isn’t any bullshit about gravity that you can invoke without understanding it. It’s just like Newton’s Balls — whack it on one end and the whack is transmitted, more or less undiminished, to the other end until thermal equilibrium is reached.

Only it is never reached, is it? As fast as you warm the top, gravity has to move the heat to the bottom to restore the lapse rate, which means that it keeps flowing through the silver to the top, where it flows back to the bottom, where it flows to the top — perpetual motion — of naked heat, absolutely predicted by high school physics.

You want to assert otherwise, you tell me what the equilibrium state is of figure 2.

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31. Joules Verne – I think you are getting at the crux of the matter here.

These “idealized” descriptions are REALLY DEADLY in this debate.

WHY? What would be the “equilibrium explanation of my coming into LAX 10 years ago, from Hawaii, and watching the temperature INCREASE until 6,000 Feet ASL, where it was 80 F. Then from that point on, until we hit the ground there was an INVERSE lapse rate, going to 65 F on the ground.

Certainly this is a demonstration that “equilibrium thermodynamics” is NOT a proper way to approach any correct modeling of the atmosphere.

It become a difficult, and intractable problem which does not yield to simple differential equations applied to idealized columns of gasses in “ideal” states.

32. Show me my mistake. Anybody. I won’t be offended.

No, I think you are generally quite right, and this agrees rather well with Caballero’s argument. Isentropic because it is dominated by convection, not conduction, in an open system heated at the bottom. Isolate the system, or heat it at the top and explain to me how the bottom will end up warmer than the top.

Yeah, right. Just like the oceans. I wonder why the argument fails for the oceans? They seem to come into thermal equilibrium at, well, thermal equilibrium (constant temperature, independent of pressure, density, “gravity” etc), below the convection-dominated thermocline.

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33. commieBob says:

Ignoring conduction and radiation for the time being and considering only convection:

A column of gas which is sufficiently tall that there is a pressure difference between top and bottom will also have a temperature difference between top and bottom.

For convection to occur, there must be a difference in density. If there is no density gradient, there will be no convection.

The ideal gas law is:

PV = NkT

where:

P is the absolute pressure of the gas measured in atmospheres; V is the volume (in this equation the volume is expressed in liters); N is the number of particles in the gas; k is Boltzmann’s constant relating temperature and energy; and T is the absolute temperature.

Density in molecules per unit volume would be:

density = N/V

Rearranging, we get:

N/V = P/(kT)

So, there will be an evenly varying gas column with no convection because:

Ntop/Vtop = Ptop/(kTtop)
=
Nbottom/Vbottom = Pbottom/(kTbottom)

and

Ptop/(kTtop) = Pbottom/(kTbottom)

So, we would expect the atmosphere at the surface of a planet to be warmer that it is at the top of the atmosphere. Of course, we can’t totally ignore conduction and radiation but, compared with convection, they are second order effects.

34. Greg Elliott says:

Clearly there are two schools of thought. One school believes that the temperature will be lower at the top due to kinetic energy being changed to gravitational potential energy. The other school believes this will not happen. The GHG controversy rests largely on this point.

Where are the learned papers where someone has actually conducted experiments to test this? Measured the temperatures in a gravitationally bound column to determine if we have built a 150 years of science on a faulty assumption.

I am troubled on one point. The argument that a continuous flow in a cycle is not equilibrium and thus is some sort of proof favoring one school over the other. Surely dynamic systems can be in “equilibrium” in that there is no net flow into or out of the system, but still allow a cyclical flow within the system.

The only definitive test is observation. Otherwise we could turn science over to theorists with computers. We cannot “test” this question with calculations that are in any way based on the same underlying assumption. They will by necessity confirm the school of thought they are based on.

Human beings have an infinite capacity to rationalize. History shows that a single faulty assumption does not in the least prevent us from building a huge body of self-confirming science in support of the assumption. In the end however, nature has an infinite capacity to surprise.

As our technology improves we gain the ability to replace assumption with observation and uncover in which direction the truth lies. Thus the development of Relativity to explain small observed variations in the orbit of Mercury as compared to the predictions of Newton.

On average temperatures are warmer at sea level than at mountain tops. We could run a silver wire between the two and heat would run through it indefinitely. This in itself does not appear to favor one school of thought over the other. I’d like to see the observation evidence.

35. I agree that a column of Ideal Gas in the Dr. Brown’s column above will be isothermal at equilibrium.

Now, let’s fill the column with a GHG, say CO2.
Case C0: Leave it in the dark. It has a pressure gradient, more CO2 at the bottom. If the Bottom of the column is at temperature T1b, what will be the top temp T1h? Since the bottom is at T1b, the column is receiving and emitting energy according to SB theory. If necessary, put the column in a room where all the walls are held at T1b.

Case C1: Leave it in the room, but turn on the lights. Bathe it in 240 w/m^2 from all directions. Will it be isothermal, or establish a gradient. I think it will stay isothermal, Despite more CO2 at the bottom of the column. Will the result depend upon T1b?

Case C2: Leave the light on, but replace the CO2 with O2 of the same mass (higher pressure). What will change?

Case C3: Same as Case C2 but use the same molarity (same number of gas molecules) as C1.

T1b is remains the temp of the base of the column, the floor, walls and ceiling of the room in all cases.

Case C1D: Return to case C1. Now turn on the lights for 1000 sec, Turn the lights off for 1000 sec. Repeat. This is an optical pumping, but T1b says the same.

Case Pxx: Same as above except now we leave the room at T1b, but pump the base of the column with T1b(t) = T1b(0) + 10 * ( int (time_sec)/1000 mod 2)
(i.e. every 1000 sec, raise or remove 10 deg K in a square wave)

36. I am not being obtuse here but there is so much wrong with the GHG theory, cooling planet and rising GHG’s, lack of the predicted tropospheric heat, and the violation of 2nd law with this heat transfer from a cool troposphere to the warmer surface. If you could do that you really would have a PMM. So an alternative mechanism must be found to explain the BB heat anomaly, assuming that this is correct.

Please, if you heat your house when it is cold outside, and then add insulation (defined to be anything that slows the transfer of heat), is the second law of thermodynamics violated if the house gets warmer? I don’t think so.

I’ll just repeat what I’ve posted on many other threads. The Greenhouse Effect itself is positively confirmed by the actual measurements of the IR spectra from above the atmosphere. Asserting that it doesn’t exist is just plain stupid when you can measure the actual radiation being given off by the CO_2 and the surface.

If you want to complain about the “upwelling” and “downwelling” radiation arguments, well, I find them unconvincing as well, but that has nothing to do with whether or not the GHE exists! The primary place the atmosphere cools is up at the top of the troposphere — via radiation from a single optical path length thickness of the optically thick (in a selected band) CO_2.

Why is it that you want to fight over physics that you can actually see with IR eyes? Save your energy for useful things, like arguing about the magnitude of the GHE, the sensitivity of it to changes in CO_2 concentration, the sign and nature of climate feedback or albedo modulation or the complex effects of atmospheric convection on local heating or cooling rates, or the ocean’s effect. The IR spectra render arguing about GH warming per se moot.

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37. Joules Verne says:

P = T*V helps to understand what’s going on. One must constantly keep in mind that in the gravitationally bound column of gas pressure is constant while temperature and volume are the variables. As its temperature goes up and down its volume goes up and down. Surface pressure is determined by gravitational constant and mass of the gas which do not vary. Temperature is not coupled to pressure therefore pressure is not coupled to temperature. So raising the surface pressure will not cause a rise in equilibrium temperature. It will cause a rise in volume and the gas law wil be satisfied by the change in volume.

38. Robert Brown says
“What maintains the adiabatic lapse rate is convection”

What maintains the adiabatic lapse rate is energy transfer between reservoirs at different temperatures. Read your own description. Turn off the radiative cooling of top of atmosphere, and the radiative heating at the bottom, and you get — not overnight, but you get — inversion.

You might try looking at the “DALR” over antarctica around July. Oooo, top of atmosphere hotter than the bottom! How did that happen?

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39. Alan Robertson says:

Joules Verne says:
January 24, 2012 at 7:04 am
“My name is Joules because I know how to find and count them no matter how they try to hide.

Thanks for playing.
______________________
How.s the family, Joules?

40. A physicist says:

It seems to me Robert Brown’s analysis implicitly makes the following claim: if all the greenhouse gases (mainly H20 and C02) were cleansed tonight from earth’s atmosphere, then the atmosphere would evolve toward a more nearly isothermal equilibrium

But how would that work, exactly? Because on the first day following the cleansing, the sun would still warm the earth during the mornings, thermal currents would still rise during the afternoons, and these afternoon parcels of air would still adiabatically cool as they rose …

So upon this cleansed-of-GHG planet Earth, how exactly would the atmosphere’s temperature profile evolve toward a more nearly isothermal profile, in which rising thermal updrafts were weaker than in the present atmosphere?

If Robert Brown answered this question clearly (and it is a subtle question IMHO), then it seems to me that his theoretical ideas would prevail.

41. I thought the compressed gas at the bottom in relation to the less compressed gas at the top simply contained more heat energy/volume even though all molecules in the column would have the same level of excitation.

42. The person who observes that temperatures, in general, decrease with height in the troposphere, and who notes that pressure does too, might well be inclined to link one with the other in a causal way not least because of course you can raise the temperature of a gas by compressing it. It is tempting. But a source of great complexity in our spinning, turbulent, inhomogeneous air is the fact that it is largely heated from below, differentially by latitude, by surface properties, by cloud cover, and by time of day and time of year. This simple exposition cuts through all that befuddling complexity to highlight the role of gravity in thermal isolation, i.e. with no heat transfer at the base, or anywhere else on the bounds of the containing surface. The thought-experiment with the silver wire applies the coup-de-grace. I also liked the notion that gravity is a poor candidate to be Maxwell’s demon! I conclude that a thermally isolated container of gas in zero gravity and at uniform temperature, will not see any temperature change if some other demon could switch a gravitational field on at will. Merely the creation or a density gradient. Is that right?

43. Schrodinger's Cat says:

The air at the bottom has a higher temperature as a consequence of being compressed by the mass of air above being acted upon by gravity. Over time, I would expect the system to reach thermal equilibrium. I am assuming that there is no introduction or loss of energy from the system.

In the real world (our atmosphere) the ground heats the air above continuousy during daylight hours and there are many other processes such as convection, radiation and evaporation that lead to energy leaving the system, so the process is never at rest and the temperature gradiant is maintained.

44. Take a single gas molecule and put it at the top of the tube. It has zero kinetic energy and zero temperature. Let it fall and just before it hits the bottom it will have a lot of kinetic energy and heat. That is the lapse rate and it isn’t in equilibrium by definition.

No, it won’t have any “heat”. You are conflating work, organized kinetic energy, and heat. Drop a jar of air. Are you asserting that a thermometer placed inside will go up as it falls? Of course not. It is when it inelastically collides at the bottom, and the organized kinetic energy (which is quite capable of doing reversible work still) becomes disorganized, moving into the far more probable state with the same total energy but with the particles of gas moving every which way, that we might talk about “heat”, but even that is really a false idea.

Temperature of a monatomic ideal gas is one thing, and one thing only. It is a direct measure of its internal, disorganized (equilibrated) average kinetic energy. Not its kinetic energy in a moving frame, not its potential energy in a moving frame or otherwise. Only its plain old kinetic energy. To be very specific, the gas will be in equilibrium at a given temperature T when the distribution of the molecular kinetic energies (or by transformation speeds) is given by the Maxwell-Boltzmann distribution.

The problem is that if you drop the molecules as you describe in a real tube, they won’t just bounce up and down. They’ll bounce sideways and quickly “thermalize” as they collide, eventually sharing the kinetic energy around so that the probable transfer of energy in every collision is the same in both (all) directions. That’s the rub. An ideal gas collides instantly — a hard sphere approximation, like perfectly elastic pool balls. Gravity has no time to act during the collision. The solution for the pressure at a constant temperature above indicates that a gas is perfectly happy to support its own weight and density/pressure profile at a constant temperature, and at a constant temperature all collisions have equal probabilities of heat transfer in all collisions in all directions. That simply isn’t the case if the MB distributions (and hence temperatures) vary with height.

But the basic point of my paper is that Jelbring is wrong not because of any possible microscopic description of a lapse rate. A lapse rate itself is wrong in thermal equilibrium, because figure 2 is very, very easy to understand. There is no question that the silver will conduct heat between reservoirs at different heights exactly the same way it does any other time. If you doubt me, put a pan on the stove, put your fingers on the pan, turn on the heat below, or hold onto a piece of solder while you heat one end of it. Or read wikipedia articles on the heat equation or Fourier’s Law. Or take a course in stat mech.

If any lapse rate is stable, the system violates the second law, as heat will flow through the silver for any difference in temperature until there is no difference in temperature, and therefore any steady state that still has a lapse rate must transport heat down the gas column on the left from colder to hotter (violating the second law all by itself, but it is so difficult for people to understand this, alas). And we’re done. No, heat will not flow forever in any physical system.

Done.

45. Alan Robertson says:

Joules Verne says:
January 24, 2012 at 8:07 am
…” The fewer molecules must have sufficient gravitational energy that, if it were converted to kinetic energy, would be able to raise the temperature of a larger number of molecules in the lower layer the temperature in that lower layer. It MUST be isoenergetic to satisfy the second law. It need not be isothermal. In politics they say to follow the money to arrive at the truth. In physics you want to follow the jewels joules.”
_______________________________
How can the conversion be isoenergetic while remaining isothermal? Is it adiabatic with an increase in pressure?

46. No. The fewer molecules must have sufficient gravitational energy that, if it were converted to kinetic energy, would be able to raise the temperature of a larger number of molecules in the lower layer the temperature in that lower layer. It MUST be isoenergetic to satisfy the second law. It need not be isothermal. In politics they say to follow the money to arrive at the truth. In physics you want to follow the jewels joules.

You leave me — almost — speechless.

I can only reiterate — you tell me what the heat flow will be in figure 2 above. Which is violated — the heat equation in silver or your absurd assertion that gravity can stably sort out a gas into a hotter temperature and a colder one?

One or the other. Only one makes you look silly, though.

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47. MDR says:

Two distinct scenarios are being discussed here in a somewhat confusing fashion. One scenario involves an adiabatically stratified system and the other involves an isothermal system. It is important to realize that thermodynamic equilibrium does not necessarily mean the gas is isothermal. It is possible for a system to be in thermodynamic equilibrium and *not* be isothermal, as in the case discussed here where gravity stratifies the gas with height.

Here is a more detailed explanation. In the system described above [without the wire], there are only two sources of energy: gravitational potential energy and internal energy. Because matter located at lower z [height] will have a lower amount of gravitational potential energy, it then follows that matter located at lower z also has a greater amount of internal energy. As a result, the total energy [that is, the sum of gravitational potential energy and internal energy] with height is a constant, and the system can be said to be in thermodynamic equilibrium. If this weren’t the case, then energy transfer would occur, in the direction so as to equilibrate the total energy.

Now, we just showed that internal energy decreases with height, as explained above. Since internal energy [of an ideal gas] is directly proportional to temperature, this must mean that temperature also decreases with height. The gradient of temperature with height is of course the lapse rate. This is an example of a system that is both in thermodynamic equilibrium and possesses a gradient in temperature.

48. Jeremy says:

Thank you Dr Brown.

As many have commented here, this blog has become a haven for rather foolish comments.

It proves that skeptics are just as gullible to poor logic and bad science as the CAGW.

When something fits with your world view there is a tendency to embrace it.

However, Science and Physics is NOT about anyone’s world view – as James Brown would say “It is what it is”.

I don’t buy the scaremongering CAGW nonsense about man-made CO2 because the Science and Physics clearly do NOT support such claims. However, for the very same reason, I cannot support some of the wildly inaccurate nonsense science being discussed here lately in these forums.

49. Greg Elliott says:

Consider sunlight reaching the earth’s surface. This heats the surface and energy is radiated back to space. The incoming and outgoing energy must balance.

Add GHG to the atmosphere and some of the outgoing radiation will be intercepted and prevented from reaching space. Thus the surface temperature of the earth must increase to increase the out-flowing radiation and restore the balance.

Now, consider what happens if at the moment a molecule of the earth’s surface is about to emit a photon to space, instead a molecule of N2 comes into contact with the surface and the energy from the surface is instead conducted into the molecule of N2. This flow of energy through conduction will reduce the surface temperature and prevent the photon from being radiated to space.

This will have the effect of decreasing the out-flowing radiation from the surface, in a manner that is for all intents and purposes indistinguishable from the effects of GHG. Thus, the temperature of the surface must rise to restore the out-flowing radiation that is being lost to conduction. The greater the atmospheric pressure, the more N2 molecules, the greater the likely-hood that conduction will take place limiting radiation from the surface to space, the more surface temperatures must rise.

But what about the energy absorbed by the N2 some might ask. Indeed and what about the energy intercepted by the CO2? Both must either heat the atmosphere or be returned to the surface and thus are indistinguishable in their effects.

However, the GHG theory tells us that only radiative transfer is responsible for warming the surface, that conduction cannot have this effect. Yet it is clear to see that convection limits radiation to space in a manner that is for all intents and purposes equivalent to GHG. The greater the pressure, the more likely this becomes, the more surface temperatures must rise.

50. Meaning Robert Brown is allowed only one heat reservoir to demonstrate his proposed isothermal gas column where the wire stays in thermal contact with the white colored gas everywhere – no U-turns as here to a 2nd thermal reservoir. Trick’s view is Robert will be unable to do so – the gas column will not be isothermal – there will be a temperature lapse rate.

Excuse me? I have no idea what you could possibly be talking about. Look, grab a copper wire by one end. Hold the other end in the flame of your stove. I don’t care what shape it has, you will burn the hell out of your fingers (and keep burning them until your fingers are at the same temperature as the flame).

My picture shows a wire insulated on the sides so that any heat that goes into the wire can’t come out anywhere but the end. It just makes the wire a one dimensional conductor of heat. Put the damn wire (insulated on the sides) right into the container, perfectly straight if you like. As long as the bottom UNinsulated end is in contact with the gas at the bottom at T_b, and the top UNinsulated end is in contact with the gas at the top at T_t, and T_b > T_t, heat will flow in the wire from the bottom to the top.

The point is that heat will flow in this system forever if you postulate that gravity will maintain a lapse between the bottom and the top stably. That means that any small packet of heat that is moved around in the gas has to eventually settle back down into equilibrium, and you are asserting that equilibrium has a lapse. So when the wire carries heat from the bottom to the top — which it will — gravity has to sort it back down to the bottom, because you assert that a lapse is the stable equilibrium.

Only it won’t. If it did, the second law wouldn’t be satisfied, heat would flow forever.

The real point is that you don’t need the silver wire to make this argument. The gas itself conducts heat from the bottom to the top as long as the temperatures are different. It’s what systems do. Conduct heat from hotter places to colder places, unless you do work to prevent it. Gravity does no work in this problem, not in steady state. So what makes the heat go round and round?

It doesn’t.

Of course.

It evolves to the isothermal state where no heat flows.

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51. Nick Shaw says:

I am not a scientist and never claimed to be so, could someone explain why the gas, or atmosphere in this case, should be colder on top than on the bottom assuming convection works in all cases (cold air falls while hot air rises) Yes, I can figure, as air gets closer to outer space (in really simple terms) it would get mighty cold but, cold air is more dense and as such it should fall more rapidly. Exactly where does gravity enter the picture? It is exerted equally on all temperature states of air, right?
Or should I up my meds? ;-)

52. RGB

thank you for this elegant demonstration that a gas in a gravitational field is isothermal when in equilibrium. I lost count of how many times I pointed this out on Willis Eschenbach’s original thread (the one that caused all the controversy). Even Willis didn’t get it at the time. I hope he does so now.
[REPLY: Indeed you did, Paul, and you were right and I was wrong. Thanks for your contribution in fighting my ignorance. I mean this quite seriously. That's how I learn. –w.]

53. Ed Fix says:

Robert, it seems that you have completely missed the fact that gravity causes a pressure and density gradient in your air column.

Your equilibrium air column is NOT isothermic, as you assert–that could only happen in the absence of gravity. Because the density and pressure decrease with altitude, the temperature at the top is much lower than at the bottom. The bulk of the mass and heat energy of the air column is at the bottom.

Remember what heat energy is: it’s defined by the kinetic energy of the individual air molecules. Temperature is defined by both that molecular kinetic energy and by the density of the atmosphere. The pressure gradient leads to a sorting; the more energetic molecules tend to be at the top of the air column–more space to allow a longer mean free path above than below. However, because the density and pressure decreases with altitude faster than the thermal energy of individual molecules increases, total temperature decreases with altitude.

Your thesis may indeed be correct, but you can’t prove it by considering only temperature and convection without considering density and pressure and conduction as well. It’s the pressure and density gradient that is alleged to cause gravitational heating of the lower atmosphere.

This is a much more complex problem than a quick, partial recitation of a freshman physics text can handle.

54. The device in figure 2 doesn’t work because it’s a closed system and the work extracted will reduce the total energy of the column until eventually there’s no more energy to extract at which point the gas reaches a temperature of absolute zero and has presumably vanished from this universe being totally converted to kinetic energy in the extracted useful work. In the real world the gas will collapse to the surface as a liquid before it gets to absolute zero and this will shut off further extraction of energy because the cold side of the thermocouple no longer has any cold gas to cool it.

Work? What work? Are you crazy? Collapse to a liquid?

Let’s try again. I-s-o-l-a-t-e-d S-y-s-t-e-m means that no energy enters or leaves. No mass transport means no work is being done In the real world, the system will evolve to an isothermal state precisely as I described it because it is in equilibrium. In any imaginary world where gravity acts on “heat” or does “work” on a gas that is in static force equilibrium and not moving, you can make it come out any way that you like, but please understand that it is nothing but a fantasy on your part.

The point is that heat will not cycle indefinitely — you can see that that makes no sense. No work is done. No energy enters or leaves — where would it go? How would it get there? That’s what the adiabatic walls around the gas and wire prevent. If gravity maintains a constant lapse rate in steady state, the second law and common sense are massively violated by the enternal heat flow. All other solutions mean that equilibrium is isothermal.

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55. son of mulder says:

Heat is Energy is mass by M=E/c^2 so said Einstein.
So what force causes Mass to rise up the silver conductor against gravity ie work has to be done?
The silver conductor is little different from the gas in a column in this respect. The top will be colder than the bottom and heat will not flow up the silver conductor unless a heat source (work) is supplied from the bottom..

56. kdk33 says:

If the atmosphere was heated from the top there would be no convection, hence no lapse rate.

The lapse rate doesn’t apply to the ocean because water is incompressible. Hot water doesn’t expand as it rises, hence does not do work on the surroundings, hence does not change temperaure, hence no lapse rate.

57. I conclude that a thermally isolated container of gas in zero gravity and at uniform temperature, will not see any temperature change if some other demon could switch a gravitational field on at will. Merely the creation or a density gradient. Is that right?

Not quite. “Turning on the field” is like “a collision” and the gas will rearrange, releasing a bit of gravitational potential energy as heat. But then it will “thermalize” to an isothermal temperature, one a tiny (and I do mean tiny, generally speaking) higher than before.

This is not unlike the mechanism that heats protostars as the gas they are made up of falls inward and stops (on average) converting their infalling KE into heat. Or what happens when a big asteroid hits the earth and stops

The key elements are movement and inelastic stopping.

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58. I have been following these threads, lurking from the sideline, for a while. Well, the time has come to add my $.02 worth. I have been studying meteorology for 40 some-odd years now & I shake my head in seeing some of the most common properties of the atmosphere being missed in these threads as it applies to these ‘thought experiments’. 1) if the several km-long tube is horizontal & the perfectly dry air is at a constant temperature throughout & is moved to the vertical, the dry adiabatic gradient will be produced (warm at the bottom, cool at the top w/ approx 8C/1000m gradient in between) due to the ‘work’ of gravity creating a pressure gradient to the compressible gas. Notice, no gradient will be produced if water is used instead of gas because water is non-compressible so no work will be done. If no heat is added or removed to the gas, the column will be in a neutral buoyant state (and will stay that way!!) – if a parcel of air is moved vertically by an outside force, it’s temperature will change to reflect the change in pressure but will still be the same temperature as it’s surroundings. 2) as to the experiment with the thermal conductive wire at the base & top of the tube, the author here is incorrect. If the wire moves heat from the bottom of the tube (the base cools) to the top of the tube ( the top heats), presuming, as the author says, “…save to note that the internal conductivity of the ideal gas is completely neglected.”, the heat from the *local* area of the wire is all that will be moved from the bottom to the top ***and nothing else*** . Why, you ask?? In moving the heat from the bottom of the tube to the top is causing the lapse rate to become **more stable** – cool at the bottom with warm air above is an inversion which inhibits vertical mixing!! THAT is why the engine will not work as it is set up. Just a few thoughts… Jeff 59. Wayne2 says: @Robert Brown: To do LaTeX in WordPress, do$\latex n^2$(except leave out the backslash in front of “latex”. It’s just like going into math mode in LaTeX, except that you add the word “latex ” after the opening dollar sign. 60. Greg Elliott says: nothing as simple as gravity can function like a “Maxwell’s Demon” There is nothing simple about gravity. it is the least understood force in the universe with many unresolved questions. 61. Frank says: Professor Brown: To some extent, two of your arguments start by assuming what you want to prove. You and the introductory textbooks start by assuming a isothermal column of gas. The situation is far more complicated if you consider a column with a temperature gradient. For a thin layer of gas in a non-isothermal cylinder, the pressure difference across that layer is produced (at a molecular level) by differences in the vertical impulse provided by the gas molecules at the top and bottom of the layer. The density of molecules and pressure in an isothermal column both change following the same exponential, -mgh/kT. This means that the difference in impulse between the top and bottom of a layer is due only to the difference in density and the average speed of the molecules moving up and down must be the same. This is consistent with the original postulate that the column is isothermal. In a non-isothermal column, however, the density of molecules and pressure don’t change in parallel. In this case, the speed of the molecules at the top and bottom of a thin layer will not be the same and energy will flow up or down. Which way is the flux? If the flux reduces the temperature gradient (and I presume that it will), does the flux persist until isothermal or are other stationary states possible? To prove that heat flow in a cylinder of gas is unaffected by a gravitational field, you assume that heat flow in the silver conductor is also unaffected by the same gravitational field. IF exchanging kinetic for potential energy were important to energy flux in a gas, it would probably also be important in a solid. In a sense, you are assuming what you want to prove. You can use the 2LoT to eliminate the possibility that a lapse rate of g/Cp develops spontaneous. If you have two equally tall columns in thermal contact with the ground which are filled with gases with different Cp’s, you could use the temperature difference which would develop spontaneous at a given height in the gravitational field to produce perpetual motion. However, this argument doesn’t work when the lapse rate that hypothetically forms spontaneously in a gravitational field is independent of composition and only depends on height. 62. Tim Folkerts says: I feel for you Robert. It seems the more challenging and subtle the physics, the more experts there are. And the more sure they are that they are right. It is a lot like playing whack-a-mole — every time you think you have explained something so well that it couldn’t be clearer, someone will find a new objection (or more likely, recycle an old objection). For example, the “it loses KE on the way up so the temperature must go down” is convincing unless you have a subtle understanding of thermodynamics. And we have seen it rear its head a dozen times in the last few days in these threads. I hate to admit that I, like Willis, even fell for this argument for a brief time until the obvious flaws were pointed out. But we both quickly reformed. I wish you patience and persistence in your efforts to bring correct science to WUWT. You will need it! 63. As an aside, it’s trivial to design a machine that seems to violate the Second Law and pumps heat from cold to hot with no input of work. On a sheet of paper draw two horizontal lines, one at the top and one at the bottom, that represent radiating surfaces at temperatures Ttop and Tbottom. Then draw a cute little flight of stairs ascending from left to right, with a smooth bottom and the usual treads on top. Cover the stairs with mylar and let them sweep from right to left at nearly the speed of light. (You can also make the stairs steeper and sweep them slower). There are a very large number of flights of stairs, looking in 3-dimensions like a venician blind with treads on one side. Assume the top and bottom emitting surfaces are very distant and finite, so photons are traveling between them in a roughly vertical direction. Photons from the bottom don’t hit the stairs because the stairs are moving out of the way as fast as the photons are traveling upward. (The stairs dodge upward moving photons). Photons moving downward cannot find a clear path between flights of stairs and always slam into a tread, getting reflected back towards the top. So photons emitted from the top surface return to the top surface, and photons emitted from the bottom surface travel freely to the top surface, regardless of temperature. The bottom surface cools and the top surface warms, even if the bottom is already cooler than the top, and the stairs aren’t doing anything but freely moving along between. At most, the stairs might extract a little work from the momentum of the photons being reflected from the top, but this would happen regardless of the difference between the top and bottom temperatures. 64. Ged says: The problem here is that heat is not temperature. Heat is energy, temperature is average kinetic motion, which is one -type- of energy. A glass of water and a bathtub full of water can have the same temperature, but the bathtub has more heat than the glass of water, as more heat is required to bring the tub up to the same temperature as the glass. Moreover, heat can be added to a system without temperature changing. When ice melts, continuous heat is required to continue the melting, yet the temperature will remain the same until a significant amount of the ice has melted. Still, the system has far more heat content now as a liquid, even at the same temperature, than it did as a solid. For instance: “This heat in turn may lift mountains, via plate tectonics and orogenesis. This slow lifting of terrain thus represents a kind of gravitational potential energy storage of the heat energy. The stored potential energy may be released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a kind of mechanical potential energy which has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy which has been stored as potential energy in the Earth’s gravitational field, or elastic strain (mechanical potential energy) in rocks.” So, this action of heat pushing against a gravity well and from kinetic to potential energy is part of what drives plate tectonics itself. Here we see heat being transformed from kinetic (TEMPERATURE) energy to potential energy by moving against a gravity field. The resulting raised land mass has lower temperature as it as lower kinetic energy, but it contains similar amounts of heat. This effect of changing kinetic energy to potential energy (E = mgh) won’t be seen measurably in a gas over a small distance, but over the miles of the atmosphere? This is why it’s hard for me to understand your explanation, which doesn’t mean you aren’t correct, Dr. Brown. But it seems like your equations are all missing the big picture: potential energy. When h (height) is very big, even though gasses have low m (mass), you’re going to have a transfer of energy into potential energy that is considerable. The only source of energy that can go into the potential energy (since conservation of energy demands transformation not creation) is the kinetic energy of the molecules. Just like bouncing balls. And if kinetic energy drops, -so too does apparent temperature-. Again, -temperature is not energy-. Temperature is not heat. Temperature is just our observation of heat in the form of -kinetic energy-. And kinetic energy can be changed to potential energy while keeping the total energy of the system -the same-. Like a bouncing ball, or a stone rolling up hill a ways. Or plate tectonics! You’re looking at far too small a case. An ideal, not realistic, case. Or maybe i just don’t get it. 65. Joe Born says: Robert Brown: “There is no question that the silver will conduct heat between reservoirs at different heights exactly the same way it does any other time.” In my post above, where I disputed Dr. Brown’s isothermality conclusion, I was silent about his proof; I concentrated on mine. For the sake of completeness, though, I’ll mention that, if the Velasco et al. paper that I’ve been evangelizing is correct, the silver actually will not conduct heat once the temperature difference that Velasco et al. specify is imposed across it. This is a result of the fact that, according to Velasco et al., entropy is maximized, not by an isothermal configuration, but by a configuration whose (again, quite small) temperature lapse rate is the one that Velasco et al.’s paper prescribes. If you think of heat transfer in the silver as a diffusion phenomenon and recognize that concentration gradients prevail all the time when maintained by forces from, e.g., electric fields, this is not as hard a proposition to swallow as it may at first sound. 66. Tim Folkerts says: Greg Elliott says: “But what about the energy absorbed by the N2 some might ask. Indeed and what about the energy intercepted by the CO2? Both must either heat the atmosphere or be returned to the surface and thus are indistinguishable in their effects.” But this is the flaw in your thinking. N2 can only transfer energy to the surface or the atmosphere, as you say. But CO2 can ALSO transfer energy to space via IR photons. That is ultimately the cause of the greenhouse effect. 67. Ged says: Oh, I should point out you cannot -generate heat- with gravity, but over a very large distance, gravity should maintain a -temperature- gradient if the heat is in equilibrium by necessity due to the change of kinetic to potential energy as one moves far enough up a gravity well. Notice that the energy of the gas column will be in equilibrium, but temperature is only the measure of kineitc not potential energy. That fact is why I can’t wrap my head around such a small case explanation as yours, which is correct on the small scale, when applied to the entire planet. Again, maybe I’m completely wrong. But I feel we’re missing out on one entire half of the equation. Gasses are still subject to potential energy as far as I know! 68. DavidB says: I think one reason that some people are taken in by Jelbring’s theory is that they are vaguely aware that if a gas is compressed, e.g. the air in a tire being compressed by a pump, its temperature goes up, so in their minds they form the vague association ‘higher pressure = higher temperature’. But the increase in temperature is a temporary effect, due to the transfer of kinetic energy from the piston of the pump to the air molecules. If you stop pumping, the tire will cool down to the ambient temperature, as it loses heat by conduction and radiation. As the air in the tire cools, it will also reduce in pressure, but not to the orginal level (otherwise there would be no point in pumping up a tire!) There is no necessary connection between high pressure and high temperature; a hot gas can have low pressure and a cold gas can have high pressure (unless it is so cold as to liquify). Incidentally, I wonder if someone could explain the opening quote from Jelbring: “An adiabatically moving air parcel has no energy loss or gain to the surroundings. For example, when an air parcel ascends the temperature has to decrease because of internal energy exchange due to the work against the gravity field”. I don’t understand the second sentence of this. If an air parcel ascends, it is surely because it has first expanded due to heating (usually from the sun). As it expands, it does work against the surrounding or covering air, compressing or displacing it, and loses some kinetic energy (heat) in the process, but it does not immediately cool to the ambient temperature. (If it did, it would not ascend at all, contrary to experience.) The expanded parcel of air is less dense, and therefore less heavy, than the surrounding air, and the entire column of air above the parcel (including the parcel itself) is lighter than the surrounding columns. At this point the parcel begins to rise as the heavier surrounding air forces it up. During the ascent the air parcel itself is not ‘doing work against the gravity field’, it is having work done on it by the surrounding air, which is ‘repaying’ the work done on it during the initial phase of heating and expansion. Does Jelbring suppose that a hot-air balloon would rise in a vacuum? I really can’t make sense of his second sentence at all. 69. D. J. Hawkins says: Joules Verne says: January 24, 2012 at 7:04 am “Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics. It is a direct, literal violation of the refrigerator statement of the second law of thermodynamics as it causes and maintains such a separation without the input of external work.” No, Robert. The second law requires that no energy gradient can be maintained without input of work. It requires the reservoir of gas to be isoenergetic not isothermal. A horizontal layer may be a different temperature than another if the cooler layer has its lesser kinetic energy balanced by greater gravitational energy. This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer. Thus the second law actually demands a temperature difference of equal and opposite polarity to compensate for the difference in gravitational energy. An isothermal atmosphere in a gravity field is the one that violates the second law. My name is Joules because I know how to find and count them no matter how they try to hide. Thanks for playing. You’ve very coyly avoided answering the objections raised by Dr Brown’s Gedankenexperiment. So according to you, we could take a perfectly insulated container several miles high in a gravitational field under a hard vacuum, fill it with gas and that gas will self-organize so that it’s warmer at the bottom and colder at the top. Now I can construct a heat engine which extracts useful work based on the temperature gradient and gravity will continue to organize the air column forever and my heat engine will never run out of “fuel”? Really?? 70. To Joules, According to Newton, gravitational force is expressed as F=m1*m2/R^2 where m1 and m2 are the mass of two attracting bodies and R is the distance between the centers of mass. The molecules at TOA have less gravitational energy than molecules at sea level but not by much because the change in R is relatively small. So the pressure at sea level is essentially the mass of the earth times the sum of the mass of all those molecules in the atmosphere divided by the radius of the earth. In a steady state condition, the pressure at sea level will be constant and the number of molecules causing that pressure will be constant. Pressure decreases with altitude because the number of molecules per volume decreases. Now apply this knowledge to the perfect gas law expressed as pv/nt= constant by integrating from TOA to the surface and see what happens to temperature as a function of altitude. 71. Joules Verne says: January 24, 2012 at 7:04 am “Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics. It is a direct, literal violation of the refrigerator statement of the second law of thermodynamics as it causes and maintains such a separation without the input of external work.” No, Robert. The second law requires that no energy gradient can be maintained without input of work. It requires the reservoir of gas to be isoenergetic not isothermal. A horizontal layer may be a different temperature than another if the cooler layer has its lesser kinetic energy balanced by greater gravitational energy. This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer. Thus the second law actually demands a temperature difference of equal and opposite polarity to compensate for the difference in gravitational energy. An isothermal atmosphere in a gravity field is the one that violates the second law. Joules is correct, and to push the point home a bit further I will be posting a new paper by Hans Jelbring on my website later this evening which demonstrates the dynamic situation. This will complement and supplement the earlier 2003 paper setting out the static situation which Robert refers to in this article. Hans has been working steadily on the new paper over the last few weeks and now seems to be the apposite time to publish it. 72. Q. Daniels says: Basically, the Second Law is used to prove the second law isn’t violated. That’s circular logic. It’s like using the Carnot Cycle to prove the Second Law. As I said at Tallbloke’s, I think the silver wire is a terrible design. You’d be lucky to extract kbT from it. IIRC, Feynmann showed it was possible to extract nearly that much from a Brownian Ratchet, without anyone getting excited. A better design would be to use a single column containing two gases, one of which is heavy with a low boiling point, and the other is light with a high boiling point. A reservoir of the light gas in condensed form at the bottom of the column also serves as a thermal reservoir. At the bottom, the light gas will be in equilibrium with its condensate. Fill the column with a significant majority of the heavier gas, such that its gravitational lapse rate dominates. The temperature/pressure profile of the lighter gas (being a lifting gas in context) will be saturated at all elevations above the reservoir. A series of basins and catchments can be arranged to collect the condensing lighter gas. By George (Westinghouse), it might work! 73. People being invited to consider an argument should have the opposing argument easily available to them. This enables people to form their own judgment as to whether the opposing argument has been correctly and fairly represented. Especially considering the paper in question was written by a Phd Meteorologist. Since Robert Brown is setting a refutation of Hans Jelbring’s 2003 paper, it would be a common courtesy to provide a link to that paper in the headline post. It is available with a new preface written at the time of publication on my website here: http://tallbloke.wordpress.com/2012/01/01/hans-jelbring-the-greenhouse-effect-as-a-function-of-atmospheric-mass/ If WUWT has some problem with providing a link to my site, the paper without the 2012 preface is available here: ruby.fgcu.edu/courses/twimberley/EnviroPhilo/FunctionOfMass.pdf [Thanks, tallbloke. I've added the link up in the head post. -w.] 74. Alan Robertson says: Roger, Your site is linked on the right column of this page, as always. 75. Kasuha says: Dear Mr. Brown, I’m sorry but your conclusion about figure 2 is completely wrong as you expect the air reservoir to conduct heat in gravitational field and the silver rod to conduct heat in zero gravity. I’m sorry to say that this assumption is incorrect and the example you are building your conclusions on is wrong. Even atoms of silver have the property of gaining potential energy and losing kinetic energy (therefore losing temperature) when traveling “up” in a gravitational field while transferring their temperature in that direction. The result is, the rod would demonstrate exactly the same temperature gradient the air container does. Your thermal engine would not work not because there is no temperature gradient but because it would not transfer any heat. 76. Bryan says: kdk33 says “if the atmosphere was heated from the top there would be no convection, hence no lapse rate. The lapse rate doesn’t apply to the ocean because water is incompressible. Hot water doesn’t expand as it rises, hence does not do work on the surroundings, hence does not change temperaure, hence no lapse rate.” Do you not remember the school experiment with a beaker of water and a single copper sulphate crystal showing fairly rapid liquid convection? How do you think an electric kettle heats water? 77. Willis Eschenbach says: Bryan says: January 24, 2012 at 6:59 am What would complement this theoretical explanation is if an experiment backed it up. So far as I know no experiment has ever been carried out. All suggested proposals seem to run into problems when real components and physically accurate numbers are used. For some of us, a thoughtful examination of the flame suffices. We don’t have to actually do the experiment and burn our fingers to know that it is hot. If you wish to do the experiment, however, be my guest. I’ll just have a quick beer while I wait for your experimental refutation of a couple centuries of scientific thought … w. 78. Joules Verne says: January 23, 2012 at 4:25 pm Gravity maintains TWO energy gradients. One kinetic and one potential. The kinetic gradient decreases with altitude and the potential gradient increases with altitude. The two opposing gradients cancel out and the column is isogenergetic. This is how you can have a perpetual temperature gradient yet not be able to extract any work from it for a perpetual motion machine – a temperature gradient can be nullified by an equal but opposite gradient of energy in a different form. You can’t connect the cold and hot sides of the atmosphere without climbing up in a gravity well and the useful energy represented by the change in temperature is exactly used up by the energy required to climb uphill against gravity. The books thus balance and conservation of energy is once again safe from the abuses of junk science. Neat comment Joules. I can’t wait for the mad inventors to put their money where their mouth is and build one of the erroneously designed machines they propose. Problem is, when it fails to work they’ll come to the equally erroneous conclusion that it failed because the atmosphere is isothermal. Hope no-one catches a nasty chill while bolting thermopiles together at the top of their 10km high rig. While they’re up there, they might notice how much thinner the air is too. That might give a bit of pause for thought about density and its effect on the ability of air packets at different altitudes to retain the heat of the Sun. 79. Paul Potter says: Look the adiabatic lapse rate exists this is basic physics equal partition of energy. it is evident in the atmosphere but is upset by clouds at low level and UV absorption at higher altitudes. If we cannot get even the basics correct we might as well give up. For those who say there is no back radiation why is the sky temperature at night not 4K For those who do not believe an warmer but still cold atmospheric layer cannot cause the surface to warm clearly do not understand the basic physics of radiative heat transfer. Why are layers of mylar used to thermally insulate space craft? Unless we get the basic physics correct then the skeptical community will be undermined. 80. Alan Millar says: A gas giant planet like Saturn radiates more than twice the amount of radiation than it recieves from the Sun. How do these planets ever die if gravity is constantly maintaining a heat gradient in the atmosphere? The Sun will die and become a cold white dwarf. What is going to kill these gas giants? If gravity is constantly maintaining hotter gases at the bottom then convection will move gases around and therefore we seem to have an everlasting living planet. What kills it and when, if Jelbring is correct? Alan 81. hotrod (larry L) says: The last few days have certainly been interesting regarding the debate of lapse rate in a gravity field. I think the point that is getting missed, but I see as intuitively obvious, is that in a real planet with a gas atmosphere, it is not and never can be in a state of thermal equilibrium. The atmospheric column is always in direct contact with a massive heat sink(source) in the form of the planetary body, and the top of the column (at its effective radiating altitude) is a nearly ?? infinite heat sink at the temperature of interstellar space. Until or unless the planetary body is at the same temperature as deep space there will always be energy input at the bottom of the atmospheric column (and a temperature gradient) and there will always be heat loss by radiation (or some other means like boiling off of the atmosphere) at the top of the column. In that sense, all these discussions regarding physically impossible constraints on the model are merely debating how many angels can stand on the head of a pin. Lets look at real planets which are always warmer than interstellar space, and real atmospheres where at the base (troposphere) heat transport by convection dominates all other mechanisms by a huge margin. Under those conditions, there will always be a lapse rate in the atmosphere (in the troposphere) as long as it can find some means to lose energy to interstellar space by radiation or loss of mass. The only discussion, is are there any realistic conditions where an atmospheric shell could not radiate heat to interstellar space? If and only if that condition can be achieved do the discussions of a system in equilibrium have any meaning. In all other cases (with or without radiant heating by a near by star) the planet will always be losing heat to space, and will always have a troposphere layer (if it has an atmosphere of non-condensing gases) where heat transport is dominated by convection. In all cases the presence of green house gases can only improve heat loss to interstellar space at the effective radiating height over the theoretical condition of no ability to radiate energy in the electromagnetic spectrum (note I did not limit energy loss to IR band width). It is my view that the atmosphere will always find a way to lose energy to deep space by some means at or near its top, and will thus always have a troposphere lapse rate which implies that the planetary body will always be warmer with an atmosphere (regardless of gas mix) than it would be without one. One other note that no one has mentioned. As I understand it, the average effective radiating altitude here on earth is around 4.5 km (14763 ft), that means that here where I live in Colorado at the summit of Pikes peak or Mt. Elbert I could just about throw a rock to the mean altitude where heat is lost to space by radiation. In short high altitude areas like the Himalayas, Andes, and the Rockies and a few volcanic peaks are “short circuits” in the troposphere, where energy absorbed by the ground from solar heating can be almost immediately radiated back to deep space directly from the ground. It would be interesting to see high resolution IR measurements of the heat loss from these areas directly to outer space. Larry 82. MaxL says: I have a question along this topic which will likely show my ignorance. If gravity alone cannot induce a thermal gradient in a gas, how then are stars formed from gases where there is only gravity as an external force? 83. Ged says: Let’s do some equation work. Let’s say we take one mole of N2. That’s 0.028 kg. Now we take that mole at 15 C and move it up from the sea surface to the average top of the troposphere which is 17,000 meters high. Gravity constant will be 9.8 m/s^2. The total joules needed to do this is around 4660 J (E = mgh). Now the heat capacity of N2 is 29.124 J·mol^−1·K^−1, so if we transformed 4660 J of heat kinetic energy, that would reduce the temp by -160 degrees, or so, or to -145 C. The real temp at the top of the troposhere is about -55 C, so we’re off by almost a factor of 3. Obviously, the atmosphere is also taking in energy from the sun (radiatively, and solar wind), there’s more than just N2, and the conversion of kinetic temperature energy to potential is probably more complex, to make up for this difference. If there was no energy from the sun, the atmosphere would shrink as energy was lost to space, and along with it potential energy, dropping molecules down till they settled on the surface of the planet and solidified (e.g. Pluto). This is what I see. And again, I may be completely off base. But conservation of energy tells me we must be changing forms as we move up the atmosphere. So for the temperature to stay steady (which it doesn’t in real life), we’ve have to have even more energy at the higher altitudes in the air column than is at the surface. And would not this energy fall back down to the surface to equilibrate, driving the surface temperature even higher? The way I see it, there will always be a -temperature- difference at such large gravity distances if energy is in equilibrium. Again, I could have done this all wrong. 84. Willis Eschenbach says: John Marshall says: January 24, 2012 at 7:26 am Very interesting but really irrelevant given that our atmosphere is not an ideal gas in a cylinder. It’s the disproof of Jelbring’s theory, which lately has attracted many supporters. As such it is an interesting and very relevant exercise. w. 85. alex says: School physics. The atmosphere stability condition is ds/dz>0, where s is the entropy density and z is the hight. Atmosphere with ds/dz 0 are stable (including the isothermal atmosphere!) What is all the ridiculous discussion about??? 86. Graeme W says: Dr. Brown, I’ve been reading this thread and the earlier thread with a great deal of interest and I understand the point you’ve raised. However, I note that it relies on the Ideal Gas Law being applicable. My question is: Is the Ideal Gas Law applicable? I’ve just done some quick research and it seems that the derivation of the Ideal Gas Law assumes that any gravitational field in question will have a negligible impact on the behaviour of the gas. That’s true in almost all reasonable cases, but it’s not true in the example we’re discussing. I would therefore ask for your comments on the underlying assumptions in the derivation of the Ideal Gas Law in this respect and if they are still true. In particular, looking at the Empirical Derivation from the Wikipedia article: http://en.wikipedia.org/wiki/Ideal_gas_law#Empirical I noticed that there is a constant C that is directly proportional to the amount of gas. But in a gravitationally stratified column, the amount of gas is not constant throughout the column, and hence the “constant” is not really constant. Similarly the derivation from statistical mechanics in that article assumes that there is no gravitational force involved. For small columns, that’s a reasonable assumption,Is it a reasonable assumption for large columns? I don’t understand the theoretical derivation well enough, but again it seems to assume that there is no conversion of kinetic energy into gravitational potential energy – something that is core to this issue. Again, thank you for your posts. I have enjoyed reading and learning from them. 87. Trick says: Robert Brown says at 1/24 8:14am: “…in an ideal gas the temperature is not determined by the total energy. That’s an absurd idea, given that one can perform a gauge transformation — change the zero of the total energy — without changing any of the physics.” Ahhh..this is the big deal. Consider this is equivalent given Caballero’s ref. in the Perpetuum Mobile thread w/gravity where in 2.1 find “Temperature is just another name for the mean kinetic energy density of molecular motion.” to Trick saying “in an ideal gas the mean kinetic energy density is not determined by the total energy”. If Trick said this, Trick would be going against 1st Law & Trick has not written any such thing. So in Trick’s view, what Robert Brown says at 8:14am is inconsistent with 1st Law. I am pretty sure but not perfectly sure that Trick’s view is consistent with all the thermo grand master Laws. Robert Brown’s 8:14am violation of the 1st Law above, Robert Brown doesn’t grok yet. He will eventually! (Trick predicts the life of the universe is longer) b/c Robert’s smart and the thermo grand master’s are right. This is all like the slow progress of thermal conduction thru a near perfect insulator. I admit this PE setting with h is actually a difficult preconceived notion to get over. It took me many years of practice to really come to grips with it. Notice that every time you see total energy equation written in thermo theory – it looks something like this: total energy = TE = PE + KE = constant. That’s all the 1st Law really can do, it doesn’t tell us what that constant equals – it can’t and be general theory. 1st Law tells us (go look!) energy can be neither created or destroyed, but can be changed from one form to another, we have to do the deducing what that means. The constant specific value is not set by nature; it is not a natural constant. TE is set in the specific experiment. Whatever the total energy in the white space top post is, it has to be constant to obey the 1stnd Law. In Robert Brown’s top post we actually can just (out of thin air so to speak!) announce that our h=0 to be at the bottom of the white cylinder of gas. Here we know at h=0 that TE=PE +KE. Always. Cite the 1st Law! At the bottom of the cylinder we just announce PE is 0 there. This is the tough nut to crack to mix my metaphors. PE is a potential energy – as such nature and the thermo grand masters allow this construct. So we can move on. At Trick’s announced h=0: TE of the molecule(s) will be constant = TE = PE + KE = mgh + 1/2mv^2 = m*g*0 + 1/2mv(0)^2. Voila we have figured the TE constant. In white area TE = constant = m*g*0 + 1/2mv(0)^2 = 0 + 1/2mv(0)^2 = 1/2mv(0)^2 where v is the velocity and m the mass of the molecule(s) at h=0. The TE constant is ½*m(0)*v(0)^2. KE varies with PE(h) in a gravity field… (can you say non-isothermal?) (Say it again: Deduce from 1st Law: molecule(s) KE or temperature must vary in a gravity field with PE, for total energy to be constant, OMG!) But we are ok, what do you know, we have a formula consistent with 1st Law that found the total energy constant of the white area*. The constant = 1/2mv(0)^2 comes from finding the v of the molecule at h=0. For that, all we need do is find the KE or temperature (= kinetic energy density) at h=0 and we will know the temperature anywhere else in the one reservoir or one thermodynamic ideal system of the white area (i.e. at any h) from bottom to top thru TE = constant = ½*m(0)* v(0) = (mgh + 1/2mv^2). A thermometer placed at h=0 will work just great for this experiment. Note 0 location IS arbitrary, I can pick ANY h and put my calibrated thermometer there and find m(h) and v(h) and get the same TE constant, it is just easier to think thru at h=0. Robert Brown needs to not read FAST but s-l-o-w-l-y to grok this; to really come to terms with it, it will take some practice. The thermo grand masters did a fine job, Robert Brown can do one too. Another big deal: Robert Brown cannot use, in Trick’s view, 1/24 8:14 statement to argue against Hans Jelbring’s 2003 paper. There may be other arguments but this Robert Brown one doesn’t work with the 1st Law. Robert Brown continues: “Is there something miraculously interesting in the thermal contact between silver and air that keeps heat from being conducted from hot to cold — in just this one special circumstance? I’m all ears.” Nope there isn’t any Trick violation of 0thLaw equilibrium or 2nd Law entropy being allowed ideally constant, either. Robert Brown’s top post just needs to get rid of 1) the second thermodynamic system of the top post – that 2nd system is not in Willis’ Perpetuum Mobile original premise and 2) the perfect ideal insulator for compliance to all three Laws. Then Robert can do the easy math & will grok the big deal. Eventually Trick & Robert Brown will be in (Tallbloke’s) violent agreement. Trick’s head cold is receding, I won’t be hanging here forever. Robert Brown should try to make this happen in a few days. If not, I predict violent equilibrium will eventually happen, that’s the 0th Law, LOL. *barring typo’s and consistent with mass conservation, the molecule(s) mass does not change thus can assume E to mc^2 in total energy is justifiably being ignored here by all posters on the original Willis’ premise GHG-free air column. 88. Ged says: “Now I can construct a heat engine which extracts useful work based on the temperature gradient and gravity will continue to organize the air column forever and my heat engine will never run out of “fuel”? Really??” Nope! Impossible. As you took energy out, the molecules would not be able to move up as high in the gravity well (the pressure of the gas would drop), as there wouldn’t be enough energy to go into potential energy, and eventually the gas would condense and settle at the bottom of the container. It would cease being gas. In short, the temperature at the surface level would steadily decrease as you took out energy, as potential energy and kinetic energy are -interchangable-, but temperature is -only- kinetic energy. And heat can -only- be transferred by kinetic collisions (if we ignore radiation). So your engine would take out the kinetic portion, leaving less to be turned into potential, making the air column decrease in height until what I said above happened. Same as what happens on Pluto. 89. Willis Eschenbach says: Wayne2 says: January 24, 2012 at 7:39 am @Joules Verne: “This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer.” Does the fact that the air in a higher layer also has fewer molecules matter? That is, are we talking individual molecules or rather volumes of molecules here? Excellent insight, Wayne. That is exactly what happens. In an isothermal column of air, individual molecules at high altitude have more energy because of gravity. But for exactly that same reason, there are fewer molecules at high altitude. As a result, and as we would expect, in the isothermal condition the energy is spread out evenly through space (equal energy per volume) rather than equal energy per molecule as Hans Jelbring and Mr. Verne assert. w. 90. Bryan says: Willis Eschenbach says “If you wish to do the experiment, however, be my guest. I’ll just have a quick beer while I wait for your experimental refutation of a couple centuries of scientific thought ” Its always better to do the experiment! If all the qualified scientists here were honest they would admit that this is an example of an experiment where prejudgement was entirely wrong. http://en.wikipedia.org/wiki/Erasto_Mpemba 91. hotrod (larry L) says: Refutation of Stable Thermal Equilibrium Lapse Rates Posted on January 24, 2012 by Anthony Watts Guest post by Robert G. Brown Duke University Physics Department What matters is that EEJ asserts that image in stable thermodynamic equilibrium. The purpose of this short paper is to demonstrate that such a system is not, in fact, in thermal equilibrium and that the correct static equilibrium distribution of gas in the system is the usual isothermal distribution. I think it is also important to note that Jelbring does not assert thermal equilibrium, they assert “energetic equilibrium” considering both heat energy and gravitational potential energy. THE “GREENHOUSE EFFECT” AS A FUNCTION OF ATMOSPHERIC MASS Hans Jelbring 2003 “The energy content in the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule, in an average sense, will have the same total energy. In this situation the atmosphere has reached energetic equilibrium. The crucial question is what temperature difference (GE) will exist between A and S?” Larry 92. Willis Eschenbach says: The iceman cometh says: January 24, 2012 at 7:58 am I find the analysis quite reasonable – but it is so idealized as to be useless. It is the formal disproof of Jelbring’s theory. It is idealized by its very nature. w. 93. eyesonu says: Thank you Dr. Brown. 94. Willis Eschenbach says: A physicist says: January 24, 2012 at 8:48 am It seems to me Robert Brown’s analysis implicitly makes the following claim: if all the greenhouse gases (mainly H20 and C02) were cleansed tonight from earth’s atmosphere, then the atmosphere would evolve toward a more nearly isothermal equilibrium But how would that work, exactly? Although that may be true, I don’t see why, I don’t see Robert Brown making the claim, and I If Robert Brown answered this question clearly (and it is a subtle question IMHO), then it seems to me that his theoretical ideas would prevail. Wait, wait, you claim to be a physicist, answer the question. Does heat flow forever in the silver wire or not? His ability to answer your random question about possible implications is immaterial to whether his proof is correct. Does heat flow forever or not? w. 95. Ed Fix says: Robert Brown says: January 24, 2012 at 9:01 am Take a single gas molecule and put it at the top of the tube. It has zero kinetic energy and zero temperature. Let it fall and just before it hits the bottom it will have a lot of kinetic energy and heat. That is the lapse rate and it isn’t in equilibrium by definition. No, it won’t have any “heat”. You are conflating work, organized kinetic energy, and heat. Robert, you’re making an inappropriate distinction here. When that hypothetical molecule hits another, and they both bounce off in random directions, how is that gravitationally induced motion distinguishable from thermal motion? Answer: they’re the same thing. Gravitationally induced motion within a gas is heat energy. Drop a jar of air. Are you asserting… Avoiding the question by changing the premise. However, that jar WILL disturb air on the way down, and add a little thermal energy to the column. 96. Septic Matthew says: Robert G. Brown, thank you again for a good presentation and determinedly addressing the criticisms. 97. Temperature depends on the altitude, because more dense atmosphere means more molecules hit the thermometer’s mercury. To assign this to gravity is maybe not correct, but truth is the gravity causes denser, and thus warmer air. When talking about Moon SURFACE temperature, what is the daily temperature there in 2m altitude? 98. Alan Millar says: “MaxL says: January 24, 2012 at 11:38 am I have a question along this topic which will likely show my ignorance. If gravity alone cannot induce a thermal gradient in a gas, how then are stars formed from gases where there is only gravity as an external force?” Gravity can indeed do that. However, that is perfectly allowable under the second Law of Thermodynamics if entropy is increased in another system. Like a fridge I can decrease its entropy but only by increasing the entropy of the room it sits in with the waste heat. Overall the entropy of the combined system will have increased and the second Law is preserved. Stars are part of the universe and you can be certain that overall entropy is increasing with the flow of time even if parts of the system are seeing entropy decreasing. The arguement here is Jelbring is trying to say he can prevent entropy increasing in a CLOSED system whilst work is being performed. There is a problem with Gedanken experiments, they can allow you to construct something that seems viable and yet breaches agreed physical laws. I could invent a closed system that was initially composed of a diffuse cloud of particles in thermodynamic equilibrium. Now that system would be near maximum entropy. However the addition of gravity starts to cause the particles to compress and voila I now have a system like the solar system or a galaxy or the universe even and I have reduced the entropy of the system without the addition of energy or increasing the entropy of another system. Perhaps someone could say that this proves gravity can reverse the flow of entropy in a closed system and the Thermodynamic laws need revising. However, in the real universe we inhabit we cannot create such a system in such an inital state. Perhaps a supreme, all powerful being could but I am not holding my breath! The existence of such a being would invalidate all known physical laws in any event. So we have to be careful with gedanken experiments. I tend to the view that if such a system is proposed, that is in breach of thermodynamic laws, that it is either in error or could not ever be created in the universe we inhabit. Alan 99. Willis Eschenbach says: Folks, a lot of you here don’t seem to get it. The beauty of Robert’s proof is that there is only one question in it—does heat flow forever in the silver wire or not? So all of your claims of deep insights into where the joules are, and all of you talking about some mechanism or other that you are absolutely sure will make the air temperature at the top and bottom different, that has NOTHING TO DO WITH THE PROOF. The proof is about the outcome, what the mechanism is that you say results in that outcome doesn’t matter. IF you are correct and any of your hotly defended mechanisms work, gravity will make the air at the bottom of the tall cylinder warmer than the air at the top. (Your claim, not mine, just following it to see where it leads.) IF there is a temperature difference in the air top to bottom, heat will flow in the silver wire. Gravity can’t stop that. IF heat flows in the silver wire, it will move heat from the bottom to the top, and thus cool the bottom air and warm the top air. Duh. IF you are correct and any of your hotly defended mechanisms work, gravity will once again make the air at the bottom warmer than the air at the top, and the cycle will continue forever. So forget about your mechanisms, forget about the joules, forget about the lapse rates and how they are maintained, and just ANSWER THE FREAKIN’ QUESTION: Will heat flow in the silver wire forever? Me, I say no, and I say Roberts thought experiment elegantly proves that the answer is no. w. 100. Alan Millar says: Should have said ‘decreasing’ in my third para of course. Doh!! Now if one of these new hotrod physicists can explain how and when Saturn dies in the Jelbring universe. Alan 101. markus says: They just don’t get it. Or, as Bono would say, “stuck in a moment we can’t get out off.” To the tune of whatever ditty you like. —————————————————————————————– I’m a little radiation, radiation, radiation, I’m a little radiation, all day long Down through the mesopause , mesopause , mesopause, down through the , menopause, all day long. Down through tropopause, tropopause, tropopause, down through,tropopause, all day long. Now I’m a little kinetic, kinetic, kinetic I’m a little kinetic, all day long Up through the pressure, pressure, pressure, up through the pressure, all day long. Back to a little radiation, radiation, radiation, I’m a little radiation, all day long. —————————————————————————————————————————- Consider how a refrigerator works – 2 thermostats going down, and a heat pump going up. What happens to pressured gas through a condenser and then a separation device? Co2 forcing, what dribble. Pick a system – greenhouse or refrigerator. 102. hotrod (larry L) says: just ANSWER THE FREAKIN’ QUESTION: Will heat flow in the silver wire forever? Yes but to no avail, as the heat flow would be exactly canceled by adiabatic heating of the gas at the bottom of the tube. The model above postulates only a temperature gradient from top to bottom in the tube but leaves out the pressure gradient developed in a sufficiently long vertical tube in a gravity field. In the case of a sufficiently long tube, where both gradients exist, the silver wire would try to transport heat from the warmer bottom of the tube to the cooler top of the tube as it must due to thermodynamic laws. The gas at the top of the tube would be warmed (thus increasing its pressure slightly (ideal gas laws temperature change constant volume tube) and like a piston this pressure increase would propagate down the tube at the local speed of sound in the gas causing adiabatic heating of the gas in each subsequent layer until it reached the bottom of the tube, instantly replacing the heat lost to the silver wire. Net effect – no heat loss from the bottom of the tube, and no net heat gain to the top of the tube as the two actions will exactly cancel each other out. The gas in the tube would never reach thermal equilibrium but would be in equilibrium energetically (PE+KE) Larry 103. Q. Daniels says: Willis wrote: Will heat flow in the silver wire forever? If you extract energy from the system, it will shut down as the entire system cools. Energy is conserved. If you extract energy, then it has to come from somewhere, and that somewhere is the thermal energy of the system. If you do not extract energy, then yes, it will. It’s a terrible design for such. See my comment above. You seem to have rejected Graeff’s work as being insufficient proof. What would you consider a sufficient proof? 104. Willis Eschenbach says: Alan Millar says: January 24, 2012 at 12:26 pmShould have said ‘decreasing’ in my third para of course. Doh!! Now if one of these new hotrod physicists can explain how and when Saturn dies in the Jelbring universe. Alan [I think I fixed it, there were two, better check and see if I got it right. -w.] 105. Graeme W says: Willis Eschenbach says: January 24, 2012 at 12:23 pm Folks, a lot of you here don’t seem to get it. The beauty of Robert’s proof is that there is only one question in it—does heat flow forever in the silver wire or not?, Well… I don’t know the answer, but I do need to point out that a closed system with a changing level of kinetic energy in different parts doesn’t violate conservation of energy. Consider on object in an elliptical orbit around a gravitational point source. Its kinetic energy changes as it orbits, but the system is in ‘equilibrium’ with no external input of energy. 106. Willis Eschenbach says: Q. Daniels says: January 24, 2012 at 12:55 pm Willis wrote: Will heat flow in the silver wire forever? … If you do not extract energy, then yes, it will. It’s a terrible design for such. See my comment above. I hate it when my perpetual motion machines are poorly designed … w. 107. Q. Daniels says: Willis wrote: I hate it when my perpetual motion machines are poorly designed … A curious thing. I’ve noticed that engineering tends to be particularly bad when people want it to fail. 108. MDR says: @Willis Heat is indeed conducted upward in the column forever. Why? There is a temperature gradient, and as long as there is a temperature gradient, conduction will occur. It doesn’t matter that the conduction is via the wire, or within the gas itself. It sounds like you are expecting the temperature profile would eventually smooth out [i.e., become isothermal] over time, and indeed if there we no gravity this is exactly what would happen – the gas would become isothermal, isobaric, and have a constant density. But in the presence of gravity, you have to take into account the potential energy imparted to the gas as a function of height. Gravity has dome more work on the gas at the bottom of the column than at the top. By virtue of being at the bottom, some of that gas’ gravitational potential energy has been spent [that is, gravity has done work on that gas parcel]. As a result, with no other outlet, this work energy has been converted into thermal energy. This is what the First Law of Thermodynamics is saying. Thus, the temperature of the gas at the bottom is higher than the gas at the top in the presence of gravity, and indeed this is a stable arrangement in thermodynamic equilibrium. 109. Joe Born says: Willis Eschenbach: “So forget about your mechanisms, forget about the joules, forget about the lapse rates and how they are maintained, and just ANSWER THE FREAKIN’ QUESTION: Will heat flow in the silver wire forever?” As I said explicitly and a couple have implied (by noting that Dr. Brown has begged the question), heat will not even begin to flow, despite the temperature gradient, if that temperature gradient is the one that Velasco et al. specify, at least if Velasco et al. are correct. As I mentioned above, this is not hard to understand if you look at heat transport as a diffusion phenomenon, i.e., as flow in accordance with the laws of probability from a region characterized by a higher concentration (of fast molecules or fast electrons) to one with a lower concentration. Superimposed upon that diffusion flow is a contrary drift flow from gravity that cancels it out and thereby maintains a gradient. I’m told that an analogous effect occurs when a semiconductor diode is fabricated. At the instant two differently doped semiconductor materials join to make a diode, there exists across the resultant junction a hole gradient in response to which a cross-junction hole current begins to flow that tends to eliminate the gradient. But that current stops flowing before the gradient disappears. The reason is that the charge thereby transported sets up an electric field that opposes the cross-junction hole current. So the electric field maintains a gradient that the laws of probability (diffusion) would otherwise eliminate. 110. kdk33 says: Brian, What is the lapse rate in the ocean? 111. markus says: Am I one of the boys yet Willis? Regards, Markus. 112. Jordan says: Gulp! I have my doubts about the above analysis. IMO, the tidy demonstration of the exponential pressure profile does not advance either position. It is merely astatesment of the profile to expect at isothermal conditions (i.e. “if we assume constant temperature”). The crux of the issue is whether the thought experiment justifies the invitation to accept the assumption. The silver may conduct energy, but this doesn’t lead to the conclusion that we have devised PM as there is no energy leaving the system (and no case is made to say that it could be removed indefinitely). The container has a mass of molecules jostling around forever (so long as we don’t take their energy away). The silver looks like an extension to the container – a somewhat circuitous route in which to carry out their mutual exchanges. If (for now) all moleculecular collisions were to transact a fixed quantum of energy, the flow through the silver (‘Q’) would be limited by the frequency of exchanges at the lower pressure end. Any additional collisions at the higher pressure end of the silver would have no potential to increase ‘Q’. It is then unclear whether the silver makes any difference to an assumed isothermal end state. If we remove the fixed quantum constraint, things may improve for ‘Q’, as the lower frequency transactions at the low pressure end may then be more energetic. But all this seems to be saying is that the silver may be a better conductor than the gas (a preferred route for mutual jostling). This alone doesn’t support the leap to an isothermal end state any more than leaving the gas to its own devices. Finally, there is the significant point that the lower pressure molecules have the greatest total energy in the isothermal state. It is this question that makes me reluctant to go with the assumption. 113. markus says: Sorry about the rapid fire. Mr Willis Eschenbach, Sir, you have done us a great service, you have helped us to reason. Thank you very much. 114. Joe Born says: I misspoke slightly when I said that heat will not even begin to flow in the wire. Whether it does or not initially depends on the temperature distribution that prevails in the wire before it is connected across the gas column. And there may be an initial transfer of energy between the air and the wire. But heat flow will stop before the temperature gradient disappears. 115. Willis Eschenbach says: When I illustrated my post called “Perpetuum Mobile“, I chose a photo of a Civil War era perpetual motion machine, because that’s what they are in my mind—a relic of a time long ago when people hadn’t grasped that such a machine is an impossibility. However, I’m starting to see that perpetual motion still maintains its historical death grip on the scientific illiterati. And I can kinda see why, everyone wants something for nothing. And truly, people, I hate to bust your bubble and maybe I can’t do so in any case, but the heat can’t flow in the silver wire forever. That would be perpetual motion, and the laws of thermodynamics don’t allow that. Look, I know that we all break various laws all the time, someone once estimated that Americans break one to three laws every day. But the laws of thermodynamics aren’t like that. They are not just good ideas, or regulations put in place to protect us from each other or from ourselves. As far as anyone has ever been able to determine (and lots have tried) those laws simply can’t be broken. That’s why they are called the Laws of Thermodynamics, and not the Good Ideas of Thermodynamics. Those laws say we can’t have a perpetual motion machine driven by gravity. So if you want to continue to believe that heat will flow through the silver wire forever and ever without end, and that the mystery power that will make it do that is gravity, or lapse rates, or unicorns, or density-driven molecular interactions, or “gravito-thermal forces” or anything else, be my guest. As I pointed out with my Civil War machine, that mistake has a long and storied history, you’re not the first to believe in energetic fairies and Maxwell’s demons. Just don’t expect your belief, that gravity can do continuous unending work forever and ever amen, to be widely shared in the scientific community … w. 116. Alan Millar says: “MDR says: January 24, 2012 at 1:14 pm Thus, the temperature of the gas at the bottom is higher than the gas at the top in the presence of gravity, and indeed this is a stable arrangement in thermodynamic equilibrium.” So MDR A gas giant planet, like Saturn, radiates more than twice the amount of radiation than it receives from the Sun. Presumably this little gravity induced energy engine is at work here according to you. How do these planets ever die, if gravity is constantly maintaining a heat gradient in the atmosphere? The Sun will die and become a cold white dwarf with no solar wind to blow any atmosphere away. What is going to kill these gas giants? If gravity is constantly maintaining hotter gases at the bottom then convection will move gases around and therefore we seem to have an everlasting living planet. What kills it and when, if Jelbring is correct? Alan 117. Q. Daniels says: Willis wrote: Just don’t expect your belief, that gravity can do continuous unending work forever and ever amen, to be widely shared in the scientific community … Such a demonstration would be worth at least a handshake from Carl Gustaf. 118. MDR says: @Willis Implicit in this discussion is that gravity is an unvarying external force being applied to the column of gas. That is what provides the [apparently infinite] source of energy. The difference between this scenario and a perpetual motion machine is that, for a perpetual motion machine to work, it cannot rely on infinite external sources of energy. Given that one is assuming here that gravity exists as an external agent, and is capable of doing work on the gas, I stand my my comments above. 119. MDR says: @Alan Millar Sorry, I can’t directly answer your question. But it’s probably worth considering that Saturn is probably not in thermodynamic equilibrium [it has seasons, weather, storms, etc.]. It may in fact still be settling, that is, not enough time has passed since Saturn’s formation to reach an equilibrium state where the heavier matter is underneath the lighter matter. If settling is occurring, gravity would still be doing work on the gas, converting gravitational potential energy into other forms of energy, and some of this energy may radiate into space making it appear that Saturn has an internal heat source. 120. glen martin says: “Willis Eschenbach says: January 24, 2012 at 12:23 pm Folks, a lot of you here don’t seem to get it. The beauty of Robert’s proof is that there is only one question in it—does heat flow forever in the silver wire or not? . . . IF there is a temperature difference in the air top to bottom, heat will flow in the silver wire. Gravity can’t stop that.” Actually it can and does, heat in the wire is being transmitted via the interaction of moving particles, gravity will cause the particles to slow slightly as its height increases thus slightly less energy is will be transferred to the atom above a particular atom than was received from the atom below it. This results in a gravitationally induced thermal gradient in the wire. 121. Ged says: @Willis, Gravity doesn’t make the air warmer at the surface, it makes the air -colder- above the surface. A silver wire has a high thermal conductivity, so it’s easy for heat to flow through its length. But what would happen if you stretched that silver wire over a mile? 12 miles? Would the heat flux be the same over its length? No. You would get microdomains, fluctuations where some areas get randomly distributed with more heat than others, and those domains will flow around. You can see this easily with objects that have very, very low thermal conductivity. You have microlattice vibrations. But also realize gas is -not a solid lattice-. I don’t understand, Willis. Before hand you were so concerned with the conservation of energy. Now are you claiming you can take a molecule with a certain kinetic energy (which is what temperature is a measurement of), and raise it 17 kilometers above the Earth (increasing its potential energy by 4664 Joules if we’re talking about a mole of N2) without inputting more energy, and have it maintain that same kinetic energy, that same temperature? Answer that question, Willis. 122. Peter Spear says: A physicist says: January 24, 2012 at 8:48 am “It seems to me Robert Brown’s analysis implicitly makes the following claim: if all the greenhouse gases (mainly H20 and C02) were cleansed tonight from earth’s atmosphere, then the atmosphere would evolve toward a more nearly isothermal equilibrium But how would that work, exactly?” The answer is easy. By conduction. Convection will shut down quite quickly as the heat transported upwards by convection reduces the environmental lapse rate. Once the lapse rate is below the moist adiabatic lapse rate even cloud formation cannot drive convection anymore. Oh, except you removed all the H2O. Therefore once the lapse rate is below the dry adiabatic lapse rate all convection will stop. Without GHG to cool the upper atmosphere there is no way to regain a lapse rate suitable to drive convection. All vertical motion will cease. Conduction will become the dominant mode of heat transport. That too will stop when the atmosphere becomes isothermal. 123. Joe Born says: January 24, 2012 at 8:21 am “…If an ideal monatomic gas subjected to gravity in a thermally isolated container consists of only a single molecule, its kinetic energy K–and thus the mean translational kinetic energy–at any altitude z is given by K = mg(z_max -z), where m is molecular mass, g is the acceleration of gravity, and mgz_max is the total (kinetic + potential) energy of the gas. This is true no matter how long you’ve allowed the gas to “equilibrate.” In other words, temperature depends on altitude at equilibrium: there’s a non-zero temperature lapse rate.” As I pointed out in the other thread, this is not a thermal system at all – or even a gas! – unless the atom is allowed to thermalise with the walls of the container. In which case the temperature (as measured by its average kinetic energy as it passes through a given level) is independent of height. I have now read the Velasco et al article, and it agrees with what I said: in either the microcanonic (totally isolated) ensemble (with a reasonable number of particles in the gas) or the canonic ensemble (in thermal equilibrium with the surface or walls, irrespective of the number of particles), the gas is isothermal. You are trying to make a haystack out of the negligible point that, for a tiny number of isolated particles, the statistics aren’t precisely the same as for the usual smooth distribution – they’re “lumpy”. However, even in this extreme case, the temperature at equilibrium will still be the same throughout the entire height, in the crucial sense that no net work could be extracted from the gas by connecting different levels, by any means whatsoever. The “lapse rate” is still zero. Note by the way that any thermometer capable of measuring the the temperature of two levels of any such system alternately is itself either extracting work from any measured temperature difference, or has to have work done on it to obviate this happening. 124. Blue Sky says: All these tree people making a joke of climate science. You have Mann with his cherry picked tree proxies and Ned Nikolov, Ph.D. Ph.D. in forestry making a joke of Thermodynamics. Any way the 600mb temp is going cold right now. http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps 125. Graeme W says: Ged says: January 24, 2012 at 2:10 pm I don’t understand, Willis. Before hand you were so concerned with the conservation of energy. Now are you claiming you can take a molecule with a certain kinetic energy (which is what temperature is a measurement of), and raise it 17 kilometers above the Earth (increasing its potential energy by 4664 Joules if we’re talking about a mole of N2) without inputting more energy, and have it maintain that same kinetic energy, that same temperature? Answer that question, Willis. I’ll take a stab to see if I can answer it correctly. The short answer is it will not maintain the same kinetic energy, the same temperature. This has never been postulated. What’s stated is that eventually the average kinetic energy (the temperature) of all molecules will be the same throughout the gas. That’s not necessarily the same kinetic energy as any individual molecule will have at any given time – it’s the average that’s the temperature. Individual molecules can be hotter or cooler than this average. 126. Jordan says: “Will heat flow in the silver wire forever?” Will the molecules continue to jostle forever? If we never take any energy away from the system, what is the difference between jostling in the gas and flow through the wire? The questions that remain are: Is isothermal state the lowest energy state for a compressible gas in a gravity field? And on what measure is there a stable (mininum energy) outcome if we are asked to accept that molecules at higher altitude have more total energy than molecules at low altitude? Just asking. 127. Tim Folkerts says: Ged says: I don’t understand, Willis. Before hand you were so concerned with the conservation of energy. Now are you claiming you can take a molecule with a certain kinetic energy (which is what temperature is a measurement of), and raise it 17 kilometers above the Earth (increasing its potential energy by 4664 Joules if we’re talking about a mole of N2) without inputting more energy, and have it maintain that same kinetic energy, that same temperature? This is a very subtle point, but one worth understanding. “Temperature” is a measure of the average thermal energy at some location. As implausible as it might seem at first, the average kinetic energy of the molecules that make it 17 km will be the same as the average KE of the molecules at the bottom. You see, only a very few molecules will make it 17 km high. The rest are pulled back by gravity before they get that high, so they never get counted. The self-selected molecules that DO make it 17 km high are the ones that had LOTS of KE to start with. Sure they lose a bunch on the way up, but that ends up leaving this subset 17 km high with the same average KE as the ENTIRE set had at ground level. (The same is true at any other level up thru the atmosphere). This has been discusses MANY times in related threads recently. 128. Willis Eschenbach wrote: Just don’t expect your belief, that gravity can do continuous unending work forever and ever amen, to be widely shared in the scientific community … So Willis, when will we start flying off the planet??? When will the pressure on my feet from standing in one place stop?? When will the oceans boil from lack of pressure? Oh yeah, gravity is apparently an unending source of energy that counteracts centrifugal force. If not unending, we haven’t yet measured its reduction. 129. Alan Millar, “The Sun will die and become a cold white dwarf with no solar wind to blow any atmosphere away.” This is an assumption without much empiraical proof. 130. Willy says: MDR says: January 24, 2012 at 9:32 am “…Now, we just showed that internal energy decreases with height, as explained above. Since internal energy [of an ideal gas] is directly proportional to temperature, this must mean that temperature also decreases with height…” The correct statement would be ” that ALL ELSE BEING EQUAL temperature also decreases with height”. But the internal energy of an ideal gas is also directly proportional to density, which decreases with height. So all else is not equal. The argument fails. In other words the decrease of internal energy with height manifests itself as decreasing density, not as decreasing temperature. (In case someone does not see why internal energy is proportional to density it is because if stuff has energy, and you have more of the same kind of energetic stuff, you must have more energy.) 131. loads of politics going on here. Sceptical AGW blogs still trying to prove that planets are at temperatures dictated by their atmospheric gas composition rather than their distance from the sun. The Greenhouse effect still rules concensus thinking be you an aye or a nay for AGW. 132. quondam says: In 1964, Manabe and Strickler published “Thermal Equilibrium of the Atmosphere with a Convective Adjustment”: 2b. Thermal Equilibrium with convective adjustment. The procedure of convective adjustment is to adjust the lapse rate to the critical lapse rate whenever the critical lapse rate is exceeded in the course of the numerical integration of the initial value problem. The observed lapse rate of temperature is approximately 6.5 deg km-1. The explanation for this fact is rather complicated. It is essentially the result of a balance between (a) the stabilizing effect of upward heat transport in moist and dry convection on both small and large scales and (b), the destabilizing effect of radiative transfer. Instead of exploring the problem of the tropospheric lapse rate in detail, we here accept this as an observed fact and regard it as a critical lapse rate for convection. In a nutshell, this adjustment eliminates the possibility that a greater potential gradient might compensate for increased transport resistance by GHGs. Instead, only flux changes are allowed which can be nullified by positive feedback. Et voilà, CAGW! 133. Ged says: @Tim Folkerts, Maybe that is the case. Maybe you are totally right. But I still find that hard to believe form observations. As you move up in altitude, the temperature, the measurable, observable temperature drops steadily. In fact, form my calculation I was less than 3x off just looking at KE turned into PE from the actual temperature at that height. So the problem is, the average thermal energy you are talking about includes -all- altitudes, and this is a value that cannot change unless absolute energy is given or take from the system. But it does not -follow- the temperature change that occurs as any molecules moves from low to high against gravity. And that’s what I’m talking about. That’s what this whole discussion is actually about. Yes, the molecules that make it 17 km up had more KE when they started than those that don’t (well, to a degree, as it’s a random walk). But once they MAKE IT 17 km up, they’ve lost a great deal of kinetic energy, temperature, into potential energy, versus what they had at sea level, as energy most be conserved. Correct? In that way, gravity does NOT DO WORK, but gravity TRANSFORMS ENERGY from one type (kinetic) to another (potential). This must drop the temperature of the molecules in question, since temperature is only a measure of the KINETIC ENERGY side of the TOTAL ENERGY equation. So, if air rises, it must lose temperature as a consequence of moving against gravity. Average kinetic energy of the entire system means little, as that will not change unless energy is removed from the system or inputted to the system. Average kinetic energy of the cohort of air that moves from low to high, now that does mean something, and that is going to be changed into potential energy. So then, gravity seems to be able to maintain a temperature gradient -in this way-, as it seems to me, and maybe I’m wrong and your way of looking at it is right. But, what predictions would we make for the real world from what I’m seeing? For starters, we’d expect that if the average energy of the entire system increased, so there was more kinetic energy at the surface, that the atmosphere would “puff up” from the Earth and it’s edge would get higher due to more KE being available for transforming into PE. And this is -exactly what we see- in the real world. And the converse is true. Which is what we see with Martian poles in the winter, or Pluto’s entire atmosphere whenever it gets far enough away from the Sun. 134. “Why is it that you want to fight over physics that you can actually see with IR eyes? Save your energy for useful things, like arguing about the magnitude of the GHE, the sensitivity of it to changes in CO_2 concentration, the sign and nature of climate feedback or albedo modulation or the complex effects of atmospheric convection on local heating or cooling rates, or the ocean’s effect. The IR spectra render arguing about GH warming per se moot.” Thank you Robert. I sometimes wonder why skeptics waste their time an energy fighting against working science. The real question is sensitivity. Think of all the energy and time devoted here on WUWT to clearly false theories. Imagine if that effort were put to better purposes. Like the surface stations project expanded on a global basis. sad to see so much human energy, curiousity and intelligence wasted on crap like this and N&Z 135. George Turner says: Actually Willis, heat flowing through the silver wire forever doesn’t mean it’s impossible, as heat always flows forever in any system above absolute zero. Take any object and an arbitrary plane that defines it. The two parts will never be in exact thermal equilibrium because atomic collisions are discrete, so half the time one side is hotter and half the time it is colder. Thus heat flows back and forth across the boundary – forever. That doesn’t mean the existance of an object above absolute zero is impossible. Or, take the case of the Maxwell Demon I constructed in my first comment in the thread. It’s made of nothing but pine and mylar but should maintain an imbalance of temperatures between two objects forever, because photon transmission and reflection can be made to be asymmetrical or unidirectional by having mirrors moving to create a path that is only valid in one direction. The concept is like the way volleyball players set the ball to each other. Given the timing of their motions, a volleyball can’t travel the reverse path and find the right hands in the right places at the right times. You can do the same with light if your mirrors are moving very fast. So if you can construct a system that never reaches the isothermal state, and attach another path for heat flow, the heat will travel from hot to cold forever. This changes the stable temperature difference between the two objects, turning the Demon into a less efficient Demon. You can’t extract anything from the permanent heat flow without having the energy dissipate. As for thoughts on the problems of heat flow through a long silver wire, the equations we use have never needed to include any gravity component because it’s unimportant to most purposes. It’s only fairly recently that physicists got irked enough to tweak heat flow equations so the heat couldn’t travel at infinite velocity, exceeding the speed of light. Equations for electricity, from Ohms law to Maxwell’s equations, likewise completely neglect gravity, implying that I can connect a copper wire to a black hole with a potential of -24 VDC and have electrons pour right up out of the gravity well. Or I could show that an atmosphere of electrons and protons (hydrogen) wouldn’t have more pressure at the bottom than the top because Ohm’s law or some other handy formula says the electrons would be evenly distributed, as gravity was never factored in to the completely accepted electrical formulas we use every day. 136. son of mulder says: I shall repeat in different words the argument i provided at son of mulder says: January 24, 2012 at 9:59 am which no one challenged (or read). If I’m wrong please challenge. Heat cannot flow up the silver conductor unless more heat is pushed in at the base. Heat is energy and hence by Einstein mass. If you consider all the heat in the silver conductor as a distribution of mass then that mass has a center of gravity in the gravity field. If heat were to flow from the base to the top (without input of new heat at the base) then there would be reducing heat (mass) a the bottom and increasing heat (mass) at the top. Overall the centre of gravity of that heat (mass) would rise. ie work would have to be done against gravity. Put another way a force against gravity would have to be applied. If no new energy is being pumped into the base then the law of conservation of energy means that heat cannot be conducted up in a gravity field and so the top will be colder than the base and remain so ie no force can be applied. The same logic can be applied to the atmosphere. You just have to ensure no new heat is applied and no heat is removed. If no new heat is applied and energy is allowed to be radiated away then eventually all temeprature would be equalised only at absolute zero. 137. Willis, Seems like folks here want to argue that the laws of thermo are not settled science. same with the laws of radiative transfer 138. Let me toss my in my idea to show what is wrong with this thought experiment. Take the earth system and remove gravity. What happens to the GHG’s, the water, loose objects, the adiabatic lapse rate… Take gravity away from the thought experiment and what happens. Nothing except a very slight redistribution of mass as the pressure equalizes through the column? 139. pidge says: For a volume of gas to have a thermal gradient requires a heat source and heat sink at each end of the gradient, so that heat is transported along the gradient from source to sink. Remove the heat source and the heat sinks from the gas, and the thermal gradient will disappear. In the case of Earth’s atmosphere, the heat source is the heating of the surface of the earth by the sun, and the heat sink is radiative to Deep Space. So it is not appropriate to dismiss Robert’s because it’s not the atmosphere – Robert is just showing the mechanism in the paper being criticised is not correct. 140. A physicist says: A physicist says: “It seems to me Robert Brown’s analysis implicitly makes the following claim: if all the greenhouse gases (mainly H20 and C02) were cleansed tonight from earth’s atmosphere, then the atmosphere would evolve toward a more nearly isothermal equilibrium. But how would that work, exactly?” Peter Spear says: The answer is easy. By conduction. Convection will shut down quite quickly as the heat transported upwards by convection reduces the environmental lapse rate. Once the lapse rate is below the moist adiabatic lapse rate even cloud formation cannot drive convection anymore. Oh, except you removed all the H2O. Therefore once the lapse rate is below the dry adiabatic lapse rate all convection will stop. Without GHG to cool the upper atmosphere there is no way to regain a lapse rate suitable to drive convection. All vertical motion will cease. Conduction will become the dominant mode of heat transport. That too will stop when the atmosphere becomes isothermal. Peter Spear, (IMHO) your scenario is correct. The resulting no-GHG Earth would have nearly isothermal, hence stratified atmosphere, for the physical reason that every thermal would carry heat into the atmosphere that could never be radiated away, making it ever-harder for thermals to rise on subsequent days. The no-GHG weather would be freezing no-wind nights followed by still cold days. As (relatively) warmer tropical air slowly circulated (colder poles), first Earth’s polar oceans would freeze, then the mid-latitudes, then even the equatorial oceans. Some folks we’ve seen this scenario even here on earth, way back when the sun was cooler and GHG’s were scarcer, a world of low GHG’s and frozen seas … This hypothesis is called Snowball Earth. Elevator Summary: GHG’s prevent Snowball Earth. 141. Tim Folkerts says: kuhnkat says: “Oh yeah, gravity is apparently an unending source of energy that counteracts centrifugal force.” Repeat after me: Force is not energy; energy is not force. Gravity can and does provide a continuing force. That does not mean that it is providing any continuing energy. Gravity only does work when there is a net movement inward. Since the atmosphere is not continually falling, gravity is not doing work. (NOTE, on the gas planets, there is no solid surface to stop contraction, so there the planets are indeed contracting and generating continued thermal energy of the sort many people seem to think exists on earth. This is also how protostars warm as they collapse inward.) 142. Camburn says: steven mosher says: January 24, 2012 at 2:38 pm 100% correct Sir. Sensativity is the question and there have been no answers with acceptable confidence from a model yet. The present parameters do not hindcast with enough accuracy to forcast with any confidence. Physiscs, as we presently know it, is physics. Unless a new law of thermodynamics is found, Dr. Robert Brown is 100% correct. 143. Nick Shaw says: January 24, 2012 at 9:52 am as air gets closer to outer space (in really simple terms) it would get mighty cold Space has no temperature. To have a temperature there must be kinetic energy which means that there must be mass. Things in space get cold because they radiate heat away. Look at photos (or drawings) of the space station – look for the radiators. These are positioned so that the Sun does not shine on them. In the case of an atmosphere without IR radiators, it will have no way to cool itself. 144. Chas says: Do I have this correct : the temperature is dependent on the kinetic energy of individual molecules(?) When I throw a single ball upwards it’s velocity decreases with height. Do gas particle’s velocities not decrease as they go higher and higher,? Can someone explain why, if their velocities do not decrease, there fewer of them at height. Sorry if I am being dim! 145. LongCat says: While I agree with the underlying point, I’m not sure why the wire would necessarily violate the laws of thermodynamics if it continuously transferred heat. Under normal circumstances, it would radiate some of this energy away and otherwise be an imperfect conductor. If, however, we’re assuming a closed system with a perfect conductor surrounded by a perfect insulator, why would any energy be lost? To put another way, assume I have a wheel with a frictionless axle at rest in a vacuum. If I spin it, it will spin endlessly. The conclusion that it will have perpetual motion doesn’t violate thermodynamics; the assumption that there is no friction does. Likewise, the wire would not violate any physical laws by endlessly transferring heat; those laws were broken by the assumption of a closed system with a perfect conductor/insulator. I know I’m disputing people far above my pay-grade, so I’m assuming that I’m wrong in this. I’m just curious as to why. 146. hotrod (larry L) says: What the recent theories regarding gravity induced temperature gradient are really saying is that the ideal gas law as commonly stated is incomplete. A factor is left out because in most terrestrial situations it is irrelevantly small. They are implying the ideal gas law should be stated as: PV = NkT +(delta PEg) where PEg = the change in gravitational potential energy. If you radically increase the gravitational potential energy of a mass of gas, you have changed the total energy in the system unless you give up an equivalent amount of energy in the form of temperature. Larry 147. Stephen Wilde says: “The real question is sensitivity.” Yes indeed it is but the lapse rate issue goes to the heart of it. If the lapse rate and thus the surface temperature is set by pressure and solar input alone then the effect of GHGs is zero. GHGs do introduce more radiative and conductive energy around themselves by virtue of their thermal characteristics so, if there is more energy in the air but the surface temperature fails to change then something else has to give. I propose a miniscule change in the surface air pressure distribution instead. That would simply change the rate of energy flow through the system from surface to space and redistribute the energy at the surface as necessary for no global change in surface temperature at all. 148. Tim Folkerts says: “Heat is energy and hence by Einstein mass.” I hate to even bring this up, but I am rather sure that gravitational red-shifting will indeed have a theoretical affect on things (but I don’t think in the way imagined by the earlier poster). A photon will be red-shifted when it rises from the surface. It would be a straightforward task to estimate the change in wavelength and hence the change in “temperature” for thermal IR photons arriving high above the earth from the surface. However, typically such effects are only noticeable very close to very massive objects. I am sure that the “relativistic lapse rate” would be microkelvins at most, and hence not important in this discussion. But, hey, if anyone wants to calculate the actual “relativistic lapse rate” and its effects — go for it. As a warm-up, I would suggest calculating the time correction for GPS satellites to make sure you know enough to get started. 149. Joules Verne says: Ged says: January 24, 2012 at 2:10 pm @Willis, Gravity doesn’t make the air warmer at the surface, it makes the air -colder- above the surface. ____________________________________________________ Bingo! 150. Joules Verne says: Ged says: January 24, 2012 at 2:10 pm “Gravity doesn’t make the air warmer at the surface, it makes the air -colder- above the surface.” Yes. And if you remove the source of heat the column will cool and as it cools it shrinks and as it shrinks the molecules fall toward the surface and as they fall they gain back the kinetic energy they lost in making the ascent. If the temperature of the column drops enough the gas turns into an incompressible liquid or solid, completely collapses to the surface, and the gravity induced gradients are history. 151. MDR says: @Willy Your statement that “the internal energy of an ideal gas is also directly proportional to density” is incorrect. Internal energy, a term with a very specific meaning in thermodynamics, is proportional only to temperature for an ideal gas. For starters, see http://en.wikipedia.org/wiki/Ideal_gas , and in particular the section entitled “Classical thermodynamic ideal gas” where it states that the internal energy $U$ for an ideal gas is $U = c_V n R T$ where $c_v$ is the specific heat at constant volume, $n$ is the number of moles of the gas, $R$ is the gas constant, and $T$ is the temperature. None of these quantities depend on volume or density. 152. dlb says: Willis at 11.54am wrote: Excellent insight, Wayne. That is exactly what happens. In an isothermal column of air, individual molecules at high altitude have more energy because of gravity. But for exactly that same reason, there are fewer molecules at high altitude. As a result, and as we would expect, in the isothermal condition the energy is spread out evenly through space (equal energy per volume) rather than equal energy per molecule as Hans Jelbring and Mr. Verne assert. Although I agree with Dr Brown, I disagree with what Willis has said here. Consider a cubic metre of soil and a cubic metre of air above it, although both are at the same temperature, they certainly have different amounts of enegy due to differing densities. 153. equilibrate the total energy This is a major misunderstanding. Thermal equilibrium does not equate the total energy. Read the equipartition theorem. Open a standard introductory physics textbook. Learn what temperature is. Then return. Besides — and I’m going to make this a standard answer for all off topic replies. The presentation above challenges you to do just one thing. Tell me whether or not the system in figure 2 permits energy to flow in a circle forever. If you answer “no, of course not” you are quite right, and you have conceded that thermal equilibrium is isothermal, because the silver wire is just a proxy for thermal conductivity in the air itself that makes it clear why not (since detailed balance computations get confused when you add an utterly irrelevant process that you dream up involving gravity to them and then try to do them in your head without the faintest idea of how statistical mechanics actually works). If you answer yes, I’ve got this bridge in Brooklyn you might want to look at, right after I convince you to invest in the machine we can build that will turn heat into energy at the rate of 100%, because I could stick a heat engine into the thermal pathway of the silver conduction and the resulting system would convert 100% of any energy added to the fixed-lapse air on the left into work. The choice is yours, of course. rgb 154. My head hurts. Is someone keeping score? If so, who is wining, the For team or the Against team? Confused minds need to know. 155. MDR says: @Willy Note that I am *not* arguing that there *isn’t* a variation of density [or pressure] with height. It’s simply that once one knows the internal energy of a gas, one also knows its temperature, irrespective of either the density or pressure. Of course, the profiles of both density and pressure must still satisfy the ideal gas law, and as you intuitively expect both decrease with height [as does the temperature]. 156. 2) The silver wire will transport heat from warmer region to the cooler region, but in so doing it short circuits the transport of heat by convection. So with the wire present, convection will be less, but the net transport of heat will remain the same. It won’t short circuit convection — in stable equilibrium there is no convection. Convection itself is a kind of heat engine driven by temperature differences that transports heat (on average) from a hot reservoir to a cold one. In stable equilibrium nothing moves, because there is always dissipation associated with movement that will slow it down, right down to the extreme quantum regime. I assume you aren’t talking about superfluid circulation and calling it “convection”. There is no input energy, also, so there cannot be net transport of heat. That’s the bit about “violating the second law of thermodynamics” in spades. A system with interminable flow of heat in a circle is a textbook violation of the second law, and it permits one to design any number of perpetual motion machines of the second kind. rgb 157. wayne says: I thought metals had free electrons and electrons were matter and gravity accelerates all matter and metals conduct heat so well due to the free electrons and …. and how again is this proposed perpetual machine supposed to refute a lapse rate? Seems lifting the electrons against gravity in the metal bar from the warm to the cool would cancel if the gradient became -0.0098C/m. The only real thermal motion it seems would be with an isothermal air column, but that would just run, backwards to the arrows on the diagram, until all relevant potential energy was minimized. I think that point would be called the DALR. http://en.wikipedia.org/wiki/Energy_minimization We sure could use a proper experiment. I have already designed one that should work fine if anyone should ever want to consider doing one. Basically Graeff’s only designed correct this time with many sensors, multiple layers of insulation, large, and with air. Why he chose a liquid I’ll never understand. “In the modern world the stupid are cocksure while the intelligent are full of doubt.” ~ Bertrand Russell 158. EthicallyCivil says: Clearly a non-isothermal dry adiabatic column isn’t a minimum energy state (as energy can be extracted, imagining an efficient thermal conduction system between top and bottom layers. Convection requires that some parcel of gas is already at an elevated energy state (or it wouldn’t be rising *due* to convection), and thus convection doesn’t violate conservation or 2nd law. The adiabatic column is (ignoring radiation) the minimum energy state with differentially heated (cool top, hot bottom) boundary conditions. I don’t have a clear picture how a heat engine connecting the top and bottom would look in T-S space, or what the minimum energy solution would look like were one to take an established dry adiabatic column, insulate top and bottom and run a heat engine within the column. It seems like it would have to go to an isothermal state as minimum energy 159. A physicist says: A physicist says: It seems to me Robert Brown’s analysis implicitly makes the following claim: if all the greenhouse gases (mainly H20 and C02) were cleansed tonight from earth’s atmosphere, then the atmosphere would evolve toward a more nearly isothermal equilibrium But how would that work, exactly? Willis Eschenbach says: Wait, wait, you claim to be a physicist, answer the question. Does heat flow forever in the silver wire or not? Willis, the short answer is “Yes”, the medium answer is “IMHO Robert Brown basically has got it right”, and the long answer is “The logical next step is discuss whether day-versus-night temperature swings alone — in the absence of GHG effects — suffice to mix the Earth’s atmosphere.” Because that claim —foreseeably (and strictly IMHO) — is going to emerge as the primary fallback position of GHE skeptics. 160. I see two assumptions above: 1. It does not matter what the density of the gas is. It will equally conduct heat at the bottom into silver wire, as the wire will be able to conduct its heat into the gas at the top, even though the density at the bottom and top is different, due to the gravitational effect on the gas. 2. The cross-section of the wire will stay the same, which means the ability of the wire to conduct the heat, which depends on its cross-section, is the same at the bottom and top. The gravitational field will actually pull down a considerable part of the mass to the bottom, making it far wider at the bottom then the top (depending on the length of the wire and its tensile strength), deforming it more into a tear drop shape. With your setup you may be able to change the lapse rate, but I doubt that you achieve an isothermal state in this way. It does not matter what the density of the gas is, or how good the contact of the silver with the gas is (as long as there is thermal contact, or how thick the wire is. The point is that if any heat enters at the top ever and the system spontaneously restores the lapse rate (which is constant, recall, for a container of fixed size independent of gas density so we can make the gas nice and thick with great thermal contact with the silver) then you’ve violated the second law, because any thermal pathway between the bottom and the top will deliver heat from the bottom to the top. All I’ve done with the wire is show you a pathway that is clearly completely independent of the supposed lapse rate in the gas, one that will conduct heat in any direction without prejudice, so that you can see why a lapse rate is impossible. If heat to the top goes back to the bottom because of “gravity”, and there is a pathway to the top that must conduct heat in the direction of a thermal gradient (the wire) you’re done. The system will circulate heat indefinitely. But no system can circulate heat indefinitely, it’s absurd. So the message is, stop trying to do statistical mechanics in your head without understanding it. Stick to thermodynamics. It is simpler, safer, and you can’t make mistakes with it as long as you remember TANSTAAFL. There ain’t no such thing as a free lunch. A nonzero thermal lapse is a Maxwell’s Demon working the free lunch counter for the suckers. Here’s the deal, really. Every book I’ve ever read on statistical mechanics or thermodynamics is wrong — and you can safely assume I’ve read a few, since I did numerical simulations of both static and dynamic critical phenomena that actually were published in places like Physical Review, with referees and everything — or figure 2 above makes it clear that there is no possibility that figure 1 is correct. That is, assuming that you can’t believe the actual words of the second law that tell you that you can’t take a system and create a permanent thermal gradient in it without doing work to maintain it, because heat will flow from the cold side to the hot side to neutralize temperature differences otherwise. That’s why you have to pay to refrigerate or air condition your house. It is why you can’t build a perfectly efficient heat engine. Tanstaafl, man. rgb 161. I find the analysis quite reasonable – but it is so idealized as to be useless. A more interesting thought experiment has a spherical planet heated by a remote star, rotating on an axis roughly normal to the line to the star, with an atmosphere of non-greenhouse gases. The equator would be warmer than the poles, so there would be Hadley-type circulation that would cool the equator and warm the poles. Would there then be a vertical thermal gradient? I think there would be, but I’m sure someone would like to argue to the contrary. Not at all. It is merely specific. I am specifically proving that EEJ, a specific paper written by Jelbring and published in a journal (God help the referees, absent that day on vacation or something), violates the zeroth but especially the second law of thermodynamics when it asserts that there will be a thermal lapse rate in an adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field. No, there won’t. Is it stupid to have to prove this? Sure, given that nearly any introductory physics textbook — I’m not talking about thermodynamics text, just things like Tipler and Mosca, or Halliday, Resnick and Walker — teach enough thermodynamics for one to be able to see that the spontaneous appearance of a stable thermal gradient in any system is impossible, because it is a direct violation of the second law, and indirectly the first, which more or less says that equilibrium is isothermal (in order to permit the definition of thermometry in the first place). If thermometers “work” to measure temperature, equilibrium is isothermal. Period. rgb 162. So your wonderful assertion, is that the radiative forcing of Co2, occur after its entry into the thermostats of the tropopause, and that extra radiative forcing, causes that missing hot spot, increasing the temperature back through the stratosphere and down again through the thermostat of the tropopause. Been there, done that. No, my “wonderful assertion” is that EEJ, Jelbring’s paper, is obviously incorrect because a stable, isolated atmosphere cannot support a thermal gradient. There is no such thing, in other words, as “gravitational heating” for a system in static equilibrium, nor is there any such thing as “gravitational heating” for a system in dynamic equilibrium. There is such a thing as gravitational heating in a collapsing system, which is what raises the temperature of protostars to the ignition point and provides the heat outflow from brown dwarfs. As the greenhouse effect is concerned, look at the IR spectrum from over the top of the atmosphere. I don’t care how you think heat gets to the top of the troposphere; the point is that one chunk of the outgoing spectrum observed from satellites comes from a gas that radiates in the CO_2 band that happens to be at top of troposphere temperatures. The net radiation in the water window therefore has to be higher (than it would otherwise be) in order to keep the Earth in detailed balance (on average). End of story. I don’t give a rat’s ass where the extra radiation comes from, or how it gets there, it is there. You can see it. It is emitted/transmitted at the blackbody temperature of the ground give or take a bit. Here, let’s use our fingers and toes. Total outflow in all frequencies has to be the same. Outflow in one band of frequencies is smaller because it comes from colder molecules. In order to keep total outflow the same, the energy radiated in the other frequencies has to: a) Go up. b) Go down c) Remain the same. That’s it. Come up with any mechanism you like for heat absorption and transportation, they’re all the same to me. Just don’t forget the incontrovertible experimental IR spectroscopy data and the finger and toe arithmetic involved. rgb 163. ikh says: Lets try a slightly different explanation of this closed static system. Of course, a closed static thermodynamic system is, per see a thought experiment that can not exist in reality. We have a quantity of gas in a sealed cylinder and the cylinder is a closed system thermodynamically. That means energy can not enter or leave the cylinder. The cylinder is *not* in a gravitational field. Therefore, the mean pressure of the gas is the same through out the tube and the temperature of the gas is isothermal. This is thermodynamic equilibrium and entropy can not change. Now, we switch on our gravitational field. The gas settles into a pressure gradient with higher pressure at the bottom and lower pressure at the top of the cylinder. Because of the gas laws, the gas at the bottom heats up and the gas at the top is cooler. We will also assume that the gas does not absorb or emit at the frequencies associated with these temps ( i.e. we can ignore radiative transfer). So convection and conduction set in and start to mix the gas. The total energy in the gas is still constant. As the gas mixes energy is transferred from the warmer gas to the cooler gas and the temperature differential reduces. convection slows. This continues until T.E ( Thermal Equilibrium ) is reached. At the new T.E. there is no more convection, the gas is isothermal and the pressure gradient remains. The gravitational field is no longer performing work on the gas so it can not add energy to the system no matter what potential it exerts on any particular molecule. Just imagine if this were not the case and convection carried on at T.E. We could have a wind turbine driven by the convection current and connected to outside the system. We would now be removing a continuous source of energy from at system at T.E. Good luck with your patent applications ;-). /ikh 164. Also, a constant temperature with altitude means that particles at the top of the atmosphere have more momentum than particles at the bottom. It means nothing of the kind. Momentum (magnitude) is p = mv. The distribution of v at the top and the bottom is identical — the Maxwell-Boltzmann distribution. Oh, do you mean more total momentum (in any given general direction) at the bottom than at the top because there are more particles? Sure — that’s why the pressure at the bottom is greater than the pressure at the top in a compressible fluid (where there are more molecules at the bottom than at the top). See “Kinetic Theory of Gases” at your friendly wikipedia outlet: http://en.wikipedia.org/wiki/Kinetic_theory rgb 165. Alan Millar says: So again you post modern hotrod physicists please answer the question. This is the real world it IS going to happen. The stupid people here, who believe in the Laws of Thermodynamiics, know what will happen in the universe ruled by the Laws. But do the clever people, who know that the Laws are wrong, know how it happens in the Jelbring universe. Now don’t be shy, it doesn’t really matter if you show that you are a complete idiot more than once, does it? A gas giant planet, like Saturn, radiates more than twice the amount of radiation than it receives from the Sun. Presumably this little gravity induced energy engine is at work here according to you. How do these planets ever die, if gravity is constantly maintaining a heat gradient in the atmosphere? The Sun will die and become a cold white dwarf with no solar wind to blow any atmosphere away. What is going to kill these gas giants? If gravity is constantly maintaining hotter gases at the bottom then convection will move gases around and therefore we seem to have an everlasting living planet. What kills it and when, if Jelbring is correct? 166. Trick says: Folks – Fellow interested posters, I am going to attempt to have a conversation with many of /y’all & all at once, skim for your handle if interested in engaging. All in time sort. Joules Verne says at 1/24 7:52am: “The device in figure 2 doesn’t work…the gas will collapse to the surface as a liquid before it gets to absolute zero and this will shut off further extraction of energy because the cold side of the thermocouple no longer has any cold gas to cool it.” Good one. Joules groks this stuff. Now by Robert Brown definition, the gas is isothermal, meaning the gas can’t cool – the Perpetuum Mobile w/isothermal gas & perfect insulator is born in Fig. 2. A neat design for Willis’ dream machine. Patent pending. Eilert sats at 1/24 7:54am: “…I doubt that you achieve an isothermal state in this way.” This actually adds to the discussion in a good way. A good thought experiment is to turn up the gravity field and see what would happen. The silver rod could react in the manner you describe. Interesting. Genghis says at 8:06am: “Take a single gas molecule and put it at the top of the tube. It has zero kinetic energy and zero temperature. Let it fall and just before it hits the bottom it will have a lot of kinetic energy and heat.” Very good one. At the top, the molecule also has lotsa’ PE. At the bottom, it also has 0 PE. No isothermal molecule down the tube, it is isoenergetic (I learned a new term) – where there is no wire! Robert Brown says at 8:14am: “Well then, by all means go patent your perpetual motion machine of the second kind or explain heat flow in the second diagram, Joules.” Robert – YOUR machine beat Joules. That is your machine design, it is still running. It will run tomorrow. It will run forever w/isothermal gas & you just have developed the perfect insulator patent. Go for it. The Perpetuum Mobile design, fig. 2 in the top post is worth A LOT!! And I’m ever so sorry, but in an ideal gas the temperature IS determined by the total energy. I cite the 1st Law consistent with oth law in one reservoir and the 2nd law constant entropy. Robert continues: “That’s an absurd idea, given that one can perform a gauge transformation — change the zero of the total energy — without changing any of the physics.” The datum concept enables many good & proper science in many texts. Insert the thermometer at any datum to compute the invariant total energy value, say TE = C, & thereafter allow temperature and PE to vary with each other from that datum thermometer reading and you will be ok. Just place the thermometer at any different h. The temperature or mean kinetic energy of the molecules it will measure will be different: KE(h) = C – mgh. Robert Brown says at 8:23am: “Heat will definitely flow in the silver, right? It’s just a chunk of metal that’s an excellent conductor of heat.” Right. This is why Robert Brown had to invent the perfect insulator design in fig. 2. How’s the patent pending process coming along Robert? Robert Brown continues: “You want to assert otherwise, you tell me what the equilibrium state is of figure 2.” I have tried elsewhere. In fig. 2, let’s say white body starts with Twhite and gray body Tgray>Twhite. Cite 0th law that says heat will flow to a paler shade of gray, both bodies at single reservoir Tavg with silver tube! Or with moving jars, dipping bird, etc. At least while Robert’s perfect insulator patent is pending. Robert Brown says at 8:28: “No, I think you are generally quite right, and this agrees rather well with Caballero’s argument.” Remember the Caballero text in the ref. given in Perpetuum Mobile thread makes an argument temperature is non-isothermal in a gravitation field section 2.3. Caballero does write: 2.1 No gravity: “Note that pressure is due to only to the local properties of the gas and not to anything going on far away.” 2.3 w/gravity “Mean velocities (insert his defn. Temperature for mean velocities here) will be greater near the bottom of the box than near, the top: in other words, pressure decreases with height. We will now work out an equation giving the precise rate of decrease.” Note Caballero defined “mean velocities” as temperature – I am just inserting for clarity, no meaning change. Thus temperature will be “greater near the bottom of the box”. This is not consistent with Robert Brown’s as yet unproven pronouncement that it is isothermal. Other than the fig. 2 w/perfect insulator inconsistent with 0th law driving an inconsistency with 1st Law. Schodinger’s Cat says at 8:57am: “Over time, I would expect the system to reach thermal equilibrium.” Welcome back from the quantum world I see you survived after all. Yes, by gosh, the system in fig. 2 with real non-perfect insulator will reach thermal equilibrium over time by 0th law. The gas temperature will be non-isothermal. Robert Brown says at 9:01am: “No, it won’t have any “heat”” Right, but Genghis molecule will have the increased kinetic energy and per Caballero’s 2.3 ref. increased temperature. Rap Genghis on the knuckles for saying “heat”. Robert Brown continues: “But the basic point of my paper is that Jelbring is wrong not because of any possible microscopic description of a lapse rate. A lapse rate itself is wrong in thermal equilibrium, because figure 2 is very, very easy to understand.” Robert Brown fig. 2 is wrong to have a perfect insulator which cannot exist by 0th Law. Jelbring cannot be proven wrong by fig. 2 which is not physical. At least until Robert Brown’s patent for the perfect insulator is granted. Robert Brown says at 9:07am: “…in figure 2 above. Which is violated — the heat equation in silver or your absurd assertion that gravity can stably sort out a gas into a hotter temperature and a colder one? One or the other.” The heat equation in silver is not violated in fig. 2. MDR says at 9:32am: “This is an example of a system that is both in thermodynamic equilibrium and possesses a gradient in temperature.” Good. This is consistent with 0th, 1st and 2nd thermo laws. Fig 2. is not & runs forever. Once fig. 2 has a non-perfect insulator admitted per 0th law, it will eventually be in equilibrium, non-isothermal gas, and not run forever. Rober Brown says at 9:51am: “Excuse me? I have no idea what you (Trick) could possibly be talking about.” Believe me I grok this. You are smart though and the thermo master’s were right in the 0th, 1st, and 2nd law development. They have stood the test of time right up to fig. 2. Robert Brown continues: “heat will flow in the wire from the bottom to the top.” Yes. Cite 0th Law. “The point is that heat will flow in this system forever…” Yes, fig. 2 is a Perpetuum Mobile. To win the patent for it though Robert Brown is going to first have to win the patent for the perfect insulator. If Robert cannot patent a perfect insulator, cite the 0th and 1st law tell us the system will stop flowing heat when it reaches thermal equilibrium and with 1st law non-isothermal gas (see Caballero 2.3 ref. telling us gravity results in non-isothermal gas column) thru the non-perfect conductor, this is less than forever but can be quite long because there are some quite close to perfect insulators. “The real point is that you don’t need the silver wire to make this argument…..Gravity does no work in this problem, not in steady state.” I whole heartedly agree. Wire is sort of useful to understand the concepts of the thermo laws. The ideal gas molecules in fig 2 lose just as much energy going up against gravity as energy they gain coming back down. Fig. 2 modified with real non-perfect rl insulator is ideal isentropic reversible process with non-isothermal gas (Per Caballero 2.3 – check it out). “So what makes the heat go round and round?” The perfect insulator. The perfect insulator is non 0th thermo law compliant. Your patent still pending? “Of course. It doesn’t.” Heat does stop flowing round and round with a patentable real non-perfect insulator. The gas will be non-isothermal per Caballero ref. 2.3. Robert Brown says at 9:58am: “Are you crazy?” No Joules Verne is eminently sane, Robert Brown misses the other poster (Joules Verne) said the work extracted was not from the system but from the ideal gas column with the perfect insulator (patent pending). Robert continues: “In the real world, the system will evolve to an isothermal state precisely as I described it because it is in equilibrium.” Not isothermal unless you think Caballero is crazy too (my view Caballero is not crazy), since his reference 2.3, disagrees with you. Caballero shows ideal gas column is non-isothermal in the presence of gravity. Caballero also shows ideal gas column is isothermal w/o gravity. JKrob says at 10:24: ?In moving the heat from the bottom of the tube to the top is causing the lapse rate to become **more stable** – cool at the bottom with warm air above is an inversion which inhibits vertical mixing!! THAT is why the engine will not work as it is set up.” A good .02 added viewpoint. Thanks for de-lurk. D.J. Hawkins: “Now I can construct a heat engine which extracts useful work based on the temperature gradient and gravity will continue to organize the air column forever and my heat engine will never run out of “fuel”? Really??” Robert Brown will demand a royalty for using his patent pending perfect insulator. Other than that cost, yeah fig. 2 works for free. Graeme W says at 11:50am: “I don’t understand the theoretical derivation well enough…” In the WUWT Perpetuum Mobile thread at the top post, there is a Rodrigo Caballero link cited by Robert Brown to the theory of ideal gas without and with gravity field. In 2.3 gravity is added to a non-isothermal gas column and this condition is theoretically justified – it is pretty simple derivation, I recommend it. Fig 2 perfect insulators needed only for a Perpetuum Mobile. Robert Brown for some reason does not grok Caballero 2.3 even though he cites it as good ref. Willis Eschenbach says at 11:54am: “In an isothermal column of air, individual molecules at high altitude have more energy because of gravity.” Bzzzt! Isothermal column of air is for no gravity case ref. Chapter 2.1 Caballero link in your Perpetuum Mobile post. Bzzzzt! “…because of gravity”. Ok, with gravity Rodrigo Caballero (bless him) tells us in 2.3 same link the air column becomes non-isothermal. Bzzzzt! Fail 1st law: individual molecules must have constant energy. Note the period. Willis “more energy” fails. More energy is not constant energy. Willis tries to knock down Jelbring paper with these fails. Not possible to knock down Jelbring with these 3 arguments. Willis Eschenbach says at 11:57am: “It is the formal disproof of Jelbring’s theory. It is idealized by its very nature.” By Willis use of “it”, my view Willis means top post where Willis summarizes his understanding of “it” at 11:54am. Willis at 11:54am fails any disproof on all 3 points of his points, see right above. Gosh, I hope Robert Brown groks Caballero & 1st law energy conservation quickly. Willis Eschenbach at 12:09pm (? to another poster): “Does heat flow forever or not?” Heat flows forever in fig. 2. The reason is a grand master thermal law is broken, the easiest one, the zeroth law. There can be no perfect insulator. Body A placed in contact with body B will always eventually equilibrate temperature. This is so easy. Geez. If Robert Brown can patent a perfect insulator, I will change my view. Patent granted: Perpetuum Mobiles will be possible. Until the patent is granted, heat will NOT flow forever in fig. 2 b/c there is no perfect insulator. Willis should grok this on his own (read Caballero slowly). Robert Brown is going to take longer I think, to reach a state of equilibrium grokness. LOL, I feel better my head cold is receding faster. Willis Eschenbach at 12:09pm: “Folks, a lot of you here don’t seem to get it.” No kidding. Including Willis viz: Will heat flow in the silver wire forever? “Me, I say no, and I say Roberts thought experiment elegantly proves that the answer is no.” For fig. 2 silver wire heat will flow forever like Robert Brown says it will in top post, his words:´ One is then left with an uncomfortable picture of the gas moving constantly.. At least until poster Joules Verne situation is reached and the gas cools & liquefies under a vacuum. That’s good thinking but beyond the intention of top post. My view is the insulator in non-perfect to be 0th law compliant and in that cas heat will not flow forever and gas per Caballero 2.3 will be non-isothermal. Willis Eschenbach at 1:04pm: “I hate it when my perpetual motion machines are poorly designed …” That fig. 2 is a WELL designed Perpetuum Mobile w/isothermal air & perfect insulator. Just gotta’ pay royalties for those: (patents pending). – – – – – – – Out of breath and w/blisters on my fingers I stopped at 1:04pm. I will happily rengage if more interested parties appear thereafter. Typo’s are possible in this post. Probable really. 167. Walter says: Robert Brown and Willis: You will never convince some people. These same people are quite sure that the reason we don’t have machines capable of giving free energy forever is due to “poor engineering”, or its a conspiracy by Big Oil or Big Gubmint to fleece us all. If only the shackles of these evil doers were thrown off we could live a life of luxury forever, with energy too cheap to meter, made in our own basements be a nice perpetual motion machine – yours for$499 from your local hardware store. But of course, us incompetent engineers and physicists wouldn’t want that… line us up against wall now because clearly thats what we deserve.

/sarc

168. Mike McMillan says:

Great theory. Baloney, but very entertaining.

The reason the silver thingy won’t generate perpetual motion is that the exposed ends will assume whatever the air temp is at that altitude. A temperature difference of 1 degree will not move any heat in a silver rod 100 meters long.

169. adiabatically isolated column of gas in a gravitational field cannot have a thermal gradient maintained by gravity.

And yet we see this stratification in the atmospheres of Venus, Earth and Jupiter. In the real world, it’s hotter at the ground because the air is heated from the ground up and rising air columns draw this warmer air up… you know, the thermopiles birds ride up instead of having to beat their wings furiously. Imagine that, it’s colder on top of a mountain than at it’s base. It’s called the triumph of empirical science over clever explanations that claim otherwise.

The details of the arguments for an adiabatic lapse rate in open systems is unimportant, nor does it matter what cp is as long as it is not zero or infinity.

What matters is that EEJ asserts that in stable thermodynamic equilibrium.

Which does not occur in the real world. That’s why we call it weather. Sorry, no sale. This is just as unacceptable as the nonsense about CO2, a trace gas having more effect than water vapor on the planet’s temperature.

170. I hasten to add that the lapse rate that does prevail at equilibrium is much smaller than that for which Jelbring contends, so Jelbring is still wrong.

If you want to bet against the laws of thermodynamics, I wouldn’t advise it.

I do not care about what generates the lapse rate. If the lapse rate is stable, so that heat delivered to the top redistributes to maintain a constant equilibrium temperature lapse between the top and the bottom — the sole case examined in the article above — then it violates the second law of thermodynamics.

Let me put it bluntly. If somebody presents a statistical mechanical computation that suggests that the second law is violated, I would knee jerk assume that the authors had made a terrible mistake unless and until proven otherwise, especially if I “could not understand” everything that they did.

Even then I would be doubtful.. To be honest, I would be doubtful if I did the work myself. I think that the paper you link has the right idea, and you will note that on other threads I propose precisely the same experiment. Show me, in other words. I’m a theorist, but I’m no fool. Experiments trump theory every time, but the Earth’s atmosphere does not exhibit a DALR:

* Uniformly. See “troposphere”, “stratosphere”, “thermosphere” etc. Why exactly doesn’t the DALR extend to the top of the exosphere again?

* Ubiquitously. See “thermal inversion”, or for extreme cases “thermal profile of the atmosphere above Antarctica in July” (there’s an IR spectrum in Caballero with the data you need). Hmmm, thermal inversion, with the upper troposphere hotter than the ground? Could that be, maybe, because the ground is cooler than the air instead of warmer? Regardless, it is nearly impossible to explain if there was an intrinsic DALR that didn’t depend on differential heating.

Nor is the atmosphere ever even crudely static. Air is always moving up, down, sideways. Even when it is “windless” down near the ground, there are damn few places on Earth where the air isn’t moving up and down and sideways from a kilometer on up, on any given day. So it isn’t really all that surprising that the air (a decent insulator and hence quasi-adiabatic a parcel at a time) has a DALR when it is differentially heated and moving all of the time, keeping it crudely “well-mixed”.

Thermal static equilibrium is something else. No mixing. Conduction matters — it can be slower, but there is plenty of time to reach equilibrium. That’s why the thermodynamic argument is so powerful — it is very difficult to explain how heat delivered to the top of any truly equilibrated air column would spontaneously redistribute to maintain a vertical lapse rate and not enable a heat loop and/or any number of PMM2Ks.

But show me the “high precision” experimental result, done with a dewar in a centrifuge filled with maybe Xenon gas at a G value such that there is sufficient pressure at the top of the vessel to justify the thermodynamic assumptions, with recording high-precision, carefully calibrated thermometers.

Just bear in mind that if it works, and there is a lapse rate, the second law itself is done. I’ll stick a thermocouple between the top and the bottom of said gas, and it will sit in there spinning forever.

rgb

171. Neil says:

Dr Brown is not correct with his explanation of Fig2
In a cylinder with gas at the usual DALR, all that his conducting wire will achieve is a infintesimally thin layer or hotter gas at the top plus an infintesimally thin layer of cooler gas at the bottom.
Both of these would reverse the lapse rate ( inversion) and thus no further heat can be exchanged without adding work to the cylinder (His statement that the system would reorganise itslf into an adiabatic column is wrong)
This situation would also apply to an attempt to use a themocouple to derive any work from the system. (Or any other heat engine)
It is thus clear that the adiabatic column cant be used as a perp -motion device so the proof that it breaks thermo laws has gone away.. The reverse holds true for an isothermal column where the bottom must be cooler than a surrounding DALR atmosphere with the opposite at the top– In this case heat can be removed at the top and added at the bottom. This would comprise a real-perp motion machine as the column would then reoganise itself into the isothermal state
Clearly it is the isothemal condition that breakes the 2nd Law

PS Much has been said about the need in the real atmosphere to maintain a DALR by pumping from below with energy from the Sun. In the real world the column is subject to all sorts of energy lossed and gains. The list is very large as Anthony has enumerated is is recent post– The water cycle is one of the most important

Most contributors seem to have ignored the fact that in the DALR cylinder all the heat losses and gains have been elininated and thus it takes an infintesimally small amount of energy to lift a parcel of air fron the bottom to the top hence an infintesimally small amount of energy will maintain the DALR.
We just need to overcome conductive and radiative transfers which have already been assumed to be zero

172. Oops, I mixed replies to the previous two comments. The paper was a separate suggestion. The answers are the same, however. Experiments talk, bullshit walks. And please, address the actual content of my argument above instead of invoking obscure stat mech or nonstandard axioms. Explain how a nonzero lapse rate does not enable second law violating, perpetual heat flow, if you would, right up to the point where real thermal equilibrium is achieved. Also remember, gravity is doing no net work while all of this is going on. If it were, things would actually be worse — you’d start violating the first law of thermodynamics as well.

rgb

173. DeWitt Payne says:

Joe Born,
Please post a calculation of the Velasco lapse rate for a gas column with the surface at STP (101325Pa and 273.15K) and g = 9.81 m/s^2. The number density/cubic meter is ~6E23 molecules/mole/0.0224m^3/mole = 2.7E25.

One minor point. Since statistical mechanics is all about probabilities, it is possible to violate the Second Law. It’s just extremely unlikely. All the molecules of air in a room could migrate into one half of the room but the time for the probability of this event reaching 50% is really, really long. It’s many orders of magnitude longer than the age of the universe, depending on the size of the room and the air pressure in the room. I suspect Velasco’s calculation is something like that. For one molecule there’s a 50% chance it will be in one half of the room at any given time.

174. Q. Daniels says:

Robert Brown,

I’ve read a number of thermodynamics texts myself.

Not once did I see a proof of the Second Law that did not rely upon circular logic. I’ve seen plenty of empirical proof, that people have been unable to violate it, but no direct proof.

Relying upon the Carnot Cycle is pretty clearly circular logic. It’s more difficult to show, but assuming that the MB distribution remains uniform under gravity may also be circular.

If you have a proof of the Second Law that is not based on circular logic, I’d be happy to read it.

Failing that, all we have is that there are no publicly recognized or understood violations of the Second Law. It is empirical, and nothing more.

Poor engineering is not proof of impossibility.

175. gbaikie says:

” “In nature, the dry adiabatic lapse rate of air in the atmosphere is maintained because the system is differentially heated from below causing parcels of air to constantly move up and down.”

I live half-way up a mountain at 6100 feet. The valley below is at 4500 feet. The temperature difference is nearly always the dry lapse rate 8 degrees F, whether it is calm or windy. Only if it is raining or snowing will it be different. It then goes to the moist lapse rate. Most of the time it is sunny, heating the ground equally, both in my back yard and in the valley below. What maintains the lapse rate temperature difference?”

Mostly gravity.
If you lived planet with 1/2 the gravity, the the temperature difference would about 1/2.
You could say you would be warmer. You could also say lower elevation would be cooler there would less difference temperature.
Less difference in temperature is undeniable.

With a silver rod, one could transfer heat from lower elevation to your elevation. Or one could use other material which cheaper and conducts heat better than air. But silver is one of best conductor of heat and air is one the poorest conductors of heat.

One can generate energy from differences in heat. Venus isn’t particularly good place to generate energy- despite being very hot.
Venus doesn’t even “have a lot of energy”- in terms of total joules of heat in it atmosphere, assuming one find a lot something which is colder one couldn’t create an extraordinary amount of energy.

Over a period of time, say 24 hours, earth absorbs more of the sun’s energy than Venus does- despite being closer to sun and getting around 2700 watts per square meter compared to Earth’s 1300 watts per square meter.
This can quickly seen: Venus is hot, it’s temperature near surface does not vary over time, and since Venus is hot, it can not be made hotter by the sun. The earth more distance and receiving less sunlight, is much cooler. And because it is cooler it can heated by the sun and there is daily variation in temperature. And on planetary scale, earth has large variation in equator and polar temperature. So earth is churning heat engine, whereas Venus is more stagnant.

So in terms of power, in terms of horsepower, earth is a more powerful engine.

It seems to me that in subject of climatology, there is measurement of the engine temperature, and there should more attention to how much power the engine produces- and what’s earth miles per gallon.

176. Robert G. Brown says

In nature, the dry adiabatic lapse rate of air in the atmosphere is maintained because the system is differentially heated from below causing parcels of air to constantly move up and down.

The dry adiabatic lapse rate determines how high thermals will go – usually, only a few kilometers. The actual lapse rate is normally significantly different from the DALR.

As this article argues, the lapse rate without IR emitters would be zero. It is the greenhouse gases that move the actual lapse rate (ELR) from zero to -6.5 K/km. The DALR is -9.8 K/km. To claim that anything “maintains” the DALR simply means that you have not looked at the data.

Related to the DALR is the concept of “potential temperature” – the temperature that a parcel of atmosphere would have if it moved adiabatically from some altitude to sea level. For instance, if the atmosphere at 10 km was -55C, its potential temperature is

10km * 9.8 C/km – 55C = 43C (109 F)

The other meaning of this is that for air to convect from sea level to an altitude of 10 km, it must be at least 43C. A more typical value in the sub-tropics would be -70C at 17km

17km * 9.8 C/km – 70C = 96.6C (206 F)

Since the surface temperature is typically a bit cooler than this, the bulk of the atmosphere does not follow the DALR. (Near the surface, the DALR is seen almost every day. But only near the surface.)

I suggest that everyone look at some real data.

177. Alan Millar says:

“kuhnkat says:
January 24, 2012 at 2:33 pm
Alan Millar,

“The Sun will die and become a cold white dwarf with no solar wind to blow any atmosphere away.”

This is an assumption without much empiraical proof”

I hope your Mum isn’t reading that because even she would be embarrassed!!

Is this the level people will sink to just because they would like to have a new theory of Thermodynamics which will disprove the theory of CAGW?

Get a grip folks. These sort of statements are going to hold this well respected site up to ridicule.

Stick to facts and real physics and CAGW will be shown to be nonsense in any event.

It will take a bit longer but I will live to see it and I ain’t young! Have patience, trust in Gaia!

Alan

178. @ Dr. Brown –

I’m curious, what if the gravity isn’t constant, but is fluctuating?

179. robr says:

“Willis Eschenbach says:
Robert Brown says:
I have been seriously trying to follow this conversation. I have my Thermo text, my Heat Transfer text, my CRC handbook, the internet, and my calculator. For a dumb ass like me (tau beta phi), I wonder if one of you would answer give me your opinion to the following questions (2):

Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?

Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?
Thank You,
Robert S Rider

180. robr says:

I’m so dumb I can’t even spell Pi.

181. says: These two idealised adiabatic processes (like the adiabatic stages in the Carnot Cycle) will result in the parcel returning to Earth with nearly the same temperature as leaving (the slight drop being accounted for by radiation at TOA).

Carnot cycles are ISENTROPIC. By definition. Isentropic means adiabatic AND reversible.

Hmm, maybe we read different textbooks. Any cyclic heat engine — being cyclic — returns to its original state at the end of a cycle. All cyclic heat engines — being heat engines — increase the entropy of the Universe while operating. In particular the Carnot cycle absorbs heat \Delta Q at temperature T_H for a change of entropy of the hot-side reservoir of -\Delta Q/T_H, and then rejects it into the cold-side reservoir for a change of entropy of the cold reservoir of +\Delta Q/T_C.

The total entropy change — per cycle — is thus:

\Delta S = \Delta Q (1/T_C – 1/T_H) > 0

To correct you — and please, bear in mind that I’ve taught this for 30 years — Carnot cycles are NOT isoentropic. Isoentropic DOES mean adiabatic (\Delta Q = 0) and reversible, but Carnot cycles contain two isothermal expansion/compressions (also reversible). The isothermal parts are not isoentropic, as explicitly shown above.

Now, what drives the circulation cycle you describe? How about absorbing heat at constant temperature from the hot ground (reservoir) and delivering it to the upper troposphere where the heat is lost to radiation at much colder temperatures. Hmm, sounds like something that increases the entropy of the Universe to me. The air that is rising and the air that is falling are not at the same temperature. They may both be isoentropic processes, but they don’t occur at the same place and the same time, and it is the thermal variations of density with temperature that ultimately provides the lift (or lack thereof) that drives the cycle, positive or negative net buoyancy.

With all that said (filling in details), I think we agree. So what is the point?

rgb

182. Joe Born says:

Paul Birch:

“I have now read the Velasco et al article, and it agrees with what I said: in either the microcanonic (totally isolated) ensemble (with a reasonable number of particles in the gas) or the canonic ensemble (in thermal equilibrium with the surface or walls, irrespective of the number of particles), the gas is isothermal.”

Of course, what we’re talking about is the microcanonic ensemble, to which Equations 5-8 apply. If you read Velasco et al.’s Equation 8 for mean single-molecule kinetic energy K as a function of altitude z, you’ll see that the expression for K is the product of a constant and (1-mgz/E), where m is molecular mass, g is the acceleration of gravity, and E is total system energy. To me that looks as though K decreases with altitude z: the temperature decreases with altitude. Is there some different way you interpret that factor? As I read it, it says there will be a lapse rate that’s small for large numbers of molecules but stll finite and non-zero so long as the number of molecules is not infinite.

Presumably, you are basing your interpretation of Levasco et al. on its penultimate paragraph, in which they made an execrable attempt to state verbally what the equations express mathematically. Unfortunately, that passage is so abysmally opaque that any exegesis thereof matching the mathematical result is doomed to appear hopelessly strained. So I will forgo the attempt. The real question is, Does Equation 8 define an altitude-dependent temperature or not? If so, there’s a non-zero lapse rate at equilibrium.

If you can’t reach the answer by considering Equation 8 itself, consider the lead-up to it, where Velasco et al point out that the state density as a function of both velocity and altitude (Equation 5) is not the product of state density as a function of altitude alone (Equation 6) and state density of a function of velocity alone (Equation 7)–as it would be if temperature were independent of altitude. They also observed that the density distribution as a function of velocity is not, as one would expect of an isothermal configuration, the Maxwell-Boltzmann distribution.

That was the wind-up, and the pitch was Equation 8, which says that, indeed, the temperature is not isothermal.

Do you interpret those equations differently?

183. A physicist says:

Mike McMillan says: Great theory. Baloney, but very entertaining.

The reason the silver thingy won’t generate perpetual motion is that the exposed ends will assume whatever the air temp is at that altitude. A temperature difference of 1 degree will not move any heat in a silver rod 100 meters long.

Mike, it was to address this specific objection that the Beach-House Block Story was conceived … this story shows that the length of the column is irrelevant.

Q. Daniels says: Robert Brown, I’ve read a number of thermodynamics texts myself. Not once did I see a proof of the Second Law that did not rely upon circular logic. I’ve seen plenty of empirical proof, that people have been unable to violate it, but no direct proof.

In particular, that page’s geometric theorem “the symplectic form ω is preserved by Hamiltonian flow” is equivalent to the dynamical principle “the state-space volume of a dynamical ensemble never decreases”, which in turn is equivalent to the thermodynamic principle “the entropy of a dynamical system never decreases”.

Whether or not this geometric reasoning conveys belief … at least it is not circular reasoning.

184. Billy says:

What a fun thread! I should be working but I’m reading it instead. (That is okay, it is 8:22 PM and I’m self-employed, so it’s not like the boss doesn’t know what I am doing.)

My thanks to Dr. Brown and Willis for their patience. I would have given up long ago. I liked Dr. Brown’s simple example.

My next comment is going to offend many people so, if you are sensitive, quit reading. The discussion in this thread reminded me of many of the discussions on RealClimate. Only the role of the climate scientists was taken by those who opposed Dr. Brown’s explanation—they knew what the truth was and they could figure out some theory to disprove it.

This thread is probably a healthy process—although somewhat painful to watch. But, it does show that one need to think hard about these issues.

I feel that this discussion is a reasonable model of how science often advances. Someone throws out a good idea. Many dump on it with facile but incorrect criticisms. A few offer support. Finally, after a long time and much confusion there is reasonable agreement that the idea is right (or wrong, depending). We now believe that bacteria cause many ulcers but that N-rays don’t exist. But, when the two theories were offered, the bacteria/ulcer theory was dumped on but the N-ray theory was not.

My guess it that a few who participate in this thread will actually learn something, which is probably more than you can say for most students in freshman physics in college.

Billy

185. Trick says:

Robert Brown says at 3:45pm:

“Tell me whether or not the system in figure 2 permits energy to flow in a circle forever.”

Robert Brown says in a top post verbatim quote, search on the text for context of his answer:

Yes. “Heat will flow in this system forever; it will never reach thermal equilibrium.”

Robert Brown at 3:45pm:

“If you answer “no, of course not” you are quite right.”

Now Robert Brown is going so fast he is not right with himself. S-l-o-w down again Robert, when you do, you are quite good. Maybe you really are struggling & working to line up with the past thermo masters to grok this stuff better like Joules Verne and Tallbloke handles.

Robert continues to struggle forward to equilibrium grokness by reading up on the subject:
“Thermal equilibrium does not equate the total energy. Read the equipartition theorem. Open a standard introductory physics textbook. Learn what temperature is. Then return.”

I have returned. Here is a quote from my standard introductory physics text book: “Equipartition gives the total average kinetic and potential energies for a system at a given temperature.”

Robert – You are advancing in your studies! This is good. You must now grok potential energy better. It is equipartitioned with kinetic energy at a given temperature. I have learned (long ago) that temperature is mean kinetic energy (reading your Caballero ref. was a cool refresher…).

So Robert is right here thermal equilibrium does not equate to the total energy. Thermal energy is equipartitioned with potential energy for the total energy. Good going Robert, I see advancement in this 3:45 post toward the thermo master’s laws.

Robert gave a little back with the two different answers to the same question but still see some progress.

Robert will be way better off moving to grokness equilibrium understanding the non-isothermal gas column upon reading Caballero section 2.3. Then return.

186. gbaikie says:

Venus atmosphere is ~4.8 x 10^20 kg
Average temperature: 737 K (464 C)

http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html

Specific heat of CO2: [kJ/kgK]
600 K 1.075
650 K 1.102
700 K 1.126
750 K 1.148
800 K 1.168

http://www.engineeringtoolbox.com/carbon-dioxide-d_974.html

To lower one degree of K requires 1.148 times 4.8 x 10^20 kg

Earth ocean:
1.4 x 10^21 kg
278 K [5 C] 4.204 (kJ/kgK)
To lower or increase one degree of K requires 4.204 times 1.4 x 10^21 kg
To freeze or melt into ice requires 334 kJ/kg
To vaporize water 2,270 kJ/kg

http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html

So how many joules does it take heat a Venus from say 20 K to it’s present
temperature?
The chart starts at:
175 K 0.709
So roughly .7 times 4.8 x 10^20 kg times [175minus 20K] 155 equals KJ
And from 175 to 375 .8 times 4.8 x 10^20 kg times 200 equals KJ
375 K to 600 K: 1.0 times 4.8 x 10^20 kg times 225 equals KJ
600 to 737 K: 1.1 times 4.8 x 10^20 kg times 137 equals KJ And sums:
5.2 x 10^22
7.68 x 10^22
10.8 x 10^22
7.23 x 10^22
Which is 30.9 x 10^22 kJ

With earth melt 1.4 x 10^21 kg ice is 334 kJ/kg times 1.4 x 10^21 which is
46.7 x x 10^22 KJ
So to heat ice from 273 K to 274 K require more joules than the atmosphere of Venus
requires to heat from 20 K to 737 K.
To warm the ocean from 276 [3 C] to 13 C
Requires 10 times 4.2 times 1.4 x 10^21 which is 5.88 x 10^22

In terms of ten millions of year, the earth oceans have had 10 C increase or difference
in ocean temperature. I don’t think many consider that Venus has had such swing
in temperature: 7.23 x 10^22 is amount joules required to heat from 600 to 737 K.
So about 100 K [or 100 C] change in Venus temperature.
In terms of ice age to interglacial periods there is about 10 C difference in average global
temperature [not ocean change in temperature- but atmospheric]. So in terms couple tens of thousands, earth temperature changes, still roughly close to comparable temperature of somewhere around 100 C change in Venus.

So it requires real absorption of energy [joules] to change “average temperature”, locally daily one can easily have more than 10 C change in temperature. Such changes reflect dynamic, and powerful heat engine.

187. So, we would expect the atmosphere at the surface of a planet to be warmer that it is at the top of the atmosphere. Of course, we can’t totally ignore conduction and radiation but, compared with convection, they are second order effects.

We might expect this if we didn’t understand convection. You’re getting things backwards, and amazingly, even though I derive the density of an ideal gas in thermal equilibrium above, you don’t even bother to read and understand it.

At a uniform temperature there is an exponential pressure and temperature gradient. If you warm the system at the bottom, the density of the fluid there decreases and there is a net buoyant force that lifts it up. Convection is cone-head complicated — I mean seriously complicated — in the general case. The equations that describe it are the Navier-Stokes equations, which are nonlinear partial differential equations so complex that mathematicians haven’t even been able to prove that a solution exists in the general case, let alone solve it. The idea is simple enough, and in simple geometries with e.g. uniform thermal gradients across the fluid one can predict some of the structure observed, e.g. convective rolls. But your base assumptions are completely false, and you have cause and effect completely reversed.

Undriven convection does not lead to warmer air on the bottom. Not ever. Heat a gas or liquid uniformly on top and you will have no vertical convection, because the density profile is stable. The stable undriven density profile is precisely what I derive, and is isothermal, with no convection. Only if you differentially heat a system on the bottom or on the sides (which is still part way to the bottom) do you get convection, and that only because the bottom is already warmer because of something else. Convection, in fact, cools the bottom!

A secondary comment is that radiation and convection make (from what I understand) roughly equal contributions to surface cooling. Either one can be dominant under different circumstances. During the day, convective cooling can be important — convection driven breezes can pick up a fair bit of heat from the surface. On a clear dry night, however, the ground temperature quickly inverts (becomes cooler than the bulk of the air immediately overhead) and radiation becomes far more important than convection.

The desert heats up to 45C or so during the day, but can still cool to 0C overnight. Not (primarily) from convection, not at all. By radiation.

Way back in boy scouts, winter camping in upstate New York, I learned about radiation and temperature. Cloudy nights are far warmer than clear nights. Clouds reflect a lot of heat back down and slow the cooling of the ground considerably. Water is a powerful contributor to the greenhouse effect. I also learned about a space blanket. A teensy thin layer of aluminized plastic, and yet it keeps you amazingly warm, because it reflects back your body’s radiant heat. You can feel it instantly if you put your hand into it. Your body loses roughly half of its heat from conduction/convection, and half from radiation. Air is a lousy conductor of heat, and often there is little or no wind. Radiation can easily be dominant, not just “second order”. I have no idea which one is dominant overall as far as surface cooling is concerned, but neither of them is negligible.

rgb

188. Myrrh says:

Robert Brown says:
January 24, 2012 at 8:28 am
Show me my mistake. Anybody. I won’t be offended.
[kdk33 says:
January 24, 2012 at 7:22 am ]

No, I think you are generally quite right, and this agrees rather well with Caballero’s argument. Isentropic because it is dominated by convection, not conduction, in an open system heated at the bottom. Isolate the system, or heat it at the top and explain to me how the bottom will end up warmer than the top.

Yeah, right. Just like the oceans. I wonder why the argument fails for the oceans? They seem to come into thermal equilibrium at, well, thermal equilibrium (constant temperature, independent of pressure, density, “gravity” etc), below the convection-dominated thermocline.

========================
The thermocline exists because of these, heated surface waters warmer and therefore less dense will sit on top of colder, denser water.

Wiki on Thermocline: ” The warm layer is called the epilimnion and the cold layer is called the hypolimnion. Because the warm water is exposed to the sun during the day, a stable system exists, and very little mixing of warm water and cold water occurs, particularly in calm weather.

One result of this stability is that as the summer wears on, there is less and less oxygen below the thermocline, as the water below the thermocline never circulates to the surface, and organisms in the water deplete the available oxygen. As winter approaches, the temperature of the surface water will drop as nighttime cooling dominates heat transfer. A point is reached where the density of the cooling surface water becomes greater than the density of the deep water, and overturning begins as the dense surface water moves down under the influence of gravity. This process is aided by wind or any other process (currents for example) that agitates the water. This effect also occurs in Arctic and Antarctic waters, bringing water to the surface which, although low in oxygen, is higher in nutrients than the original surface water. This enriching of surface nutrients may produce blooms of phytoplankton, making these areas productive.

As the temperature continues to drop, the water on the surface may get cold enough to freeze and the lake/ocean begins to ice over. A new thermocline develops where the densest water (4 °C) sinks to the bottom, and the less dense water (water that is approaching the freezing point) rises to the top. Once this new stratification establishes itself, it lasts until the water warms enough for the ‘spring turnover,’ which occurs after the ice melts and the surface water temperature rises to 4 °C. During this transition, a thermal bar may develop.”

Because going through 4°C to lower temperatures water gets dense enough to sink and doesn’t freeze, freezing water floats, so not independent of density and pressure and as these are due to gravity, not independent of that either. Salt water has lower temperature before freezing, -1.9°C.

Some extra bits.
In this description of how oil is formed in the oceans, increased pressure means increased temperature:

“Other sediments continued to be deposited and further buried the oganic-rich sediment layer to depths of thousands of feet, compressing the layers into a rock that would become the source for oil. Over the years, as the depth of the burial increased, pressure increased, along with the temperature.”

“Water pressure at the deepest point in the ocean is more than 8 tons per square inch, the equivalent of one person trying to hold 50 jumbo jets.”

“Atlantic sea water is heavier than Pacific sea water due to its higher salt content.”

“The Antarctic ice sheet that forms and melts over the ocean each year is nearly twice the size of the United States”

“90% of all volcanic activity on Earth occurs in the ocean. The largest known concentration of active volcanoes (approximately 1,133) on the sea floor is located in the South Pacific”

“Under the enormous pressures of the deep ocean, sea water can reach very high temperatures without boiling. A water temperature of 400 degrees C has been measured at one hydrothermal vent.”

“The top ten feet of the ocean hold as much heat as our entire atmosphere”

The above from: http://www.savethesea.org/STS%20ocean_facts.htm

“90% of the total volume of ocean is found below the thermocline in the deep ocean. The deep ocean is not well mixed. The deep ocean is made up of horizontal layers of equal density.”

http://www.windows2universe.org/earth/Water/temp.html

And bearing in mind heat rises.., http://www.esr.org/outreach/glossary/insulation.html

“Ice is a great insulator. A lot of what causes climate and weather involves the exchange of heat and fresh water between the ocean and atmosphere. If the ice cover is high, very little heat escapes from the warm ocean to the cold polar atmosphere in winter. But the heat loss through open water is so high, maybe 10-100 times more than through ice, that even a small fraction of open water has a big effect on area-averaged heat loss. Typical heat loss values are ~10 W/m2 through thick sea ice, and ~1000 W/m2 in winter through open water (depending on wind speed, air temperature, etc.)”

189. Q. Daniels says:

Robert Brown wrote:
I do not care about what generates the lapse rate. If the lapse rate is stable, so that heat delivered to the top redistributes to maintain a constant equilibrium temperature lapse between the top and the bottom — the sole case examined in the article above — then it violates the second law of thermodynamics.

Let me put it bluntly. If somebody presents a statistical mechanical computation that suggests that the second law is violated, I would knee jerk assume that the authors had made a terrible mistake unless and until proven otherwise, especially if I “could not understand” everything that they did.

Even then I would be doubtful.. To be honest, I would be doubtful if I did the work myself. I think that the paper you link has the right idea, and you will note that on other threads I propose precisely the same experiment. Show me, in other words. I’m a theorist, but I’m no fool. Experiments trump theory every time, …

I agree with this in detail, and find it a completely reasonable attitude. I will note that some people have difficulty understanding particular pieces of math, independent of their complexity. The Lorenz Transform is one such.

Graeff’s work is probably not sufficient proof for you. He believes he has successfully measured said temperature differential. http://www.firstgravitymachine.com

I also don’t think that a PMM2 machine violates TANSTAAFL. For one thing, the energy must come from somewhere, even if it’s just being exhausted as waste. For another, such a device would require an insight and a good deal of skill to build and use, even if it was as simple as rain. Doing takes effort, even if you’re just recycling waste.

190. glen martin says:

The essence of this Robert Brown’s ‘refutation’ is that if the wire and the gas do not have the same thermal gradient i.e. if the wire is isothermal and the gas is not then, there is a violation of the laws of thermodynamics.

The problem with the refutation is that the wire is not isothermal for essentially the same reason as the gas is not: the atoms at the top of the wire will move slower than those at the bottom due to gravity and will therefore be at a lower temperature.

The atoms of the wire will lose velocity as they rise in the gravitational field just as those in the gas, thus there is less energy available transferred in interactions this will produce an gradient in the kinetic energy of atoms that make up the wire resulting in a temerature gradient due to gravity. That the distance covered between interactions is much smaller in the solid than it would be in the gas and that there are other interactions in a solid does not change this fact.

191. Willis Eschenbach says:

glen martin says:
January 24, 2012 at 2:07 pm

“Willis Eschenbach says:
January 24, 2012 at 12:23 pm

Folks, a lot of you here don’t seem to get it. The beauty of Robert’s proof is that there is only one question in it—does heat flow forever in the silver wire or not?

IF there is a temperature difference in the air top to bottom, heat will flow in the silver wire. Gravity can’t stop that.”

Actually it can and does, heat in the wire is being transmitted via the interaction of moving particles, gravity will cause the particles to slow slightly as its height increases thus slightly less energy is will be transferred to the atom above a particular atom than was received from the atom below it. This results in a gravitationally induced thermal gradient in the wire.

Phew … gravity slowing electrons in a wire … thought I’d heard everything.

In any case, even if your interesting theory about gravity slowing heat transfer in wires were correct, it doesn’t matter. That just slows down the transmission of heat, it doesn’t stop it. So it doesn’t mater for the disproof.

w.

192. MDR says:

@Robert Brown

OK, after pondering some more, I have identified a flaw in my reasoning. I think you and Willis and the others are correct – the column of gas does indeed eventually relax to an isothermal state if the column is in fact thermally isolated. It is still stratified, of course, but it would end up isothermal. Apologies for confusing everyone.

Here is where I was going wrong. I mentioned that gas near the bottom of the column has a smaller amount of potential energy than gas the top. While this is undoubtedly true, that potential energy only comes into play if the gas is being mixed or is otherwise dynamic, that is, if such energy is being released as a result of changing the height of some of the gas parcels. But of course the equilibrium state does not have any such mass motions, and so no work is being done on the fluid. As a result, the internal energy of the gas is the same everywhere, and thus the gas has the same temperature everywhere.

Of course, for a column of gas subject to heat exchanges at the top and at the bottom [such as a column of gas in a planetary atmosphere] but is otherwise thermally isolated, there will be a temperature gradient established in accordance with those boundary conditions. But that scenario is apparently off-topic in this thread.

193. Trick says:

Robert Brown says at 4:10pm:

“I am specifically proving that EEJ, a specific paper written by Jelbring and published in a journal (God help the referees, absent that day on vacation or something), violates the zeroth but especially the second law of thermodynamics when it asserts that there will be a thermal lapse rate in an adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field.”

Robert Brown needs to read Caballero sec. 2.3 that proves the zeroth is not violated & the 2nd is not violated for “adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field” which Caballero proves is non-isothermal & there will be a thermal lapse rate.

I imagine Caballero is just like every other thermo text book (but I have not read them all like Robert) & the thermo grand masters assert. Thus Jelbring EEJ is not in violation & not refuted if Jelbring asserts same as Caballero and Caballero is right.

194. Khwarizmi says:

Q. Daniels says:
Willis wrote: Will heat flow in the silver wire forever?
If you extract energy from the system, it will shut down as the entire system cools. Energy is conserved. If you extract energy, then it has to come from somewhere, and that somewhere is the thermal energy of the system.
If you do not extract energy, then yes, it will.
=======
LongCat says:
While I agree with the underlying point, I’m not sure why the wire would necessarily violate the laws of thermodynamics if it continuously transferred heat. Under normal circumstances, it would radiate some of this energy away and otherwise be an imperfect conductor. If, however, we’re assuming a closed system with a perfect conductor surrounded by a perfect insulator, why would any energy be lost?
To put another way, assume I have a wheel with a frictionless axle at rest in a vacuum. If I spin it, it will spin endlessly. The conclusion that it will have perpetual motion doesn’t violate thermodynamics; the assumption that there is no friction does. Likewise, the wire would not violate any physical laws by endlessly transferring heat; those laws were broken by the assumption of a closed system with a perfect conductor/insulator.
I know I’m disputing people far above my pay-grade, so I’m assuming that I’m wrong in this. I’m just curious as to why.
==============
Trick
Heat flows forever in fig. 2. The reason is a grand master thermal law is broken, the easiest one, the zeroth law. There can be no perfect insulator.
==============

Correct.
All real heat engines increase entropy. Engines do work. Figure 2 doesn’t.

195. A physicist says:

Robert Brown says: But show me the “high precision” experimental result, done with a dewar in a centrifuge filled with maybe Xenon gas at a G value such that there is sufficient pressure at the top of the vessel to justify the thermodynamic assumptions, with recording high-precision, carefully calibrated thermometers.

Robert, thank you for making this excellent point.

Precisely the situation you outline is present in all of the world’s high-speed centrifuges containing uranium hexafluoride (UF6) for isotope separation.

If an adiabatic lapse were present in the centrifuges, between the high-pressure rim and the low-pressure central axis, then solid UF6 would condense at the cold central axis … which needless to say, is not observed.

Elevator Summary: Gas centrifuges prove that gravito-thermal theory is wrong.

196. Willis Eschenbach says:

kuhnkat says:
January 24, 2012 at 2:32 pm

Willis Eschenbach wrote:

Just don’t expect your belief, that gravity can do continuous unending work forever and ever amen, to be widely shared in the scientific community …

So Willis, when will we start flying off the planet??? When will the pressure on my feet from standing in one place stop?? When will the oceans boil from lack of pressure? Oh yeah, gravity is apparently an unending source of energy that counteracts centrifugal force. If not unending, we haven’t yet measured its reduction.

kuhnkat, you are conflating a constant force with unending work. Gravity is just there all the time, a force pulling in one direction, keeping you on the planet. When you move upwards against gravity, it takes energy to do that. When you move with it you get the energy back.

But when you come back to where you started, it’s a zero sum game (less with friction). No matter how many times you go up and down the hill, you don’t gain any energy at all, despite the constant presence of gravity. Which is another way of saying that in all of those trips up and down the hill, the lazy bum gravity hasn’t done a net lick of work. It did do work, but what gave with one hand, it took with the other by requiring the exact same amount of work in the other direction.

It’s like running a waterwheel by continuously filling the headrace up with buckets of water from below the wheel. Sure, you can get work out of the wheel … but that’s work that you are putting in by continuously lifting the water, not work that’s coming from gravity. Stop lifting the water and see what your friend gravity does for you … nothing.

Hope that helps.

w.

197. Tim Folkerts says:

Wayne says: “Seems lifting the electrons against gravity in the metal bar from the warm to the cool would cancel if the gradient became -0.0098C/m. ”

Very insightful.
IF the gradient for air and electrons and all other materials were the same 0.0098C/m, THEN maintaining a lapse rate would not lead to a perpetual motion machine.

However, since the lapse rate is given by C_p / g, and since different gases have different values for C_p, then different gases will have different lapse rates. So the premise is indeed wrong, and a stable lapse rate in gases would indeed violate the laws of thermodynamics.

198. Clearly there are two schools of thought. One school believes that the temperature will be lower at the top due to kinetic energy being changed to gravitational potential energy. The other school believes this will not happen. The GHG controversy rests largely on this point.

No, it doesn’t. There isn’t any controversy. Gravity is incapable of providing net heat to the Earth’s energy budget, and the GHE only deals with the rate at which the Earth loses heat in that budget. Nobody argues that there is a lapse rate in the actual atmosphere. I have just definitively proven above that it is not a feature of static equilibrium, it is a dynamic phenomena caused by differential and irregular time dependent heating and cooling, where the bulk of the heating is at the surface, but where heat loss occurs to some extent very high up in the atmosphere as well.

This has nothing to do with “schools of thought”.

I am troubled on one point. The argument that a continuous flow in a cycle is not equilibrium and thus is some sort of proof favoring one school over the other. Surely dynamic systems can be in “equilibrium” in that there is no net flow into or out of the system, but still allow a cyclical flow within the system.

Surely they cannot, not as long as they are thermally connected at the microscopic scale to allow internal energy transfer within the system. This is precisely the point. Heat never “flows in cycles” in a system in thermal equilibrium. It flows from hot to cold. It never ever spontaneously flows from cold to hot as an steady state thermal process unless one does work on the system. This is what the second law of thermodynamics is all about. The only systems that can “move”, transporting energy around in cycles are ones without mechanisms for energy sharing or dissipation, like planets going around the sun in the limit that you ignore tidal heating and gravity waves and light pressure. In enough time, even those weak effects move energy around and damps periodic motions.

In the case of the gas in the figures above, one could take the silver wire, replace the middle of it with a thermoelectric junction, use the electricity to drive a fan or light a bulb. This, too, would violate the second law — the heat content of the container would systematically lower (as some of the heat in the cycle was converted to work). The net effect would be that all of the energy lost from the container would be converted to work — its temperature would drop as the work appeared in the outside world, quite independent of the temperature out there. This, too, is a direct, textbook case of the violation of the second law of thermodynamics, both the refrigerator statement and the heat engine statement.

At least you are troubled by the right things — you should be troubled by this because your mere common sense tells you that heat, which is basically random motion, cannot remain organized enough to flow around in a circle without something reorganizing it. The microscopic form of the second law says that basically, systems evolve in time from less probable states to more probable states. Take a jar full of identical marbles, some blue and some red, organized with the blue on top and red on the bottom and shake it. You can shake a long, long time before you can expect to see all of the blue on the bottom and the red on top — there are a near-infinity of ways for the marbles to be mixed; only one for them to be cleanly separated red on blue.

That’s the sad thing about this — people don’t understand how much of a law the second law is. Your odds of winning 150 million dollars in the lottery and having the IRS forget to charge you taxes on it due to a clerical error are a gazillion times better than the odds of shaking that jar and getting even a very modest number of mixed-color marbles sorted out by random chance, and that is precisely the reason that heat flows from hot to cold and not the other way around. There are way more states where the energy (per degree of freedom in the system) is approximately equally shared than there are states where it is split up.

Otherwise, your observations about ability to rationalize and so on are well made, but — my advice is don’t bet against the second law. You’ll just lose.

rgb

199. Bill Illis says:

For 13.7 billion years, …

… Gravity fields have been heating up matter.

That is long enough to be called perpetual.

Just look out at your night sky and see the proof of that. Or maybe even the day-time. The big bright white thing in the sky started shining because of gravity fields heating up matter.

We can extract energy from that we figure out it works exactly. Just like the other ten sources of energy that we didn’t have clue about in times past.

Anyone disputing Jelbrings hypothesis needs to prove that gravity does not provide a minimum heat/energy level in matter when that matter is being held back from falling further through the gravity field by the electro-magnetic and strong forces of the atoms in the rocks at the surface of the planet. The matter is still being pulled through the gravity field, it is just being stopped by the other forces in the atoms of the rocks/liquid.

Has anyone proved that? How could you? We don’t even know how the force of gravity extends its pull. Maybe Higgs bosons increasingly accumulate/stick to matter as it moves into a gravity field and they are attracted to each other. Maybe the Higgs provides heat energy to the matter. If you don’t how it works, you cannot say it has no impact.

200. Willis Eschenbach says:

George Turner says:
January 24, 2012 at 2:40 pm

Actually Willis, heat flowing through the silver wire forever doesn’t mean it’s impossible, as heat always flows forever in any system above absolute zero. Take any object and an arbitrary plane that defines it. The two parts will never be in exact thermal equilibrium because atomic collisions are discrete, so half the time one side is hotter and half the time it is colder. Thus heat flows back and forth across the boundary – forever. That doesn’t mean the existance of an object above absolute zero is impossible.

George, if you do not know from the context that we are talking about net heat flow through the wire, and not freakin’ brownian movement of electrons, you are not paying enough attention.

w.

201. If the column of air is not isothermal, that is an emergent phenomenon in the presence of several things:

– A planet
– An active star
– An atmosphere

By this excessive logic, a solar panel can’t possibly be a perpetual motion machine either, so there is no such thing as renewable energy. Especially after the sun fizzles out…

202. Trick says:

Robert Brown says at 4:36pm:

“The distribution of v at the top (of the atmosphere) and the bottom is identical — the Maxwell-Boltzmann distribution.”

Maxwell-Boltzmann is not applicable in a gravity or electrostatic field. M-B quite clearly limit their derivation of particle velocity to special case of particles with no external forces like no gravity, no electrostatic etc. M-B applies to our famous gas column when it actually is isothermal – in the no gravity case. Caballero 2.2 shows that is the fact and in my view Caballero is correct.

203. Joe Born says:

Dewitt Payne: “Please post a calculation of the Velasco lapse rate for a gas column with the surface at STP (101325Pa and 273.15K) and g = 9.81 m/s^2. The number density/cubic meter is ~6E23 molecules/mole/0.0224m^3/mole = 2.7E25.”

I’m a little pressed for time this evening, so I’ll just give you what I have handy, without using your particular values or double-checking. Note that this assumes a monatomic gas. I’ll revise it tomorrow for diatomic (after I read up on rotational degrees of freedom; I’m a layman). As you can see, the lapse rate would be hard to measure experimentally.

f = 3 ; # degrees of freedom
E = 2.2e9; # guesstimate of total energy in a meter-square gas column arbitrarily high
VRW_LapseRate = function(f, E){
k = 1.38e-23; # Boltzmann’s constant
N_0 = 6.023e23; # Avogadro’s number
w_m = 29; # “molecular weight”
m = w_m / N_0 /1000; # molecular mass
g = 9.8; # acceleration of gravity
P_0 = 1.01e5; # atmospheric pressure at sea level
M = P_0 / g; # atmospheric mass per unit earth-surface area
N_m = 1000 * M / w_m; # moles of atmosphere per unit earth-surface area
N = N_m * N_0; # number of molecules per unit earth-surface area
– (2/3) * f * E / (f * N + 2 * N – 2) * m * g / E / k;
}
VRW_LapseRate = function(f, E)
[1] -6.389722e-32

The last line of the function is the result of differentiating Velasco et al’s Equation 8 and converting from kinetic energy to temperature.

As I said, I haven’t double-checked, so there’s likely an error here. You may want to check it yourself.

204. Willis Eschenbach says:

dlb says:
January 24, 2012 at 3:42 pm

Willis at 11.54am wrote:

Excellent insight, Wayne. That is exactly what happens. In an isothermal column of air, individual molecules at high altitude have more energy because of gravity. But for exactly that same reason, there are fewer molecules at high altitude. As a result, and as we would expect, in the isothermal condition the energy is spread out evenly through space (equal energy per volume) rather than equal energy per molecule as Hans Jelbring and Mr. Verne assert.

Although I agree with Dr Brown, I disagree with what Willis has said here. Consider a cubic metre of soil and a cubic metre of air above it, although both are at the same temperature, they certainly have different amounts of enegy due to differing densities.

Um … er … well … I must confess, I’m picking my jaw up off the floor.

Here’s the first thing. Nobody is talking about a cubic metre of soil here but you. Why?

Because it has nothing to do with the energy distribution of an ideal gas in a cylinder connected with a piece of silver wire.

I can only shake my head in amazement, dlb. Perhaps if you read the head post again?

w.

205. Willis Eschenbach says:

A physicist says:
January 24, 2012 at 3:58 pm

Willis Eschenbach says:

Wait, wait, you claim to be a physicist, answer the question. Does heat flow forever in the silver wire or not?

Willis, the short answer is “Yes”

Dang. Well, can’t say I’m really surprised. Turn in your PhD at the door, or demonstrate it will flow forever and ever amen, and win the Nobel Prize.

w.

206. P = T*V helps to understand what’s going on. One must constantly keep in mind that in the gravitationally bound column of gas pressure is constant while temperature and volume are the variables. As its temperature goes up and down its volume goes up and down. Surface pressure is determined by gravitational constant and mass of the gas which do not vary. Temperature is not coupled to pressure therefore pressure is not coupled to temperature. So raising the surface pressure will not cause a rise in equilibrium temperature. It will cause a rise in volume and the gas law wil be satisfied by the change in volume.

OK, Joules, you’re scaring me. P is absolutely, categorically never equal to V*T. Have you ever heard of “units”? You might look them up some time. Nor is pressure proportional to T*V in an ideal gas (or any gas I can think of). PV = NkT, so P = NkT/V. Nor is pressure constant in a gravitationally bound column of ideal gas. Don’t be absurd — pressure is never constant in any vertical fluid column in a gravitational field. The equation for static force equilibrium is:

$dP/dz = - \rho g$

Density is (in any situation where this might apply) a strictly positive number, so the pressure must vary with height. I actually derive its isothermal variation with height at the top of this thread. Surface pressures on the Earth vary all of the time, by a few percent. Pressure variations help cause “weather” — that’s why God invented “barometers”, because falling air pressure often warns of a storm, while high pressure usually indicates a fair, sunny day.

Temperature isn’t necessarily “coupled to pressure” — one can certainly have different contains of fluids at any pressure and any temperature — but that doesn’t mean that in various thermodynamic systems:

$\partial P/\partial T = 0$

as a general rule. If you think that, take a soda bottle, screw the lid on good and tight, and put it into some boiling water. Hell, I have a problem just taking those large plastic refillable water bottles back to the store — if you put them into a car with the lids tight you’ll get there with them (often irreversibly) blown up like a balloon. Works the other way too — screw the lid down when it is hot and come back to them partially collapsed.

As for “raising the surface pressure” causing changes in temperature — well, if the surface in question is the cylinder of a gas piston that is being compressed, I beg to differ, especially if it is done rapidly.

Here’s a cute toy that I like to teach my students about:

http://www.practicalsurvivor.com/firepiston

http://www.phy.duke.edu/~rgb/Class/review_53/review_53/node64.html

Lost the figure that went with the problem, sorry, but the pictures in the first one should give you the idea. The point is that whether or not increasing pressure changes the temperature depends on where and how you do it. It certainly can raise the temperature — it depends on the path followed on the P-V curve. Only if you follow an isothermal path does it not change the temperature, but isothermal paths are just one of a myriad of possible paths between a myriad of possible pairs of state points.

I’m also waiting to hear you acknowledge that a static lapse rate in an ideal gas at thermal equilibrium violates the second law of thermodynamics as per the example given above. Since you actually tried to make fun of the textbook physics I’m presenting, it might be appropriate as it sounds like you might be coming to grips with the truth of it.

rgb

207. Bill Illis says:

The wire suffers from the same loss in gravitational potential energy as it goes higher in the column.

208. Joseph Murphy says:

Dear Lord this thread is entertaining. I moved some joules reading through it. Thank you to everyone.

209. Q. Daniels said @ January 24, 2012 at 5:08 pm

Robert Brown,

I’ve read a number of thermodynamics texts myself.

Not once did I see a proof of the Second Law that did not rely upon circular logic. I’ve seen plenty of empirical proof, that people have been unable to violate it, but no direct proof.

Relying upon the Carnot Cycle is pretty clearly circular logic. It’s more difficult to show, but assuming that the MB distribution remains uniform under gravity may also be circular.

If you have a proof of the Second Law that is not based on circular logic, I’d be happy to read it.

Failing that, all we have is that there are no publicly recognized or understood violations of the Second Law. It is empirical, and nothing more.

Poor engineering is not proof of impossibility.

I have commenced an extremely empirical experiment what is designed as a empirical disproof of the Second Law of Thermodynamics. This very morning, I mixed 400 ml sterile H2O with 400 ml of the best Italian balsamic vinegar in a bottle and sealed it. Having sealed it with much twisting of the Stelvin seal, I shook it vigorously. Seven times seven times did I shake the Stelvin sealed bottle. When the balsamic vinegar spontaneously separates out from the H2O, verily I shall know that I have violated (desecrated even) the Second Law of Thermodynamics and fully expect to be deported to the US of A for having engaged in a successful conspiracy theory contrary to US law.

210. t seems to me Robert Brown’s analysis implicitly makes the following claim: if all the greenhouse gases (mainly H20 and C02) were cleansed tonight from earth’s atmosphere, then the atmosphere would evolve toward a more nearly isothermal equilibrium.

Wow, I implicitly said that? Well, imagine that. Who knew? I certainly didn’t.

But let’s try. The problem is difficult because even if there are no GHGs in the atmosphere you still get lateral convection and convective turnover because you are heating the surface more at the equator than at the poles. There would therefore be heat moved from the equator (where the hot air rises) towards the poles (where it cools and becomes less dense) — errr, depending on the shape of the planet. An oblate sphereoid, hmmm, yeah, I think there would likely still be enough surface transport to establish a large scale convective roll with the air rolling north (say) up high, deflecting to spinward as it goes, falling down in a massive spinward spiral, cooling along the ground and being displaced back to the equator. But I’m far from certain about this.

To put it another way, my intuition is that the stratosphere, which currently sits above the greenhouse gases in the troposphere where their is good vertical convection, ought to extend all the way down to the surface. The stratosphere isn’t static — far from it! It just has little vertical shear, and actually warms with height. But the details of the circulation that is established might be difficult to predict (chaotic even). As long as you have day and night and poles and equator, though, you’d have some vertical and lateral convective transport.

This is a good question for a real climate scientist. I’m not even a Sears climate scientist — I’m just a physicist who is trying to keep people from abusing the poor, innocent, second law of thermodynamics in their eagerness to come up with non-GHG surface warming mechanism. It doesn’t really help the anti-CAGW “cause” (Gawd, how I hate that word in the context of climatology post-Mann) if the proposed non-AGW mechanism is nonphysical, especially if it is obviously nonphysical and likely to justly earn the derision of “warmists”. There are plenty of physically plausible places to press them on instead, no need to just make stuff up…

rgb

211. DeWitt Payne says:

Joe Born,
After reading the Velasco, et.al. note, it’s quite clear that the authors agree that there is no gravitationally induced lapse rate. For a small number of particles in the control volume, temperature is no longer strictly proportional to the average kinetic energy. But that says precisely nothing about a gravitationally induced lapse rate. In fact the authors specifically state that:

In conclusion, in our opinion a full explanation about why answer (2) [(2) The temperature decreases with the height because of the following two reasons.] to the paradox formulated by Coombes and Laue is wrong must discern between the cases of a finite system and an infinite system. In the former case, statement (2) is wrong because the assumption in statement (2b) is wrong. In the latter case, statement (2) is wrong because the conclusion in statement (2a) is wrong (as it has been established by Coombes and Laue).

[my emphasis]

Or in short, statement (2) is always wrong, but for different reasons depending on how many molecules are in the control volume. Nowhere in the paper is there a formula for calculating the magnitude of a non-zero lapse rate in the presence of a gravitational field. This has been pointed out to you in one of the previous threads.

212. Willis Eschenbach says:

Alan Millar says:
January 24, 2012 at 5:22 pm

… Get a grip folks. These sort of statements are going to hold this well respected site up to ridicule.

I couldn’t disagree more. The fact that all sides are welcome to show up at WUWT to advocate for their particular point of view is the strength of the site, not the weakness. Yes, there’s a host of folks out there that believe loop-de-loop stuff. There are even more who are kinda scientific but who could not, right now, give a clear distinction between force, work, and power. There are far too many issuing solemn pronouncements who didn’t even realize that there is a difference between force, work, and power.

But that’s how it is, that’s how the world is. And there are plenty of logical and scientific voices here, including most of those voices who have weight because of their demonstrated understanding of those kinds of distinctions and their willingness to post their views under their own name and history. Not only that, but we’re doing our best to explain this stuff, and discuss it, and debate it.

Finally, the presence here of many believers from the First Church of Gravity is because their Holy Scrolls are being unwound here for everyone to see. In other words, if their claims were being taken apart on Judith Curry’s site, they’d be there screaming as loudly as they are here at the moment. Doesn’t say anything about the site.

It is an issue that I have pushed hard on, however, because the Seekers After Gravity tend to be climate skeptics. I’d like to distinguish that kind of wishful thinking from true skepticism, and make it clear that the latter is very distinct from the former. True skepticism accepts the existence of such controversial and radical new theories as something known as the “Three Laws of Thermodynamics”.

So, I have pushed for and written about the issue here, precisely to see who would say “Don’t be stupid, heat can’t flow indefinitely” and who would say “But you don’t understand, if the force of the adiabatic lapse rate is twice the work, then clearly …”

It’s kind of a modern day scientific shibboleth.

w.

213. Myrrh says:

What has Brownian motion got to do with electrons?

And by “net heat”, do you mean the photons from colder to hotter thing?

214. I thought the compressed gas at the bottom in relation to the less compressed gas at the top simply contained more heat energy/volume even though all molecules in the column would have the same level of excitation.

Precisely. Energy is extensive. Temperature is intensive. Right off of the list:

http://en.wikipedia.org/wiki/Intensive_and_extensive_properties

The one caveat is that a gas does not “contain heat” in the sense that I can say that jar of air at thus and such a pressure and temperature contains so many joules of “heat”. Energy is the proper extensive property, and heat describes a quality of some of the internal energy in a system, namely its availability for doing work.

Good job, keep it up. This sort of thing is all very interesting (and you are pointing out an extremely common error many respondents are making), although I’d have to just turn this thread into an online college thermo course to correct them all. I’m trying to focus on just one thing. No violations of the zeroth or second law of thermodynamics. Oh, hell, people shouldn’t oughta violate the first, either, with their various proposals.

rgb

215. DeWitt Payne says:

Joe Born says:
January 24, 2012 at 7:20 pm

The last line of the function is the result of differentiating Velasco et al’s Equation 8 and converting from kinetic energy to temperature.

But temperature is only strictly proportional to the kinetic energy in the canonical limit and Velasco, et.al. agree that in the canonical limit, the column is isothermal. So you can’t directly convert kinetic energy to temperature for a microcanonical ensemble. Or in other words, your calculation is flawed.

216. Willis Eschenbach says:

MDR says:
January 24, 2012 at 6:52 pm

@Robert Brown

OK, after pondering some more, I have identified a flaw in my reasoning. I think you and Willis and the others are correct – the column of gas does indeed eventually relax to an isothermal state if the column is in fact thermally isolated. It is still stratified, of course, but it would end up isothermal. Apologies for confusing everyone.

Here is where I was going wrong. …

I would like to commend and laud this action. He is actually seeking knowledge and understanding. When he finds it, and corrects some prior misunderstanding he had, he not only comes back to say he “identified a flaw” in his reasoning. He explains where he went wrong, and how he got out, so others can avoid the same mistake. I did the same thing in my post “Perpetuum Mobile”.

My thanks to you sir. Your actions represent the best of this site, where people (definitely including myself) can learn something and move the understanding forward.

Warmest regards,

w.

217. I am not a scientist and never claimed to be so, could someone explain why the gas, or atmosphere in this case, should be colder on top than on the bottom assuming convection works in all cases (cold air falls while hot air rises) Yes, I can figure, as air gets closer to outer space (in really simple terms) it would get mighty cold but, cold air is more dense and as such it should fall more rapidly. Exactly where does gravity enter the picture? It is exerted equally on all temperature states of air, right?
Or should I up my meds? ;-)

No, your meds are just fine as they are. It is difficult to explain, impossible in the thread. You need to learn a few things and follow some algebra. The online thermodynamics textbook by Caballero describes the basis for an adiabatic lapse rate, and provides actual graphs of actual soundings of atmospheric temperatures along a vertical column at various locations to show how sometimes the atmosphere follows it, approximately, sometimes it doesn’t, some times (and some places all of the times) it inverts and goes the way you intuitively expect cold below to warm above, and how things like “atmospheric instability” (stormy weather) often depend on local inversions or convective rolls.

The point is that it is actually pretty complicated. To start with, you need to understand what an adiabatic process is, and why lifting, expanding air is expected to expand approximately adiabatically (cooling as it goes) instead of isothermally. Both are possible, mind you, but isothermal expansion requires heat/energy exchange with “something” because the gas does work but its internal energy doesn’t change.

rgb

218. Trick says:

Robert Brown says at 7:04pm:

“I have just definitively proven above that it is not a feature of static equilibrium…”

If Robert Brown means the top post where he attempts to prove the adiabatic gas column in the presence of gravity is isothermal by ignoring the 0th Law?

No, this is not proven since it is in direct conflict with what Caballero in the link in the Perpetuum Mobile thread proves in Sec. 2-3 – the real world gas column is non-isothermal w/gravity and the device in figure 2 will not run forever with a real non-perfect insulator.

Robert Brown’s disregard for the 0th law means he can use a perfect insulator to prove the column is isothermal in the presence of gravity. This is incorrect theory and cannot be used to disprove EEJ. Ignoring the 0th law means Robert Brown can create a Perpetuum Mobile machine (to sell to Willis’ along with a bridge) with the correct non-isothermal gas column.

219. Willis said:
Phew … gravity slowing electrons in a wire … thought I’d heard everything.

I’m not sure if I did this right, as it’s not normally the type of electrical calculations I do, but:

One coulombof charge contains 6.24150965e18 electrons, and an electron weighs 9.10938291e−31 kg, so 1 coulomb of electrons weighs 5.68563013e-12 kg. 1 coulomb of electrons 1 kilometer up has a gravitational potential energy of 5.5719175e-8 Joules, and a Volt is defined as 1 Joule/Coulomb, so that would be 0.05571917 microvolts/km, or 17.947 kilometers in height per microvolt. You can do the same calculation in electron volts, with 5.5719175e-8 eV per kilometer..

220. Robert, it seems that you have completely missed the fact that gravity causes a pressure and density gradient in your air column.

You mean, except for the place where I derived the actual functional form, starting from the gradient required for neutral buoyancy, for the pressure (and by trivial extension, density) of an ideal gas in static, isothermal equilibrium? Missed it except for there?

Funny, I thought that was what most people would have called completely not missed it…

This is a much more complex problem than a quick, partial recitation of a freshman physics text can handle.

No, it’s not. I’ve reduced the whole damn argument to two pictures, and only one counts. It doesn’t involve trying to do statistical mechanics in your head, badly, only pure thermodynamics.

Look at figure 2 above. You explain to me how any supposedly stable thermal lapse rate — I don’t care at all how it is established — in the gas does not violate the second law of thermodynamics when one includes a simple heat conduction pathway between the hot gas at the bottom and the cold gas at the top.

If you agree that the silver will transfer any heat at all between the two reservoirs as long as there is a temperature difference, the only possible way a thermal lapse can be stable is if the perturbation is damped out of the system and the lapse rate restored. This, in turn, requires heat transport down the gas column to restore the lapse rate. This, in turn, causes more heat to be conducted up through the silver wire. Forever, round and round in a cycle.

There is nothing to stop you from cutting the silver wire in the middle and inserting a heat engine instead of conducting pathway, and turn all of the heat energy in the gas into work, violating all of the versions of the second law in the process, or putting the engine inside the gas itself (and inside the adiabatic container) where it will run forever, a PMM2K. A suitably designed (ideal) Dippy Duck placed inside the container is my own personal favorite heat engine — a Perpetually Dippy Ducks run just fine between any two thermal reservoirs at different temperatures, and you assert gravity will create and maintain two such reservoirs spontaneously.

So forget the treatment of pressure, density, and buoyancy. I actually can — and have — treated them, but you obviously haven’t yet made it through that intro physics textbook so that you understand what I’ve done. But you cannot possible be willing to assert that heat will flow in a loop forever, which is a pure consequence of a static, stable, thermal separation in the isolated gas no matter how you think it might come about. You therefore can be certain that no such thing does come about.

rgb

rgb

221. Heat is Energy is mass by M=E/c^2 so said Einstein.
So what force causes Mass to rise up the silver conductor against gravity ie work has to be done?
The silver conductor is little different from the gas in a column in this respect. The top will be colder than the bottom and heat will not flow up the silver conductor unless a heat source (work) is supplied from the bottom..

Oh, sweet Jesus.

Tell you what. The next time you cook, you be sure to put the food on the bottom of your pan and heat the top. Otherwise, how is all that heat going to manage to make it uphill against gravity?

You can’t seriously be proposing that the silver wire won’t permit heat to flow upwards either.

rgb

222. MDR says:

@Willis

But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety ["Open a standard introductory physics textbook. Learn what temperature is. Then return."] and not of the collegial variety ["If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?"] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?

223. From Tricks conversation above

Quote

Robert Brown says at 9:07am:

“…in figure 2 above. Which is violated — the heat equation in silver or your absurd assertion that gravity can stably sort out a gas into a hotter temperature and a colder one? One or the other.”

Unquote

Is this not exactly the basis for astrophysics?. gas collects by gravity, warms up, gets denser, then warms enough to become a star!!!!!!

224. Myrrh says:

MDR says:
January 24, 2012 at 8:35 pm
@Willis

But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety ["Open a standard introductory physics textbook. Learn what temperature is. Then return."] and not of the collegial variety ["If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?"] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?

=========

Lots I imagine. The trick is to ignore it, it’s a form of bullying when they can’t answer your questions, for the most part.

Carry on throwing them in every now and then … I’ll enjoy it for one, who’s been on the receiving end rather a lot.

225. Re: Jupiter giving off more heat than it absorbs.

Just where is the proof that there is not a large radioactive core at its center, similar to what Earth has, but at 10 to 1000 times its size? Everyone making the claim that gas compression is responsible for Jupiter’s IR signature is making the same mistake Lord Kelvin made in estimating the age of the Earth.

226. William Sears says:

To Robert Brown,

Quote “This is a good question for a real climate scientist. I’m not even a Sears climate scientist”.

Hey, I hope you mean Francis Weston Sears. I have only superficially followed this discussion, but I feel your pain.

227. Will Nelson says:

When temperature decreases with altitude that’s gravity driven lapse rate…
When temperature increases with altitude (very common this time of year where I live), why that’s just weather /sarc

228. 1) if the several km-long tube is horizontal & the perfectly dry air is at a constant temperature throughout & is moved to the vertical, the dry adiabatic gradient will be produced (warm at the bottom, cool at the top w/ approx 8C/1000m gradient in between) due to the ‘work’ of gravity creating a pressure gradient to the compressible gas. Notice, no gradient will be produced if water is used instead of gas because water is non-compressible so no work will be done. If no heat is added or removed to the gas, the column will be in a neutral buoyant state (and will stay that way!!) – if a parcel of air is moved vertically by an outside force, it’s temperature will change to reflect the change in pressure but will still be the same temperature as it’s surroundings.

2) as to the experiment with the thermal conductive wire at the base & top of the tube, the author here is incorrect. If the wire moves heat from the bottom of the tube (the base cools) to the top of the tube ( the top heats), presuming, as the author says, “…save to note that the internal conductivity of the ideal gas is completely neglected.”, the heat from the *local* area of the wire is all that will be moved from the bottom to the top ***and nothing else*** . Why, you ask?? In moving the heat from the bottom of the tube to the top is causing the lapse rate to become **more stable** – cool at the bottom with warm air above is an inversion which inhibits vertical mixing!! THAT is why the engine will not work as it is set up.

Nonsense. I provided a stable isothermal solution, one that is straight out of a textbook. Well, all the textbooks. Why, exactly, is gravity going to further compress any of the fluid, when it is all in static force equilibrium?

You’re thinking of the local heating that you’d get if you dropped a uniform density of air into a column and it settled down into something with a transient lapse rate, because the falling air would indeed heat up. But it isn’t stable! Once it “hits the bottom”, it will gradually conduct heat and adjust pressure and density until it reaches the isothermal distribution that is demonstrably in both force and thermal equilibrium.

As for 2) — you clearly miss the point entirely. I don’t know if you are clueless about fourier’s law or are just being stubborn.

Look, forget gravity. Take two insulated reservoirs filled with anything, one at temperature T_h and one at temperature T_c. Put a wire in between them that can conduct heat. Heat will be conducted from the hot to the cold reservoir. I don’t care if they are uphill, downhill or side to side from each other. Don’t care if one contains air, the other water, or both air, or one a chunk of iron and the other a bucket of feathers. Don’t care if one is at high pressure, the other at low pressure. If you are a “40 year meteorologist”, then presumably you know what the zeroth law of thermodynamics is because otherwise you don’t even know what a thermometer is or how it works or what it does.

The wire in figure 2 doesn’t move heat from “the local area of the wire” and nowhere else. The gas is a conductor of heat. If you cool even a tiny bit at the bottom near the wire, and heat the gas only a tiny bit at the top near the wire, you push the gas away from what you — in 1) claim is the stable equilibrium of the gas. The meaning of stable equilibrium is that if you perturb it away, it comes back. So you can’t make your lapse rate “more stable” by cooling the bottom and heating the top, you either destroy it the lapse rate altogether by heating the top and cooling the bottom until there is no lapse rate or else the system restores the lapse rate, moving the heat from the top back to the bottom.

The former is what happens, because in the second case the second law of thermodynamics is violated. Except that you don’t have to, because:

An Ideal Gas Is Not Really Adiabatic

If you are a meteorologist — which I seriously doubt, at least I doubt that you are a competent one who has actually studied physical climatology since I’ve studied exactly one textbook on it and seem to know more than you do — then you know perfectly well that no gas fails to conduct heat.

The container the gas is in (in our ideal world) might be adiabatic. An parcel of ideal gas moving up or down the air column might be approximately follow an adiabatic expansion curve because air is a relatively poor conductor of air so the error made assuming it is adiabatic is small if the transport time is much shorter than the time for conduction to make secular changes in temperature. But air is not, I repeat not, adiabatic. Once it comes to rest, with no vertical transport, it instantly starts to conduct heat around to bring the system into real thermal equilibrium, which is isothermal.

The silver wire is just a way of hurrying the process up, and letting you see a channel that carries energy. There is absolutely nothing that will restrict heat flow in the wire but the departure of the distribution of heat in the gas from the lapsed distribution that you claim is a stable equilibrium one.

Either you were mistaken (and the system thermalizes to an isothermal state where heat no longer flows) or else heat flows forever as the gas restores equilibrium, permitting more heat to flow in the wire to the top, which the gas moves to the bottom to restore equilibrium, to infinity and beyond.

Because the gas itself conducts heat, you don’t really need the wire. The dry air adiabatic lapse rate isn’t stable because air conducts heat.

rgb

229. The essence of the Jelbring hypothesis appears to be that as a parcel of air is raised or lowered in the Earth’s gravitational field its gravitational potential energy is increased or decreased with a corresponding decrease or increase in temperature, which maintains total energy constant.

But is this notion not refuted by consideration of packets of air in rigid sealed capsules, which can be raised or lowered in a gravitational field as much as one likes without causing adiabatic change in temperature, even though the air packets are experiencing changes in gravitational potential energy?

230. MDR said @ January 24, 2012 at 8:35 pm

But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety ["Open a standard introductory physics textbook. Learn what temperature is. Then return."] and not of the collegial variety ["If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?"] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?

That’s the nature of learning; you can only learn for yourself — nobody can ever do your learning for you. At university, you go to the lecture, afterward you do the set reading, exercises/pracs and finally go to a tutorial where you discuss what you’ve learnt and it all gradually falls into place. Most people around here want to skip the lecture, the set reading and exercises/pracs and lecture everyone in the tutorial about how they have it all wrong. Students who do this at university are called failures. That’s in the nature of being a student.

231. Doesn’t the silver thread require energy input to keep it at top of atmosphere?
Would not the top of atmosphere have to have tremendous amounts of energy to maintain the same temperature as it is less compressed? Would that energy be great enough to actually break the gravitational bounds of earth? If the molecules escape earth gravity, does that cool the top of atmosphere?

The thing is that the Top of atmosphere is not bound. As energy is increased in the atmosphere, the top of atmosphere moves further away from the earth surface. As energy decreases, it moved closer to the earth surface.

The silver thread does not even need an atmosphere though to move energy away from the earth surface, as it can just simply radiate at beyond the top of atmosphere.

Holding the silver wire at the top of atmosphere ends up requiring the exact same amount of energy to be expended as the energy that the wire can transfer to the top of atmosphere would be my argument. The work required to keep it up there increases the energy at that point. Work is being done.

I do not think the author has convinced me that there would not be a lapse rate in our atmosphere. I can see that there would eventually be equal amounts of energy at each and every place in the atmosphere, but that energy does not translate directly into temperature. The column could come to equilibrium only at the point in which the earth surface is the same temperature as the lapse rate effected temperature of the air immediately above it. At that point, there would be no heat transfer from a steady state temperature surface to the atmosphere that is at the exact same steady state temperature. It would require outside forces at that point to cause turbulence.

232. Jim D says:

Two points.
1. Jelbring is wrong, not because of the adiabatic lapse rate but because he defines the greenhouse effect as the adiabatic temperature difference between two levels. This definition is wrong because the greenhouse effect is purely a radiative effect, not a gravitational effect. You can simulate the radiative greenhouse effect sideways in a lab just as well as vertically.
2. Brown is wrong. The heat flux in a gas depends on the potential temperature gradient, not the temperature gradient. Potential temperature is related to temperature by a function of pressure only. An isentropic atmosphere has uniform potential temperature. An isothermal atmosphere has potential temperature increasing upwards leading to a downward heat flux. An isentropic state is the state of maximum entropy and will not separate into a state with a different potential temperature profile because that would have a lower entropy, given that total potential temperature has to be conserved when integrated over the mass in adiabatic processes. Closely related to potential temperature is dry static energy, cp*T + g*z, where cp is the heat capacity at constant pressure (1004 J/kg/K). This form shows that potential energy is part of the total energy with the other part being an enthalpy or internal energy +PV. This is approximately conserved.

233. robr says:

Robert Brown says:
Willis Eschenbach says:
My guess is that if my questions are ignored long enough they will go away. But I will keep asking, in your opinion:

Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?

Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?

A simple answer like – No, no or Yes, No will suffice.
Thank you,
robr

234. Right. This is why Robert Brown had to invent the perfect insulator design in fig. 2. How’s the patent pending process coming along Robert?

Oh, for Pete’s sake. Have you even read Jelbring’s paper? Of course not. Do you know what the word “adiabatic” means? Obviously not.

Just FYI, since your childish rant is complete lunacy and seems to be nothing but logical fallacy from end to end, Jelbring begins by assuming an entire adiabatic planet. No energy in, no energy out. He surrounds the planet with that “perfect insulator”. He does this to assert that the gas will have an adiabatic lapse rate in stable thermal equilibrium, with no energy in or out. I prove, quite clearly, that no lapse can be thermodynamically stable.

Wait, wait, wait. It’s obvious that I’m wasting my time. You think that the thermal insulator around the gas — present in both Jelbring’s model and mine — matters to the argument. You also think that Joules ravings about the gas collapsing to a supercooled liquid is somehow lucent and relevant.

I gotta ask it. Are you on drugs? I keep reading your “rebuttal” and it is lunacy, utterly incoherent. Do you think that you could maybe go cold turkey for a day or two, maybe drink some coffee, and see if you could actually winnow an argument out of all of the straw men, ad hominem, sarcasm, and so on? I dunno, maybe an actual statement of what the final temperature distribution of the system drawn in figure 2 will look like?

No? Sigh…

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235. I believe Robert G Brown’s explanation is correct. On the other hand, kdk33 gives us a detailed argument, also apparently correct, that shows why temperatures must follow an adiabatic lapse rate.

The resolution is, I believe, simple; Brown is talking about a thermally isolated (equilibrium) hypothetical atmosphere, whilst kdk33 is talking about a steady state atmosphere with sources of incoming and outgoing energy.

Putting it simply, the ALR is the maximum temperature gradient per unit change of pressure. Greater T gradients are prohibited by convection: A warm air parcel, on rising, will still be less dense than the air around it at the higher altitude, and so will rise even more. Air will keep on rising until the lapse rate is no greater than the ALR. It is just like the slope of the pile of sand in an hourglass: sand falling through the hole piles up in the centre until the critical slope is achieved, and then sand grains roll downhill to maintain the maximum gradient. But once the sand flow stops, there is no longer anything to maintain the gradient: a few jiggles and bumps and the sand evens itself out. In the same way, in an isolated column of air, a few jiggles and bumps (i.e. molecular collisions) will even out the temperature. But in the real atmosphere, there are sources and sinks of energy, and so an active process keeps on ‘topping up’ the imbalance and so all planetary atmospheres are at or close to the ALR. (The fact that they all are is conclusive evidence that there is little or no scope on real planets for changes in ‘greenhouse’ gasses to have significant temperature effects – even if the process worked just the way the AGW theorists claim!)

236. Because that claim —foreseeably (and strictly IMHO) — is going to emerge as the primary fallback position of GHE skeptics.

But who cares? There’s direct observational evidence for the GHE. Maybe I should make that my next article, simply showing the evidence without talking about the details of the mechanism. The IR spectra speak for themselves. Even if Jelbring were right instead of deluded it wouldn’t stop there from being a GHE. You can see it — with IR eyes.

In the meantime, first Jelbring, to clearly demonstrate that DALR is a consequence, not a cause, of differential heating and cooling of surface and atmosphere. Next N&Z because their “miracle” model for planetary temperatures is complete bullshit (and we’ll see what they have to say about DALR after Jelbring isn’t there any more as a crutch).

Then maybe we can start looking at actual skeptical science. Remember, I’m a skeptic, especially of the “C” in CAGW. I just don’t like bullshit arguments and bad science on either side of the issue. Good science, plausible arguments are just fine.

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237. clazy8 says:

I don’t believe there can be a lapse rate in a closed system at equilibrium. We observe a lapse rate because a continual flow of energy heats the planet’s surface, which heats the atmosphere above it. The heated gas at the bottom of the column is continually shedding the energy onto the gas just above it, and so on, so that the energy is passed along as if by a bucket brigade. TUrn the sun off, and everything will begin to settle down. As the atmosphere cools, it no longer has the energy that allowed it to extend so far from the planet, and it shrinks, becoming denser and denser as it is pulled down by gravity. At some point it will condense, if the planet’s gravity is sufficient, and then it will freeze, unless there are liquids that do not freeze at 3K. At this point, it is safe to say there is no lapse rate.

238. What is going to kill these gas giants?
If gravity is constantly maintaining hotter gases at the bottom then convection will move gases around and therefore we seem to have an everlasting living planet.

Screw gas giants in our solar system — they are wussies.

You want gravitational heating, check out:

http://en.wikipedia.org/wiki/Brown_dwarf

A subcritical brown dwarf — one just a bit too light to ignite fusion — heats from gravitational collapse that continues (IIRC from when I taught astronomy) for something like 100 billion years. Brown dwarves will still be gradually releasing heat from gravitational collapse when our own sun isn’t even a faint memory. If the Universe turns out to be closed, some might make it to the next Big Crunch.

Jupiter and the other gas giants are too light (and hence cold) to be considered brown dwarfs, but they are still slowly collapsing and hence give off more radiant heat energy than they absorb from the Sun.

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239. The reason the silver thingy won’t generate perpetual motion is that the exposed ends will assume whatever the air temp is at that altitude. A temperature difference of 1 degree will not move any heat in a silver rod 100 meters long.

Why not? I could fill the space inside the insulated chamber with insulated rods so that A is huge. Also, it isn’t correct to say that it won’t move any heat. It will just move heat slowly. But I don’t care how fast it carries heat because any heat causes perpetual heat flow. This is a gedanken experiment intended to show that Jelbring’s equally gedanken “adiabatic world” will not have a thermal lapse rate in static thermal equilibrium, nothing more. I don’t care how long it takes to reach equilibrium. Equilibrium has no thermal lapse.

I don’t even need the silver. Air conducts heat all by itself. It’s not a great conductor, but it doesn’t have to be to establish equilibrium.

The point may seem minor, but it transforms “adiabatic lapse” from a sort of “miracle heating” that starts from an outside boundary condition and heats to the surface via lapse into a consequence of forced convection due to the differential delivery of heat to the surface, a dynamic process and not a static one, one that goes away if you stop actively maintaining the surface and some part of the atmosphere overhead at different temperatures. It goes from being the great, noble cause that will replace the GHE and prove that it is all part of the nasty CAGW-IPCC conspiracy and was never true at all to being a possibly important mechanism that helps establish the GHE.

I don’t know why people are so stubborn about this. It could be that an improved understanding of the dynamical transport mechanisms associated with the DALR and convection might help place limits on the climate sensitivity to GH forcing, and that people on this list could be thinking about things like that instead of trying to pretend that the GHE isn’t real. Especially in the face of IR spectroscopy that pretty much directly proves that it is.

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240. clazy8 says:

It now occurs to me that it’s true: the greenhouse gases actually do keep the planet cool. Without them, there would only be radiation from the surface to get rid of the solar energy — the GHGs collect translational and vibrational energy from the atmosphere and toss it out the window, albeit in very sloppy fashion, spilling almost as much on the ground. They’re basically scavengers. Dare I say it? If we really are concerned about overheating, maybe we should increase CO2 emissions.

Wow. Considering I actually believe this, I am now a crackpot.

241. Which does not occur in the real world. That’s why we call it weather. Sorry, no sale. This is just as unacceptable as the nonsense about CO2, a trace gas having more effect than water vapor on the planet’s temperature.

Which is fine, I agree. As I noted at the beginning, I’m specifically addressing Jelbring’s EE paper, EEJ. Read it, and you’ll see what I object to. The nonphysical assumptions in my toy above precisely mirror his, except that I don’t bother making a “round planet” as that has nothing to do with his assertion that an isolated gas in a gravitational field will have a stable thermodynamic equilibrium with a temperature lapse.

If you agree with that, well, that’s all I was trying to sell. I’m not asserting that a DALR doesn’t occur — only that it is a dynamical feature of differential warming on the bottom and cooling on the top. If you do look at where there is a DALR in planets, it is in the convective zone where this differential heating drives atmospheric turbulence and turnover. I’m not sure I would put Jupiter and the gas giants into this particular picture, as they probably have at the very least different mechanisms for differential heating at the “bottom” of their “tropospheres” (whatever that means for planets that don’t really have much of a surface, at least where it is relevant). But none of that is the point of this thread. My purpose is to drive a stake through the heart of the Jelbring paper, once and for all so we can all leave bad, law-of-thermodynamics violating physics behind. The DALR isn’t due to Jelbring, and if you take away his assertion that it is a stable equilibrium in an isolated system there is nothing left.

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242. In a cylinder with gas at the usual DALR, all that his conducting wire will achieve is a infintesimally thin layer or hotter gas at the top plus an infintesimally thin layer of cooler gas at the bottom.
Both of these would reverse the lapse rate ( inversion) and thus no further heat can be exchanged without adding work to the cylinder (His statement that the system would reorganise itslf into an adiabatic column is wrong)

Piffle. First, the proposed lapse rate is supposedly stable. This means that if one makes a small perturbation — or for that matter a large perturbation — from it, the system will move around to restore the lapse rate. Second, why do you have this fantasy that gas, ideal or not, doesn’t conduct heat? If you cool “an infinitesimal layer” of the gas next to the bottom piece of silver, and warm “an infinitesimal layer” of gas next to the top piece of silver, that is not stable, because that infinitesimal layer of gas is in excellent thermal contact with the next infinitesimal layer over, and that one with the next one, and so on.

Here’s a very, very easy way to see that you are speaking nonsense. The gas in the column doesn’t “know” that it is in a very large column. All it knows is that locally it is supported in static force equilibrium and otherwise is in thermal equilibrium. It is exactly like an ordinary jar of gas at the same pressure and density and temperature. Exactly as in you could not measure any property of the gas in the jar and differentiate it from an identical chunk of gas from the column that isn’t in a jar.

So fill (mentally) the two jars and seal them. Now they are ordinary chunks of air, not unlike chunks of air in any laboratory. Put the two jars next to each other and connect them with a silver wire. Are you seriously suggesting that heat won’t flow between two reservoirs at different temperatures and bring them into equilibrium?

This is, incidentally, yet another excellent way to understand detailed balance. Detailed balance doesn’t depend on the pressure or density of the air in two jars. They can be anything you like. The (adiabatic) jars themselves will always exert exactly the same force on the fluid inside of them that a surrounding fluid would exert on them in equilibrium if we match pressure, density, and temperature in the jars.

So asserting that heat won’t flow in figure 2 above, or will stop flowing before all of the gas reaches thermal equilibrium, is just like saying that heat won’t flow between two ordinary jars of gas at different temperatures in the laboratory, and well over a hundred years of experiments, the entire refrigeration and air conditioning industry, a huge body of technology and engineering, and well understood physical theories all say otherwise.

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243. Walter says:

Robert Brown – stop before you go mad.

These people here are trolls who don’t want to listen or learn anything.

Leave it… walk away… you won’t ever convince them.

Once upon a time, in places like the Royal Institute, back in the glory days of the 1800’s, physicists were respected, argued with. But they presented to people who wanted to learn. From this, many great discoveries and theories were formed – some of which carry the names of those who discovered them, or who popularised them.

Now instead we have physicists and engineers attacked and torn down by “post normal science” and armchair ignorami who think they know better. What a sad, sad state of affairs. Time to let the ignorami wallow in own cesspool for a while. Imagine a world where the engineers all stopped making things and the physicists stopped helping them with theories – and they all went and played gold for 50 years. What a fun place that’d be.

I’m slightly pissed off – in case you had not gathered.

Enough… I’m off to count the UFO’s at the bottom of the garden.

244. Not once did I see a proof of the Second Law that did not rely upon circular logic. I’ve seen plenty of empirical proof, that people have been unable to violate it, but no direct proof.

Well, I’ve taken actual statistical mechanics course, and I have seen proofs of the second law that don’t rely on circular logic. Anyone with a child’s understanding of stat mech knows this. If you want a good derivation, look at the general approach of Jaynes, starting from information theory, or if you prefer, from Cox’s algebra of probable inference. The second law is technically a statistical law of large numbers. As Dewitt just pointed out, it can be violated, sure, as long as the violation doesn’t break the first law. It is just very, very, very — (repeat a google to the google power times or so very) unlikely. As in the probability isn’t zero, but it lives right next door, is good friends with zero, their kids go to the same schools, that sort of thing. It is difficult to convey how unlikely it really is, but Dewitt’s example of all of the air in the room bouncing just right and ending up as a drop of liquid air over in a corner leaving you gasping in a vacuum that happens to maintain itself because air molecules just don’t seem to have the right directions to bounce back into the room — that sort of unlikely.

But that hardly matters, does it? All of the laws of physics are empirical, observational laws. I’ve never seen a proof of the law of gravitation, or of energy conservation, or of Newton’s Laws. The more fundamental a physical Law is, the less we are able to prove it, the more the law relies on consistent observation instead of deduction or derivation. I should point out that this is my real interest at the moment — the philosophy of knowledge and the basis of science — and I am happy to cite you chapter and verse.

On that basis, the second law is actually rather derivable, certainly compared to e.g. energy conservation or Maxwell’s Equations. But that isn’t really the point. The point is that the U.S. Patent office will no longer accept patent applications for perpetual motion machines — without a working model. The point is that unless you are a complete idiot you wouldn’t invest a nickel in a company claiming to have one, not even if someone “showed” you that it worked. You’d believe with all of your heart and soul that there was a trick in it, and you’d be right. Yet here, because it contradicts something you want to believe, you choose to doubt it. Are you nuts?

That’s one of the truly amazing things about this list. Doubting the second law of thermodynamics is insane. How can you even seriously propose that?

If somebody claims they can violate it, no they can’t. If somebody claims to build something that they can prove violates it, no it won’t. I’d believe in an antigravity machine before I believed in a machine that does nothing but convert heat into work, or a system where heat moves spontaneously from cold to hot and maintains it there without work and against perturbations — those are all “free lunches”, and most of us old enough to tie our own shoes know that there ain’t no such thing as a free lunch.

Using this rather conservative approach, one might, possibly, conceivably make a mistake. Sure, why not? Magic could be real! People might be able to come back from the dead (one famous second law violation) or walk on water (another) or heal the blind with spit and mud (a third). But don’t bet on it!

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245. What maintains the lapse rate temperature difference?”

Mostly gravity.

Mostly gravity plus the differential heating and cooling. Move your house to Antarctica and look up mid-July. See all that sky that is warmer than you are?

But generally, I agree with your reply. As I stated, my objection is specific to EEJ — the DALR is not a stable thermal equilibrium, which is precisely what EEJ asserts. I’m not suggesting that there is no ALR, as a general rule, only that a) it isn’t precise, constant, ubiquitous; b) that it depends on differential heating and cooling and active transport in the atmosphere, and goes away when you stop heating the ground underneath it. The layer where the DALR approximately holds is the troposphere, the layer with vertical convective mixing, and it goes away as the ground temperature drops — making it look a whole lot more like an effect, rather than a cause, of warmer ground temperatures.

Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere. Heresy, I’m sure, on this blog, but there it is.

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246. dp says:

This is all stupid. You don’t need gravity or miles tall cylinders. Fill a cylinder with gas to a bzillion PSI. Put it on an atmospherically evacuated centrifuge. Spin it up to 100G. A thousand G – doesn’t matter. Measure the temperature along the length of the cylinder.

No matter how fast you spin the centrifuge, no matter how may G’s you impress, so long as the G force is constant the gas temperature will be the same along the length of the centrifuge. It is in equilibrium. It is happy gas. Is there more energy/CF at the outer extremity of the cylinder? Yes – the gas is more dense there. No surprise. This is not new energy.

247. The dry adiabatic lapse rate determines how high thermals will go – usually, only a few kilometers. The actual lapse rate is normally significantly different from the DALR.

As this article argues, the lapse rate without IR emitters would be zero. It is the greenhouse gases that move the actual lapse rate (ELR) from zero to -6.5 K/km. The DALR is -9.8 K/km. To claim that anything “maintains” the DALR simply means that you have not looked at the data.

Oops, sorry, answered the previous one before I read yours. As you can see, I agree. I was speaking sloppily about one factor of a trinity consisting of differential heating (greenhouse effect), convection and other mechanisms for heat transfer, and gravity that together make a self consistent troposphere that tops out roughly where the greenhouse gases become transparent and greenhouse cooling of the upper troposphere goes away.

But I’m sure you understand this better than I do. As I’ve pointed out myself, though, the DALR does go away as soon as you eliminate solar driving, e.g. the poles in the winter night. You can easily end up with the upper troposphere as warm as or warmer than the ground, easy proof that it isn’t just “gravity”.

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248. I’m curious, what if the gravity isn’t constant, but is fluctuating?

Then it constantly does work on the system. Probably not a lot of work, but some. Think of a perfectly insulated jar full of air. If you shake it back and forth violently, you do a bit of work on the gas in the system every time, and some of that work gets transformed into heat. The gas in the container gradually warms, just as it would if it were stirred. Shaking it is absolutely indistinguishable (to the gas) to having a wildly variable gravitational acceleration (equivalence principle).

This actually happens. Tidal pseudoforces cause small fluctuations in “gravity” all over the Earth, every day. The Earth and the oceans actually expand and contract. Some of the energy associated with lifting and dropping turns into heat. At the same time, the Earth’s rotation slows just a bit. The moon picks up the angular momentum and moves into a higher orbit. The moon’s orbit is lifting around 3cm a year, IIRC, and has been for the last 3 or 4 billion years. That sounds like a lot, but 3 x 10^9 x 3 = 10^10 cm, where there are 10^5 cm in a km, so this is only around 10^5 km. The moon was nearly half of its current distance from the Earth around the time it was formed. Interestingly, it is only in a fairly narrow window of time (geologically speaking) that the moon will be just the right distance away for the kinds of eclipses that we have, close to perfect equality of the angle subtended by the sun and the moon as seen from Earth.

HTH.

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249. Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?

Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?

I’m not the best person to answer either one, but my short answer is that without GH gases there would be no or a vastly reduced DALR, one maintained by a very different convective mechanism (such as equator-polar circulation). The atmosphere might even entirely invert. But this is only a slightly better educated guess than yours might be.

Similarly, I have little doubt that an atmosphere with no GH gases would have a very different overall equilibrium temperature, and probably a different distribution. It would certainly depend somewhat on pressure, because atmospheric density depends on pressure, and the actual heat capacity of the atmosphere where it picks up heat from the ground would therefore depend on pressure. I’m still thinking about how it might vary — I’d like to/need to run some actual models (necessarily based on assumptions) to get a feel for it. One really can’t answer every complex question off of the top of one’s head (although I certainly try, unafraid of and even embracing error as an essential step towards learning:-).

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250. Camburn says:

Mr. Brown:
Thank you for taking the time to post and answer questions.
While the assertion of Hans Jelbring is an interesting thought experiment, it does not pass the laws of physics.

251. Walter said @ January 24, 2012 at 10:55 pm

Robert Brown – stop before you go mad.

Hope he doesn’t; he’s a helluva better physics teacher than I had back in 1969.

These people here are trolls who don’t want to listen or learn anything.

That’s almost certainly true.

Leave it… walk away… you won’t ever convince them.

Not so sure about that one; I know people who managed to kick heroin and alcohol addiction. Tough, but obviously not impossible.

Once upon a time, in places like the Royal Institute, back in the glory days of the 1800′s, physicists were respected, argued with. But they presented to people who wanted to learn. From this, many great discoveries and theories were formed – some of which carry the names of those who discovered them, or who popularised them.

Now instead we have physicists and engineers attacked and torn down by “post normal science” and armchair ignorami who think they know better. What a sad, sad state of affairs. Time to let the ignorami wallow in own cesspool for a while. Imagine a world where the engineers all stopped making things and the physicists stopped helping them with theories – and they all went and played gold for 50 years. What a fun place that’d be.

I think you might mean golf rather than gold. Ayn Rand wrote books about the “doers” going AWOL. They made a big impression on the Git in 1969.

I’m slightly pissed off – in case you had not gathered.

Nothing wrong with being a grumpy old fart. Gits actually enjoy it :-)

Enough… I’m off to count the UFO’s at the bottom of the garden.

Watch out for the giant invisible mutant space goat. You’re probably safe though; apparently it prefers eating documentary film-makers, hairdressers, telephone sanitisers etc etc.

252. Robert will be way better off moving to grokness equilibrium understanding the non-isothermal gas column upon reading Caballero section 2.3. Then return.

Or, you could explain why the heat flow in figure 2 isn’t established if the temperature at the bottom is higher than the temperature at the top. It saves so much time when you just use the laws of thermodynamics instead of attempting a stat mech computation in words.

In the meantime, lift a jar of air up and see how much it cools.

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253. Neil says:

I thought that in the adiabatic case (in order to mirror the atmosphere) there is nil radiative or conductive heat flow.That is the standard atmosphere model where conduction is very small compared with other energy transfers. Also the column is deemed to be devoid of GH gases
Obviously we are talking about different thought experiments
If you want to have conductive gas why dont you suppose a perfectly conducting cylinder on the inside and perfectly insulating on the outside instead. This gets ride of hundred of words about about molecules interacting etc
Then we get the isothermal case
You did not comment on the fact that in the adiabatc case it needs a negligable amount of energy to raise a parcel of air from botton to top but if your silver wire delivers heat from the bottom layer to the top layer the outside work must be done to restore DALR. Of course the gas at the bottom does not know it is at the bottom of a tall column but it knows that there is warmer gas above and so it cant move upward
This is because the gas cant move upward against an inversion without an outside driver
The heat transfer cannot continue without this input.
I would like an answer to what happens to the initial small hotter layer at the top — dont quote conduction as we have none in the adiabatic case
Your transfer of heat between two horizontal jars is nothing to do with this case and requires a gas conduction which is assumed to be zero in the adiabatic column

PS What do you think insulates your house. I could bet 500:1 it is not a vacuum — even your double glazing is gas filled

254. The atoms of the wire will lose velocity as they rise in the gravitational field just as those in the gas, thus there is less energy available transferred in interactions this will produce an gradient in the kinetic energy of atoms that make up the wire resulting in a temerature gradient due to gravity. That the distance covered between interactions is much smaller in the solid than it would be in the gas and that there are other interactions in a solid does not change this fact.

Good try! I was waiting for somebody to try this one. However, imagine a vertical stack of pool balls. Hit the bottom one up. What happens to the top one? Does it depend on the size of the stack?

One of the many errors you and so many others make is that gravity does no net work in the upward conduction of heat. Really.

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255. Here is where I was going wrong. I mentioned that gas near the bottom of the column has a smaller amount of potential energy than gas the top. While this is undoubtedly true, that potential energy only comes into play if the gas is being mixed or is otherwise dynamic, that is, if such energy is being released as a result of changing the height of some of the gas parcels. But of course the equilibrium state does not have any such mass motions, and so no work is being done on the fluid. As a result, the internal energy of the gas is the same everywhere, and thus the gas has the same temperature everywhere.

So absolutely perfectly correct, I award you the A+ for the day. In isothermal equilibrium, the system is in perfect force balance, there is no net dynamical transport of mass up or down, no net change whatsoever of gravitational potential energy — but heat conduction still functions to maintain equal temperature and restore equilibrium after a perturbation.

So simple.

Now at nearly 3 am and with a busy day tomorrow (which starts at 5 am) I think I’ll quit, at least for the day, er, night, er, whatever. I really tried to answer each and every comment, but after some 20 or 30K words of text, some people are having a really hard time grasping this simple idea, others are extending the error to the solid wire, still others are doubting the second law of thermodynamics instead of a static lapse (!), and a few are just crazy.

The only kinds of potentials that contribute in statistical mechanics are the ones associated with state changes. The oscillator mode for a diatomic gas, for example, doesn’t get two degrees of freedom, only one. The exact same thing is true for gravity, and for the forgotten forces between all of those ideal gas molecules, and for the walls. In equilibrium, the average potential energy of each and every molecule in the systems is constant. That’s all that matters. They are constantly borrowing and returning energy to gravity, but their average gravitational energy is constant, and it does not count as an additional degree of molecular freedom unless it can change to take up additional heat. Does anyone recall adding “gravity” to the number of degrees of molecular freedom in C_v or C_p? I don’t think so…

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256. Robert Brown needs to read Caballero sec. 2.3 that proves the zeroth is not violated & the 2nd is not violated for “adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field” which Caballero proves is non-isothermal & there will be a thermal lapse rate.

OK, Trick, I’ll try one last time. You like Caballero? Well, so do I. Turn to page 36. Read section 2.17. Work through it carefully — this principle is called “detailed balance”. Then be sure to do exercise 2.17. I quote:

Exercise 2.17: Extend the argument above to show that (2.75) also applies to a vertical column of air in hydrostatic equilibrium.

Don’t forget that last little quote at the bottom of 2.17 right before the bloody textbook exercise:

Thus, heat flows down the temperature gradient (from hot to cold) and ceases to flow when temperature is uniform, exactly as required by the Second Law. A more precise calculation using the full apparatus of kinetic theory gives the same qualitative result. (Emphasis my own.)

Goodness, could Caballero be saying that thermal equilibrium is isothermal, regardless of whether you move up or down in a static air column? Even in Climate Science? Do you think? Is he asking you to (gasp) actually prove it? Well heck, it ought to keep you out of trouble for a while. Give it a shot. In the meantime, meditate upon that “exactly as required by the Second Law” bit. It’s important!

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257. Correct.
All real heat engines increase entropy. Engines do work. Figure 2 doesn’t.

It is left as a not-terribly difficult exercise to the reader to work out how, if the heat flow in figure 2 is stable, it can be transformed into a perpetual motion machine that amazingly, does not increase entropy as it blithely converts heat into work.

The violation of the second law is in the assertion that a non-isothermal state is at stable thermal equilibrium. That means that any heat engine that runs between the reservoirs can turn some of the temperature difference into work, increasing the entropy of those reservoirs, but gravity sorts it all out again and makes the energy available for re-use. EEJ is particularly pernicious in this regard, as it proposes a static DALR, one that is independent of the actual temperature of the gas. So if one uses the heat engine to do external work, the gas in the cylinder will indeed drop to zero in temperature as all of its internal energy drops to the bottom to maintain a constant temperature difference right up to where the temperature of the ideal gas at the top reaches zero.

If that doesn’t fail both the heat engine and refrigerator statements, nothing does.

Besides, we know that heat flow only happens until the system becomes isothermal. As this one would, with or without a silver wire or heat engine, because a gas with a DALR is not in equilibrium and ideal gas is still a thermal conductor of heat.

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258. AJB says:

I’m getting sorely dismayed by these threads so let’s try a different tack. For those who understand plain English rather better than accepted basic physics, why do you think Rankine coined the phrase Potential Energy in the first place? Do you imagine he just used fancy words for the sake of it? Here, read about the guy and let’s have no more nonsense about engineers versus physicists for starters.

http://en.wikipedia.org/wiki/William_Rankine

Forget decent basic physics text books; they’re obviously never going to help you. Look the word up in a dictionary instead.

Potential:
(noun): Capacity for development
(adjective): Possible but as yet not actual
(synonyms): Impending, Would-be.

Why do you think he used that word when he could have used any of the dozen or so more common ones that writers of dumbed-down textbooks often substitute? It’s because he was being precise – like any good engineer or physicist.

It means “not manifest until realized by some phenomenon doing something”. And it’s always realized in some actual form – kinetic, in the case of gravity. It does not, for example, mean ‘stored’ energy. Any text book that says that should be incinerated on the spot IMHO, it leads to exactly the sort of immovable confusion displayed in these threads.

Aside from kinetic energy there can be no other joules present at equilibrium, only the potential with altitude to have more when gravity does its stuff by causing something to move and acquire actual energy (thereby becoming capable of ‘doing work’).

As for conservation of energy, look at it this way: PE is a measure of the energy that will appear in future when gravity does its stuff and actually moves something. It isn’t actual energy present at rest. If that sounds like magic to you, it’s why we can’t explain gravity. PE is just bean counters’ double-entry book-keeping, necessary only because we can’t.

You cannot therefore count joules of PE and trade them off against KE at equilibrium. It makes no logical sense. No auditor will sign off accounts done on that basis, not even in Brussels!

If you’re going to maintain this concept is wrong you’re flying in the face of not only Rankine but Maxwell, Carnot, Clausius, Thompson, Hugoniot and all the rest even with the benefit of all subsequent experience they did not have (space, etc.).

You’re saying that potential energy is somehow actual energy in gaseous matter and you’ve therefore effectively explained gravity. In that case, how does gravity act on solids and liquids in a vacuum? Why do they still behave the same way? What then does compressibility have to do with PE being actual energy?

Next up you’ll be somehow extending your new found principle to plasmas to explain the coronal heating problem on the Sun or claiming gravity must be ever so gradually being used up so you’ve re-written the expansion of the universe turning the whole of contemporary physics on its head.

Sorry, but no (not for now anyway, show me some extraordinary proof first like producing a perpetual motion machine that works and explaining how your gravity works with solids and liquids). Lunacy seems an apt description.

259. Q. Daniels says:

Robert Brown wrote:
I should point out that this is my real interest at the moment — the philosophy of knowledge and the basis of science — and I am happy to cite you chapter and verse.

It’s a subject I have an interest in as well. Perhaps we can discuss it over a beer some time, should you find yourself so inclined.

260. son of mulder says:

“Robert Brown says:
January 24, 2012 at 8:31 pm

Oh, sweet Jesus.
Tell you what. The next time you cook, you be sure to put the food on the bottom of your pan and heat the top.”

You have misunderstood the point I was making. I had already clarified at
son of mulder says:
January 24, 2012 at 2:41 pm.

261. Anyone disputing Jelbrings hypothesis needs to prove that gravity does not provide a minimum heat/energy level in matter when that matter is being held back from falling further through the gravity field by the electro-magnetic and strong forces of the atoms in the rocks at the surface of the planet. The matter is still being pulled through the gravity field, it is just being stopped by the other forces in the atoms of the rocks/liquid.

OMG. Seriously, dude. First of all, none of this has anything to do with Jelbring’s hypothesis, which basically consists of the following:

1) There exists this thing called the DALR, that I read about somewhere.
2) It exists in isolated gases ideal gases in stable thermal equilibrium in a gravitational field.
3) Therefore, it is responsible for why the surface is warmer than the top of the atmosphere.

1) is true without question, although it isn’t simple or uniform.

2) is false — that’s the point of my proof. The rest of your list of absurd assertions is utterly ignorable. We actually understand gravitational heating in brown dwarfs and stars and so on. We understand why falling asteroids release a lot of heat. We understand why you can stand on the surface of the planet at rest until hell freezes over and gravity ain’t gonna give you no heat! Take a physics class or two or get out of the game.

3) Given that 2) is false, 3) is not a valid conclusion. In fact, it is sort of half-true. The Greenhouse Effect is responsible for the DALR, which is a convective manifestation of differential surface warming and upper troposphere cooling. Although probably more complicated than “just” that.

But I don’t care about 1) or 3) — I’m just concerned with 2) and Jelbring says nothing about bizarre electro-magnetico-gluonic-gravitonic energy transfers that are responsible for breaking the second law of thermodynamics, any more than he talks about the invisible Maxwell Demon Fairies that sort out the hotter molecules in the gas and send them all down to the bottom.

It doesn’t matter how a lapse rate happens. No lapse rate that isn’t maintained by external input of energy or work is thermodynamically stable — if it were it would violate the second law.

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262. Julian Braggins says:

Re,
Ed Caryl says:
January 24, 2012 at 7:36 am. I agree with you Ed, also living at some altitude. I do not believe that the surface at altitude receives less radiation than at sea level, in fact it should receive more because it passes through less atmosphere.
Which is why the following quote from Wikipedia seems to make no sense, if the conductive source is at say 3000 metres and is heated from the same source, the Sun, then the lapse rate should start from there at the same temperature as that at sea level.

“In the lower regions of the atmosphere (up to altitudes of approximately 40,000 feet [12,000 m]), temperature decreases with altitude at a fairly uniform rate. Because the atmosphere is warmed by conduction from Earth’s surface, this lapse or reduction in temperature (is?) normal with increasing distance from the conductive source.” from Wikipedia, ”Lapse Rate”

263. No, this is not proven since it is in direct conflict with what Caballero in the link in the Perpetuum Mobile thread proves in Sec. 2-3 – the real world gas column is non-isothermal w/gravity and the device in figure 2 will not run forever with a real non-perfect insulator.

Sure, Trick. Just like a 100% efficient heat engine with friction isn’t a violation of the second law, because look, it isn’t really 100% efficient.

As I said, put the damn wire into the container and give it up. Where’s the heat going to go now? It still flows from the bottom to the top, and then flows back down. If it flows (slowly) out the sides of the wire, who cares? Gravity still sends all of the faster molecules down and all of the slower molecules up, to maintain the lapse, right? So heat will flow up the wire forever. Or a dippy-duck will dip forever. Personally, I like the dippy duck. I should have made that my example.

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264. GabrielHBay says:

Not so fast DP… sounds tempting, but surely the G force will NOT be constant throughout the cylinder. It will increase with the radius. Now there… any of the smart people here want to start some new convoluted thought experiments and circular reasoning based on that? C’mon.. we have only had 2 weeks (well it feels like 10) of that here.. /sarc
Just cannot believe that the simple issue of energy balance vs temperature balance can cause so much angst, so many futile thought experiments and so much isoteric maths and mis-applied physics to see the light. Not to mention the emergence to prominance of so many clearly educated beyond their intelligence. Luckily I consider myself educated well below my intelligence, so I can safely say that Jelbring and what has followed on that makes elegant and intuitive sense to me, unlike the other c**p that I have been diligently following to exhaustion here. Even for my 40 year old physics it hits the sweet spot, perhaps because I only remember the principles, not the maths. So much easier to see the wood in spite of the trees. And gosh, are these recent threads crowded with trees!

Rant over… Sorry, but I felt driven to it.

Off in anticipation to see the the second paper at Tallblokes’ if its there….

Gabriel van den Bergh (So you know who I am… I’ll be waiting…)

265. I’m not sure if I did this right, as it’s not normally the type of electrical calculations I do, but:

The mistake is in doing the computation at all. No (net) electrons move “up the wire”.

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266. Is this not exactly the basis for astrophysics?. gas collects by gravity, warms up, gets denser, then warms enough to become a star!!!!!!

Sure, but that is not a stable state. The gas heats while it collapses. When it stops collapsing, it stops heating. The Earth and its atmosphere are not collapsing, so the process exists, and is irrelevant to the discussion.

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267. Ed Zuiderwijk says:

I am just coming back from the shed having constructed my first Perpetium Mobilae. This is how it works: I have attached a copper wire to the bottom of my adiabatic container and a silver wire to the top. They nearly meat in the middle. The thermal conductivity in these metals is such that the wires are practically of uniform temperature so that the copper end is a warmer then the silver end. I have therefore a thermocouple in the middle producing energy out of nothing since gravity, without doing any work will restore the resulting termperature changes inside the adiabatic container.

Now I’m off to the shed to see how much energy I can produce. I’ll let you know: you’ll read about it in the newspapers.

Hint: sell your oil stocks, that’s so passee!

268. But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety ["Open a standard introductory physics textbook. Learn what temperature is. Then return."] and not of the collegial variety ["If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?"] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?

That was probably me, and my bad. I wasn’t trying to be condescending; I’m just answering several hundred comments, in detail, and I’m feeling a bit rushed. Also I admit my patience gets a bit tried by some of the “rebuttals”. As Willis noted, there are people conflating force with energy with power, LOTS of people who want to include gravity (somehow) in the list of degrees of freedom for a molecule in a gas in spite of the fact that direct measurements of the specific heat show — no gravity contribution (for perfectly understandable reasons). As I also noted elsewhere, you get an A+ for the day because you did go out and educate yourself. Doing a bit of work to learn something new is laudable. More readers and participants should take a lesson.

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269. Just where is the proof that there is not a large radioactive core at its center, similar to what Earth has, but at 10 to 1000 times its size? Everyone making the claim that gas compression is responsible for Jupiter’s IR signature is making the same mistake Lord Kelvin made in estimating the age of the Earth.

Dunno. I was citing prevailing wisdom, not holy writ. Jupiter is too small for fusion AFAIK, but maybe fission.

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270. Hey, I hope you mean Francis Weston Sears. I have only superficially followed this discussion, but I feel your pain.

It’s Frank Zappa: “Is that a real poncho or a Sears poncho?”

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271. The essence of the Jelbring hypothesis appears to be that as a parcel of air is raised or lowered in the Earth’s gravitational field its gravitational potential energy is increased or decreased with a corresponding decrease or increase in temperature, which maintains total energy constant.

But is this notion not refuted by consideration of packets of air in rigid sealed capsules, which can be raised or lowered in a gravitational field as much as one likes without causing adiabatic change in temperature, even though the air packets are experiencing changes in gravitational potential energy?

In equilibrium there are no parcels of air being raised or lowered.

Air is also not an adiabatic medium. An ideal gas is not either. Both conduct heat. I’ve clearly shown that a stable equilibrium with a lapse rate violates the second law. I’ve given numerous examples of how the actual location of parcels of air connected with a conducting pathway is completely irrelevant to Fourier’s Law in a conductor inserted between them. The adiabatic jar one simply helps you to see how gravity is irrelevant to the state space in the jar. Capture air inside a perfect dewar flask and seal it. You can carry it anywhere you like, up or down the stairs, and its temperature inside won’t change. Put it next to a flask similarly filled at some other location and temperature. Put a conductor in between the flasks. If the temperatures are not equal heat will flow. Moving the flasks doesn’t matter, what matters is the conducting pathway and difference in temperatures.

I don’t even care how much heat flows. One lousy joule conducted from the hot bottom to the cold top is enough. If it flows back to the bottom — which it must of the lapse rate is stable — then it will go round and round, violating the second law.

How hard is this to understand?

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272. gbaikie says:

“Robert Brown says:
January 24, 2012 at 11:09 pm

What maintains the lapse rate temperature difference?”

Mostly gravity.

Mostly gravity plus the differential heating and cooling. Move your house to Antarctica and look up mid-July. See all that sky that is warmer than you are?

But generally, I agree with your reply. As I stated, my objection is specific to EEJ — the DALR is not a stable thermal equilibrium, which is precisely what EEJ asserts. I’m not suggesting that there is no ALR, as a general rule, only that a) it isn’t precise, constant, ubiquitous; b) that it depends on differential heating and cooling and active transport in the atmosphere, and goes away when you stop heating the ground underneath it.”

Hmm. I don’t think it goes away when stop heating from the ground. I would agree that if you heat from the top, warm air stays on the top. I could point to our stratosphere as example of that. But perhaps that isn’t good example, as one could also say it’s due to the low density of air- the lack of buoyancy, which is also sort of saying the lack of gravity affecting it much.
I could claim/assert that Venus not warmed by the surface. I am not sure this is the case, but many people would agree with it:) One thing seems fairly certain, the sun doesn’t do much heating of Venus surface. NASA has Adiabatic Lapse Rate, Dry:

Here it say earth is 9.760 K per 1000 meters. And Venus is 10.468 K per 1000 meters.
A difference maybe due to different atmospheric composition- N2 vs CO2.
And seems Jupiter is different [1.963 K per 1000 meters] due to it’s mostly Hydrogen and helium atmosphere.

As general rule, I would say lapse rate is controlled by gravity [and the mass of the gases- also gravity related]. Water vapor is lighter than air- therefore it lowers the lapse rate. From 9.8 K to 6.5 C per 1000 meter [or 3 F per 1000']
Or how well does a balloon fly. In dense high gravity worlds balloons have good buoyancy.
In high gravity world with hydrogen atmosphere, you have less balloon lift.

“What determines stability is the difference in density between the rising parcel and the environment. At the same pressure density differences are determined by temperature differences (ideal gas law). The rate of change of temperature with height in a dry air parcel – the adiabatic lapse rate – is fixed: 9.8 °C/km, but the rate of change with height in the surrounding atmosphere varies from place to place and time to time. The measured local vertical profile of temperature in the air is called the environmental lapse rate.”

http://eesc.columbia.edu/courses/ees/climate/lectures/atm_phys.html

An addition factor is I believe the a pressure vessel, would alter the lapse rate- or make a more uniform density.
But back to idea of not heating from the bottom. Problem is you have to heat somewhere.
I think if you heated in the middle, you retain the lapse rate- because heating in the middle causes instability in such instability gravity would sort into a lapse rate. So in even uniform heating or middle heating one would have a lapse rate.
Of course massive amount heating at surface would disrupt a lapse rate- hotter air would rush up and more or less stay up until it cools.

273. Steeptown says:

Robert you say:
Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere. Heresy, I’m sure, on this blog, but there it is.
Not heresy, as nobody would argue that “greenhouse” gases don’t absorb and emit IR and radiate to space. As long as we all understand what we mean by “the greenhouse effect”, then we are all happy here.

274. Joules Verne says:

Robert Brown says:
January 24, 2012 at 3:45 pm

“equilibrate the total energy”

“This is a major misunderstanding. Thermal equilibrium does not equate the total energy. Read the equipartition theorem. Open a standard introductory physics textbook. Learn what temperature is. Then return.”

The misunderstanding is yours. Equipartition does not hold unless the energy is quadratic. Gravitational potential energy is linear.

This doesn’t appear in introductory physics texts. Maybe try opening a more advanced text then return.

275. Brown is wrong. The heat flux in a gas depends on the potential temperature gradient, not the temperature gradient. Potential temperature is related to temperature by a function of pressure only. An isentropic atmosphere has uniform potential temperature. An isothermal atmosphere has potential temperature increasing upwards leading to a downward heat flux. An isentropic state is the state of maximum entropy and will not separate into a state with a different potential temperature profile because that would have a lower entropy, given that total potential temperature has to be conserved when integrated over the mass in adiabatic processes. Closely related to potential temperature is dry static energy, cp*T + g*z, where cp is the heat capacity at constant pressure (1004 J/kg/K). This form shows that potential energy is part of the total energy with the other part being an enthalpy or internal energy +PV. This is approximately conserved.

None of which I care about. I think I follow all of the entropic and potential temperature stuff, but address figure 2!

Heat flow in the wire does not give a damn about potential temperature. It runs between any real temperature gradient. If you wish to assert that removing heat from the bottom of the gas column and adding it to the top leads to a gas that is no longer in isoentropic equilibrium and that the gas will move the heat back to the bottom to restore it, then you have established a clear violation of the second law. I therefore must respectfully doubt that the gas is in actual thermal equilibrium in the isoentropic state, probably because the basic assumption of a gas being actually adiabatic is utterly false. What you are really looking at is a difference in time scales, as is fairly clearly indicated in at least Caballero where he derives this. Because conduction is much slower than convection, one can neglect it, making the gas parcels adiabatic as they move up and down. But once the system reaches isoentropic equilibrium at the DALR, heat will flow via real conduction, not adiabatic movement of parcels, and the system will, I believe, relax to isothermal equilibrium that — as I’ve clearly shown — is an entirely valid thermodynamic state that is dynamically stable.

Anything else still violates the second law of thermodynamics. If you throw that out, why bother speaking about entropy in the first place?

That’s the primary reason I conceived of this thought experiment. Even though I can’t imagine gravity functioning as a Maxwell Demon, even though Caballero in section 2.17 both states and leaves as a student exercise the proof that the thermodynamic equilibrium state of a vertical column of gas is isothermal, there has been a lot of confusion and strange assertions about a gas arriving at a state because of bulk transport that sorts out temperature differences approximately adiabatically (neglecting conduction), but that is somehow thermodynamically stable without transport and with conduction in the end. It didn’t feel right. Figure 2 indicates that it isn’t right, no matter how elegant your argument, because the resulting energy flow clearly violates the second law.

True equilibrium is still isothermal, but that doesn’t mean that there isn’t a wide range of time and temperature fluctuation scales that suffice to maintain the approximate DALR because the atmosphere is never sufficiently static for long enough for conductive relaxation to occur.

If you disagree, please describe the steady state heat flow in figure 2.

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276. Putting it simply, the ALR is the maximum temperature gradient per unit change of pressure. Greater T gradients are prohibited by convection: A warm air parcel, on rising, will still be less dense than the air around it at the higher altitude, and so will rise even more. Air will keep on rising until the lapse rate is no greater than the ALR. It is just like the slope of the pile of sand in an hourglass: sand falling through the hole piles up in the centre until the critical slope is achieved, and then sand grains roll downhill to maintain the maximum gradient. But once the sand flow stops, there is no longer anything to maintain the gradient: a few jiggles and bumps and the sand evens itself out. In the same way, in an isolated column of air, a few jiggles and bumps (i.e. molecular collisions) will even out the temperature. But in the real atmosphere, there are sources and sinks of energy, and so an active process keeps on ‘topping up’ the imbalance and so all planetary atmospheres are at or close to the ALR. (The fact that they all are is conclusive evidence that there is little or no scope on real planets for changes in ‘greenhouse’ gasses to have significant temperature effects – even if the process worked just the way the AGW theorists claim!)

I wouldn’t argue with most of that. However, the biggest source of imbalance is the greenhouse effect itself. The evidence is in the actual measured thermal profile of the atmosphere, where the ALR stops at the tropopause, right where the greenhouse gases radiate out and end up cold, compared to the hot surface. It’s a self-sustaining process.

I think you’re probably right about the lack of sensitivity, though. CO_2 would basically have to move the tropopause higher and colder to increase surface warming, I’m guessing there are powerful negative feedbacks opposing this; simply altering convective flow in the upper troposphere or the stratosphere might do it. But here the physics gets too difficult to do in your head with a simple argument, and I don’t find anything at all “conclusive” about the planets except that they all seem to have tropospheres and the tropopause seems to be related to the height where their greenhouse gases top out, much like the Earth. That doesn’t really tell us much about the sensitivity. Or am I missing something?

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277. I refuse to conform to the idea that scientific laws must be obeyed and never questioned.

Me too! I try to disobey the law of gravitation all the time, and then I question it closely, asking it why it stubbornly insists on pulling me down. It isn’t terribly verbal, though — indeed, it’s a bit childish, and inclined to demonstrate its existence by means of the falling excrement of an overhead bird.

Do you hear me, Gravity? I know that these are your paltry attempts to force me to comply with your patriarchal demands! But I refuse to obey!

Still, after a while, I do admit to questioning it less, and I try to make sure that my sly attempts at disobedience don’t involve windows in tall buildings, or leaps out of trees, or walking underneath heavy and precariously balanced objects. It’s one thing to be heretical and intellectually daring, another to be stupid and earn yourself a Darwin award.

As for the difference between a theory and a law — I’d summarize it a lot more succinctly. A physical law is an empirical axiom. A theory is derived from a mix of experiment and physical law. It’s much like the mathematician’s separation into axioms and theorems combining to make a theory, except that in physics a lot of the support of a theory is inferential, not strictly deductive.

Was there a particular law you were ready to refuse to conform to or obey?

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278. Stephen Wilde says:

Robert Brown said:

“Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere.”

But not the so called radiative greenhouse effect.

It is the conductive/convective greenhouse effect involving ALL the atoms in the atmosphere and not just GHGs.

Gravity puts more molecules near the surface and those molecules pick up more energy from the heated surface because there are more of them and they are closer to the source of heat than molecules higher up.

It is that simple and nothing to do with radiative abilities of molecules of GHG. The so called backradiation from the sky is simply the temperature of the molecules in the air that are directly in front of the sensor. They have reached that temperature because the outward flow of energy to space has been slowed by the molecules in the air and the slowdown is greatest where density is highest at the surface. There is no net downward energy flow and so no back radiation.

http://en.wikipedia.org/wiki/Lapse_rate

“the concept can be extended to any gravitationally supported ball of gas.”

“the atmosphere is warmed by conduction from Earth’s surface, this lapse or reduction in temperature is normal with increasing distance from the conductive source.”

After all your efforts in this thread you have come full circle to that which I told you previously.

Now take one more step. You suggest that the greenhouse effect and gravity work together to MAINTAIN heat differentials.

Look at it slightly differently.

Solar input to the surface together with gravity acting on the atmosphere to cause pressure CREATE the heat differentials (the greenhouse effect) within the atmosphere (primarily the troposphere) which WEATHER and CLIMATE seek to MAINTAIN.

Thus the atmosphere and all the features of it must configure themselves around the lapse rate set by pressure and solar input.

That is the only way that diverse atmospheric compositions can achieve the same outcome on different planets.

To my mind the jigsaw is complete.

279. It now occurs to me that it’s true: the greenhouse gases actually do keep the planet cool. Without them, there would only be radiation from the surface to get rid of the solar energy — the GHGs collect translational and vibrational energy from the atmosphere and toss it out the window, albeit in very sloppy fashion, spilling almost as much on the ground. They’re basically scavengers. Dare I say it? If we really are concerned about overheating, maybe we should increase CO2 emissions.

Wow. Considering I actually believe this, I am now a crackpot.

Not a crackpot, but you might want to look at some curves. The problem is that the IR curves show that emission in the CO_2 band occurs at very cold temperatures — I’m not looking them up, but I want to say -70C or thereabouts. Emission from the ground is occurring at maybe 30C — a 100K difference, around of 1/3 of the ground temperature. The radiation from both ground and CO_2 follow — very approximately — irregular and weakly modulated “blackbody” curves associated with the temperatures in their respective bands — the ground in the “water window” close to the ground temperature peak, but a chunk of the tail in the much cooler CO_2 band. There are pictures (of actual data at specific locations) in e.g. Caballero if you want to look at them, and I’m sure there are some online as well.

Now, BB radiation at any given wavelength is roughly proportional to T^4. If there was no atmosphere or GHGs, the ground could use all of the BB curve (weakly modulated by lines here and there) to radiate its energy away. That means that it would be radiating in the CO_2 band at an effective ground temperature of (say) 300K. If there is a GH layer at 200K, then in that chunk of the spectrum it radiates (2/3)^4 = .2 times the power it would have radiated, per square meter, at 300K. The ground and air together still have to balance incoming radiation, and since they radiate less in part of the spectrum, they have to radiate more in the rest. Ergo the ground will heat up until the two together balance what the ground alone could have managed at a lower temperature.

This argument is based strictly on the graph of the IR data. I don’t care how the heat gets up, or down, or sideways. I say nothing about upwelling or downwelling, radiation vs conduction or convection or the DALR. If you basically block 80% of the outgoing radiation in one band high in the atmosphere, the ground temperature has to go up until radiation from the rest of the spectrum can compensate. So I think the effect works differently from the way you imagine. Forget “how” the warming occurs. Why it occurs is much clearer, and can be understood strictly in terms of detailed balance in energy flow.

Note that I’m ignoring lots of stuff in this. Some radiation is absorbed at place X and laterally transported to be radiated away at place Y. This “some” is a substantial amount — Europe is kept “warm” by the Gulf Stream, heat absorbed in the tropics (net cooling the tropics) and moved north. I suspect that the net effect of this heat transfer is improved cooling efficiency because thermally driven self-organized systems generally work that way rather than the other way. Even though radiation from the troposphere is much slower, the heat is much more widely distributed; a lot of it is moved over what would have been much cooler ground — it isn’t just low level atmospheric heat transport that matters.

But then things get complicated, still figuring them out.

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280. gbaikie says:

“The layer where the DALR approximately holds is the troposphere, the layer with vertical convective mixing, and it goes away as the ground temperature drops — making it look a whole lot more like an effect, rather than a cause, of warmer ground temperatures.”

I know of no data that indicates DALR “going away”- arctic regions with lack of humidity tend to have around 9 K per 1000- a larger change compared to regions with more humidity.
Inversion layers are common in arctic and inversion layers inhibit lapse rates- they are layers of warm air and are due number of factors.

“Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere. Heresy, I’m sure, on this blog, but there it is.”
A greenhouse effect generally is about “trapping warm gases”, and as such would inhibit a lapse rate. If you created a uniform warm atmosphere, rather than one which cooled quickly with elevation, most people would call that “the greenhouse effect”.
I think if increase the DALR from 9 K per 1000 meters, to 20 K 1000 meter, you need higher gravity and/or denser gas. Oh, I suppose more atmosphere also. If seems to me more or less atmosphere can both reduce and increase DALR- but not sure I can quantify it.
It seems to me if we had 1/2 the amount of our present atmosphere, it would lower the troposphere, and would also increase solar energy reaching the surface. Therefore air temperature might be same or higher at surface and cool in shorter distance of elevation.
And it seems if we doubled the existing atmosphere, less sunlight would reach the surface, have higher troposphere. It seems it would cooler but more uniform temperature. But I doubt such increase of atmosphere would affect the tropics in term heating the surface by very much.
It seems the tropics would have slighter higher or equal height of troposphere, and significantly more troposphere elsewhere. Hmm. Well if doubled atmosphere a certain result would be a doubling of psi- 14.7 to 29.4 psi. This doubling a pressure would not occur in higher elevation- Mt Everest would more psi, but not double. Or as wild guess half of mass of atmosphere would rise by about 1 km.
It seems halving the atmosphere has bigger effect, but neither could increase above lapse 9.8 K per 1000 meters but might lapse rate to be on average closer to 9.8 K per 1000 meters.

281. LazyTeenager says:

Yep. Score is:
skepticism +1
crank science -1

Those coffin nails seem to be bending a lot lately.

282. Thank you Robert Brown. So simple and easy to understand and yet so many here get it wrong.
You are absolutely correct that convection causes the lapse rate. Gravity is an indirect cause. No gravity, no convection.
Solar shortwave heating the ground which by conduction heats the air in contact with it drives the convection. Infrared absorbing gases and water droplets are carried to altitude where they radiate this energy to space and return to lower altitudes. So the “greenhouse gases” keep the system working by providing cooling. Some of the long wave from the ground is absorbed in the atmosphere and convection brings this warmer air to the surface thus making the lower level air a little warmer than otherwise. You do not need to invoke “back radiation”.
BTW the prevailing average lapse rate in the troposphere is close to the SALR (Saturated adiabatic lapse rate). That’s because in many parts of the atmosphere, particularly the tropics there’s lots of water vapor which condenses to form clouds.
One more thing – in the stratosphere the lapse rate is decidedly non DALR because solar UV is absorbed at high altitudes which heats that air and causes higher temperatures at higher altitudes. This effectively puts a lid on the convection. So yes, there is a top to the “greenhouse”, it is called the tropopause.

You cannot break the laws of thermodynamics (there are NO exceptions- the lapse rate article totally misses the point), why does WUWT publish drivel like this to continue to support the failed greenhouse effect??

Again, see the work by the “Dragon slayers” for more info. The sky Dragon is dead, time the world woke up to the fact.

Are you a closet warmist Anthony???

284. LazyTeenager says:

Richard says
Hmmm. Temperature is the integral of the number and energy of particles seen at the measuring surface.
——-
It is not. If it was then temperature would depend on the amount if gas. It does not.

Temperature has nought to do with measuring surfaces either.

It’s really simple. Temperature is related directly to the average kinetic energy of the molecules in the gas. This is year 11 physics.

285. Joules Verne says:

The conversation gets pretty dopey when gravitational potential energy is conflated with thermal (kinetic) energy. GPE does not register on a thermometer. Thus in any atmosphere in equilibrium the temperature decreases as height above the ground increases as thermal energy is exchanged for gravitational potential energy. That atmosphere is isoenergetic but it is not isothermal. It would violate conservation of energy if it were isothermal. An isothermal atmosphere is a fictitious entity that is used for first approximations of gas layers where the layer is not thick enough for adiabatic lapse rate to be a significant factor. No real atmosphere is isothermal. WRITE THAT DOWN, PROFESSOR!

286. wayne says:

A Two Planet Example Refutation of the Refutation of Stable Thermal Equilibrium Lapse Rates

I would like to believe what many of the commenters here seem to believe, that a static column if gases in a gravitational field would be isothermal with no difference in the temperature from the top to the bottom, that is unless this column was continuously warmed adequately from the base to support the rate, only then would it show a DALR (dry adiabatic lapse rate). However, I find that I cannot accept this as I did a couple of weeks ago after detailed consideration of the dry lapses on Venus and Earth.

I spent an hour or so search the archives on the ten Russian Venus Venera Landers for some inkling of the wattage of solar radiation that actually reaches the surface after traversing through some ninety-four masses of the earth’s atmosphere. I never was able to find a firm figure but the brightness was said to be like under a cloudy cover in the summer at any mid-latitude location. I took the mention of summer to mean thick rain clouds and the photos sem to support that conclusion. Seems to me a five-watt flashlight would be equal or brighter when limited to one square meter that that limited illumination so I will use that approximation.

My problem with Robert’s refutation is that Venus itself refutes his conclusions. The ten Russian Landers all recorded a steady lapse rate from about 62 km down to the surface by charts placing the lapse rate found there to be about a mean of 8.2°C/km. The natural DALR can be calculated to be between 7.7 and 12.7°C/km depending on the temperatures, a mean of 10.2°C/km.

Now one last piece of data; Venus reflects 90% of solar rays at the top of the atmosphere. So even though the total solar irradiance is 2614W/m2 there is only 261W/m2 of direct radiation. Due to the high velocity latitudinal winds of 100-300km/hr the dark side actually radiates more longwave radiation that the daytime side. Therefore, unlike the earth we can very well divide the 261W/m2 by four to give a close average of 65w/m2 anywhere on Venus’s surface.

Now, I don’t know about anyone else but I can’t buy that the 5W/m2 at the base of the column and the remaining 60W/m2 of energy whose absorption is evenly spread downward throughout the entire column can cause such a large lapse rate. the Earth has a smaller DALR with about fifteen times of constant energy in fluxed at the base. With Robert stipulation that the column has no energy either input or output, Venus’s atmosphere is about as close as you can get to that condition in our solar system. This is especially noticeable when now turning back to the earth where we have on the daytime side at a minimum average of 240W/m2 absorbed by our atmosphere and surface and nearly four times that when nearly underneath the sun. With all of the energy through our column it only musters a mere 6.5°C/km compared to Venus’s 8.2°C/m2.

Also, how can you believe that somehow Venus’s 8.2°C/km lapse with 65W/m2 warming somehow is operating on the same core physics principle of earth’s 6.5°C/m2 lapse with energy absorption near the base of 240-960W/m2. Makes no sense to me. My physics intuition is throwing up red flags. I watch twice a day radiosondes and overall, they usually do not budge off 6.5°C/km but the small wiggles at cloud levels or rare fronts, 6 a.m. or 6 p.m, no difference.

I conclude that the DALR is in fact real and in effect in every atmosphere and yes, the molecular mean velocities sort in a manner that keeps the KE+PE per unit mass constant at every specific level.

So how does that work, I can only tell you what my intuition says. That gigantic excess energy found at the surface of Venus, right at 17,000W/m2, is not created by the gravity in any stretch of the imagination; actually, it a way, it initially originates from the sun itself ages ago as the atmosphere formed. I’m not saying the photons many millions or even billions of years ago are the same photons found there today but that same level of energy has been residence there on the surface of Venus for a long, long time.

From that time of creation onward it only requires maintenance of that energy level; just enough gain to balance any temporary losses or vice versa and evidentially that 65W/m2 is enough. The potential energy gradient allows the higher temperatures deep inside the gravity well to be physically equivalent in a KE+PE sense and to lower temperatures higher outside the gravity well.

At any level the KE+PE is constant per unit mass when at the DALR unless some variance in the energy pushes the balance one way or the other at that level, you see this in radiosonde skewT plots. If that statis is disturbed the lapse no longer follows the natural DALR as is usually occurring on earth. On earth our atmosphere nearly always has more than enough excess energy in the atmosphere to push it from 9.8 to 6.5°C/km and most of that is due to the always-present specific humidity which merely altering the Cp which alters the instantaneous lapse rate.

I think that is impossible and the molecular velocity sorted DALRs do in fact occur as specified and give a lapse rate base that is the zero rate in all very tall columns.

THE CRUX: What I cannot seem to answer: How can nearly 1,000,000 kg per square meter of atmosphere as on Venus be physically rearranged vertically and lifted against a gravitational field merely by removing 65W/m2 of energy input that is then supposed to be isothermal. There, that is my real logical problem with your conjecture Robert. Excuse the length.

For any to refute me conjecture, just explain in math how these two actual examples do exist as they are while would also transform to a totally isothermal state if all radiation is removed:
Venus: 8.26°C/km DALR — 5W/m2 constant input at the base — 65W/m2 total
Earth: 9.8°C/km DALR — 160-640W/m2 constant input at the base — 240-960W/m2 total

Well, that how I see it. Robert, you almost had me convinced but Venus changed my mind.

287. Joe Born says:
January 24, 2012 at 5:52 pm
Paul Birch: “I have now read the Velasco et al article, and it agrees with what I said: in either the microcanonic (totally isolated) ensemble (with a reasonable number of particles in the gas) or the canonic ensemble (in thermal equilibrium with the surface or walls, irrespective of the number of particles), the gas is isothermal.”

Joe: “Of course, what we’re talking about is the microcanonic ensemble, to which Equations 5-8 apply.”

Actually, we’re not. We’re talking about the canonic ensemble in which, although the container is isolated from the rest of the universe, the gas is in thermal equilibrium with the walls, or, at least, the floor – the planetary surface. However, for any reasonable number of particles, it makes no difference; as Velasco et al themselves point out, in the limit the microcanonic ensemble has to give the same result as the canonic ensemble.

Joe: “If you read Velasco et al.’s Equation 8 for mean single-molecule kinetic energy … ”

As I have pointed out twice already, the isolated (microcanonic) single molecule case is not a thermal system at all. It’s a ballistic system. In this limiting case the concept of temperature has no meaning.

Again I repeat, that, for a tiny number of isolated particles, the statistics aren’t precisely the same as for the usual smooth distribution; velocity and height are not completely separable (Eq 8), and nor is temperature strictly proportional to kinetic energy (see Eq 10). However, even in this extreme case, the temperature at equilibrium will still be the same throughout the entire height, in the crucial sense that no net work could be extracted from the gas by connecting different levels, by any means whatsoever. The “lapse rate” is still zero. Velasco et al does not claim otherwise.

You are still trying to read far too much into a mathematical subtlety you don’t understand, in an extreme regime corresponding to a ridiculously hard vacuum, which has absolutely no relevance either to real planetary atmospheres or to the kinds of thought experiment being discussed in these threads.

Joe: “Presumably, you are basing your interpretation of Levasco et al. on its penultimate paragraph.. ”

No. Unlike you I understand the physics of what they’re doing. I’m not “interpreting” anything – I’m telling you what the basic physics is. I haven’t checked that their gory statistical details are absolutely correct, because they don’t actually matter; they’re of the right general form, and correct in the canonic limit.

Joe: “The real question is, Does Equation 8 define an altitude-dependent temperature or not? If so, there’s a non-zero lapse rate at equilibrium.”

No, it doesn’t.

288. Joules Verne says:

dp says:
January 24, 2012 at 11:11 pm

“This is all stupid. You don’t need gravity or miles tall cylinders. Fill a cylinder with gas to a bzillion PSI. Put it on an atmospherically evacuated centrifuge. Spin it up to 100G. A thousand G – doesn’t matter. Measure the temperature along the length of the cylinder.”

So adiabatic lapse is what, a figment of the imagination?

LOL – an isothermal atmosphere is the imaginary thing that doesn’t exist in the real world.

289. kdk33 says:

rg: Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere. Heresy, I’m sure, on this blog, but there it is.

kdk33: The ALR is a necessary result of convection. It seems to me that, even if all GHG were removed, once radiation warms the planet surface, a small amount of condution to the air just above the surface will start convection, which must follow the ALR. The greenhouse effect overlays on that. It seems to me.

290. Joe Born says:

Dewitt Payne: “But temperature is only strictly proportional to the kinetic energy in the canonical limit and Velasco, et.al. agree that in the canonical limit, the column is isothermal. So you can’t directly convert kinetic energy to temperature for a microcanonical ensemble. Or in other words, your calculation is flawed.”

First, thank you very much for the detailed explanation of your position in the post before last, in which you relied on Velasco et al.’s penultimate paragraph.

Let me preface my response by saying that I read the same passage you did, namely, that “statement (2) is wrong,” and, believe me, I recognize that out of context it is hard to give that passage an interpretation other than yours. Initially I interpreted it much as you and a couple of other folks have. Moreover, that interpretation would have confirmed what I thought I had learned from that Science of Doom discussion the summer before last: at equilibrium the gas is isothermal. I was looking at the paper because, just before, Hans Jelbring told me that my understanding was a popular misconception, so I was looking for a paper to resolve the issue. Certainly, I was looking to choose between two alternatives, i.e., between what I’d previously thought and what Jelbring told me. I was definitely not looking for an interpretation such as I’m now giving the paper, which is different from either alternative.

So why did I come not to accept that the words on which you and others rely meant what they seemed to? The reason is that the equations seem inconsistent with that interpretation. Accordingly, while I respect others’ opinions and am certainly open to being educated her, my interpretation is not just the first thing that popped into my head, and I hope you will indulge me by considering my reasoning and, if necessary, showing me precisely where I’m wrong.

There are two issues. One is the definition of “temperature,” and the other is how that definition applies to Equation 8.

I had heretofore been operating under the assumption that temperature is a measure of mean translational kinetic energy. To find the temperature at a certain altitude, I thought, you add up all the translational kinetic energies of the molecules at the altitude, divide by the number of molecules at that altitude, and divide by the three-halves Boltzmann’s constant.

And (except for dividing by three-halves Boltzmann’s constant) that seems to be what’s going on in Equation 8. As you can see, the authors there compute a mean kinetic energy for an altitude z by integrating, through all possible velocities, the product of (1) the kinetic energy associated with that velocity and (2) the velocity distribution density function evaluated for altitude z at that velocity. That should be a quantity proportional to the kinetic energy per unit vertical distance at that altitude. This quantity the authors divide by the height-distribution function for that height, i.e., a quantity proportional to the molecule density at that altitude. So what I see in Equation 8 is the mean translational kinetic energy at that altitude–which is what I had heretofore thought temperature was a measure of.

But you say, “you can’t directly convert kinetic energy to temperature for a microcanonical ensemble,” from which you conclude that my calculating temperature from Equation 8 is flawed.
This would seem to imply that your view is either (1) that temperature is not mean translational kinetic energy or (2) that Equation 8 doesn’t give mean translational kinetic energy as a function of altitude–even though the authors immediately follow Equation 8 with “i.e., for a finite adiabatically enclosed ideal gas in a gravitational field the average molecular kinetic energy decreases with height.” Could you tell which one your view is and explain why?

I might add in this connection that I am mindful of your statement above that “you can’t directly convert kinetic energy to temperature for a microcanonical ensemble.” Perhaps you based that on the authors’ statement that, for the microcanonical ensemble, “the assumption in statement (2b) [that temperature is proportional to kinetic energy] is wrong.” But, although their expository style leaves entirely too much room for interpretation, my conclusion, based on the Román et al. paper’s discussion preceding the its Equation 41, to which the Velasco et al. paper refers, is that the authors tend to use “temperature” to refer to a property of the whole column, not of a particular height within that column.

I am well aware that I am no physicist and that autodidacts are particularly prone to not recognizing what it is they don’t know. But I am a serious person, and I’ve given this enough thought that I need to have a clear explanation of where I went wrong if I’m to change my mind. Can you give me that?

291. wayne says:

Robert, excuse again. The crux statement was my last typed line and it is very wrong. Why do I always notice such misstatements after pressing the SUBMIT on my way for more coffee☺? This should more read:

THE CRUX: What I cannot seem to answer: How can nearly 1,000,000 kg per square meter of atmosphere as on Venus have the huge thermal gradient removed by merely making there no thermal input at all at the base (remove the 5W/m2 at the surface) and that is then supposed to cause the entire column over time to be isothermal. There, that is my real logical problem with your conjecture Robert.

I’ve been up far too long! Will read the response tomorrow.

292. Kasuha says:

Okay, I stand corrected. The temperature must be constant throughout the whole column however counterintuitive it may seem to be.
I think the most ‘classic’ explanation for it is that at any given height, there are particles which just make it there with their energy being so low that they can’t travel any higher. These particles have absolute zero temperature at that level but as they can’t travel any higher, they are cooling down (or rather decreasing the average) just this level any anything below, leaving the column above untouched. This effect exactly counteracts the kinetic/potential argument’s effect.

293. Joules Verne says:

Robert Brown writs:

I”’m not suggesting that there is no ALR, as a general rule, only that a) it isn’t precise, constant, ubiquitous; b) that it depends on differential heating and cooling and active transport in the atmosphere, and goes away when you stop heating the ground underneath it. ”

Yeah well your suggestion is wrong. In the absence of unequal heating it is precise, constant, and ubiquitous. In the presence of unequal heating it gets different names like environmental lapse rate and saturated adiabatic lapse rate. The most UNstable air masses are temperature inversions where the adiabatic lapse rate is reversed.

Gravitational potential energy does not show up on a thermometer. Yet it exists. Molecules that manage to acquire gravitational potential energy do so by trading off thermal energy for it. Follow the joules.

294. I haven’t read all comments, so forgive me if someone has already mentioned that in the real world you also need to take into account energy released by phase change – this having the effect of reducing the effective lapse rate perhaps by about a third.

Now, using http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps here are my rough (sight) estimates of mean 2011 temperatures (deg.C) at the altitudes shown in feet ,,,,

0 (SS): 21.7
14,000 -19.7
25,000 -35.4
36,000 -46.8
46,000 -55.6
56,000 -62.4
68,000 -58.8
82,000 -51.9
102,000 -43.2
118,000 -33.1
135,000 -21.6

We see 41.4 degrees in the first 14,000 feet, then 15.7 deg in the next 11,000 feet, 11.4 degrees in the next 11,000 feet etc.

Make what you wish of it!

295. Robert Brown – stop before you go mad.

These people here are trolls who don’t want to listen or learn anything.

Leave it… walk away… you won’t ever convince them.

A few are, but some are not. I’m a compulsive teachaholic is the problem. I’m also very patient and very tenacious. I’m perfectly happy to be convinced that I’m wrong, as well, but that won’t happen because somebody says “You’re wrong, and your little dog, too…” but because they offer a cogent and plausible physical argument that is better than my own or discover a fundamental flaw in my reasoning. Both have been known to happen.

That’s why I kept the argument in the top post above simple — limited to addressing only Jelbring and the EEJ paper so we could do adiabatic apples to apples reasoning, limited to a picture that even people who don’t know much physics can understand — anybody who has tried to touch the handle of a heating pan and found it hot to the touch has direct experience of Fourier’s Law, so whether or not they fully understand the algebra they know this happens — and appealing to their intuition as much as to the letter of the various forms of the second law (there are at least four or five that I know of offhand). Accompanied by a proof that a manifestly stable isothermic equilibrium exists for the gas, to put the lie to anyone that wishes to assert that it doesn’t.

The latter is in nearly every introductory physics textbook, including mine — I just grabbed the latex out of my own book to stick in the article. The former required a few minutes to draw a simple picture. At least some people — primarily the ones that aren’t heavily psychologically invested in there being intrinsic “non-Greenhouse heating” of an isolated atmosphere so they could continue to disbelieve in the GHE altogether — seem to get it. Others have offered arguments against it that range from utterly absurd (a matching ALR for heat conduction in a vertical silver wire!) to restating the party line, that an isolated gas with an ALR is in a stable thermal equilibrium (generally not addressing the clear violation that implies via figure 2). A very few have tried to respond by citing work that isn’t overtly terrible done that explores at least the possibility of some sort of lapse rate, if not the adiabatic one (which is almost impossible to justify, given that air isn’t really adiabatic and the atmosphere does not uniformly exhibit the ALR, and flattens or even inverts when relative surface heating is removed).

At this point I’m fairly doubtful that anybody on the list is going to find a good argument against figure 2. Most of the people who appear to actually understand some physics (or are physicists) seem to agree with it; most of the people who oppose it (but not all) appear to not even understand what temperature is, let alone how heat flow is supposed to work. But as I said, I’m open minded and could be wrong. Convince me by addressing figure 2 that there can exist a consistent stable equilibrium with a lapse rate that doesn’t violate the second law. Not with complex stat mech argued verbally while conflating temperature and energy or pressure or whatever — just address the heat flow. I’m offering up a thermodynamic argument, and these are actually more powerful than statistical mechanics. It is rare indeed that a conclusion reached using thermodynamics fails in the statistical mechanics, which is why there has been so much effort expended to ensure that one can do “good” statistical mechanical computations and get results that agree with thermodynamics.

This isn’t easy, even today. It’s why I spent a hell of a lot of time and computational energy on doing Monte Carlo simulations over the last 20 years — it’s often easier to use “brute force” to sample the equilibrium phase space of a system than it is to solve the algebra and calculus to solve a problem “exactly”. That’s why people who have found exact solutions to specific problems, e.g. Onsager, are rather famous. Even for this problem, I’d feel way better about my own answer if I wrote a massive molecular dynamics program and ran a large scale simulation — Joe P. had the right idea for this in another thread, but his simulation was way too small and failed to sample the velocity distribution in various strata.

Anyway, “I’m not dead yet. I’m just sleepin’.” I might leave this thread for a bit and go check on Willis’ “N&Z Equation 8″ thread, where I discovered that their “miracle” fit had characteristic pressures of 54 Kbar and 202 bar, respectively. N&Z were sometimes visiting, and I’d love to hear their response to this.

rgb

296. Myrrh says:

thepompousgit says:
January 24, 2012 at 9:13 pm
MDR said @ January 24, 2012 at 8:35 pm

But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety ["Open a standard introductory physics textbook. Learn what temperature is. Then return."] and not of the collegial variety ["If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?"] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?

That’s the nature of learning; you can only learn for yourself — nobody can ever do your learning for you. At university, you go to the lecture, afterward you do the set reading, exercises/pracs and finally go to a tutorial where you discuss what you’ve learnt and it all gradually falls into place. Most people around here want to skip the lecture, the set reading and exercises/pracs and lecture everyone in the tutorial about how they have it all wrong. Students who do this at university are called failures. That’s in the nature of being a student.

===========

But what we have here is tutorials in which the tutors fall short, discovered when students go away to do their own research, and when said students raise this and ask for explanations they are bombarded with ad homs and told to go read physics text books, which they’ve just done to be able to point out the tutors are saying something different.., and then the tutors arrogantly announce they don’t answer stupid questions hoping they’ll go away when it’s the stupid answers they’ve given that are being questioned.

Examples:

Willis Eschenbach says:
January 24, 2012 at 7:07 pm
George Turner says:
January 24, 2012 at 2:40 pm
George, if you do not know from the context that we are talking about net heat flow through the wire, and not freakin’ brownian movement of electrons, you are not paying enough attention.

I
His bold.

“What has Brownian motion got to do with electrons?”

“And by “net heat”, do you mean the photons from colder to hotter thing?”

Because, I want to know what electrons have to do with Brownian motion, which is about movement of particles in fluids. Because I discovered this when I went away to research this term a couple of years ago having been given this as a reason carbon dioxide gets thorougly mixed in the atmosphere and finding that carbon dioxide was itself part of the fluid etc.

Because, I want to know if Willis is referring to the “heat flows from hotter to colder and colder to hotter to give net flow from hotter to colder” – because if so, I’ve already concluded, from going away and doing my own research, that there’s a missing link in this reworking of the 2nd law.(*)

And now we have the main tutor tell us:

“Because the gas itself conducts heat, you don’t really need the wire. The dry air adiabatic lapse rate isn’t stable because air conducts heat.” when earlier he said air was a lousy conductor of heat.

When physics text books say air is a good insulator, and good insulators are bad conductors of heat and the tutor says they’re both, one has to ask for clarification, perhaps I missed some emphasis or other.

So my question is, what do you mean here?

It’s not lack of willingness on my part to go away and do my own homework.

(*)

http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-871156

http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-872023

Not having science formally beyond ‘high school’ level and what I have learned generally since including reading such range as Lederman, Hawkings and Dawkins, and without easy knowledge of mathematics as bandied about here, I have to rely on the willingness of tutors to engage in English. I’ve been sadly disappointed. I was quite excited to find these discussions and thought I would at last have the pleasure of getting some science education I’d missed out on in having the opportunity to follow such discussions and in having any, I thought, my simplistic, questions answered. Seems these are so simple they’re now avoided altogether by some who claim they are science experts.

So, I don’t know what Robert is saying in any of his replies any more because one moment he is saying that “air is a lousy conductor of heat” and the next “Because the gas itself conducts heat, you don’t really need the wire. The dry air adiabatic lapse rate isn’t stable because air conducts heat.”

297. Joules Verne says:

This is exasperating Professor Brown. Gravity CAN NOT maintain an energy gradient. That would be a violation of 2LoT. We KNOW for a fact that gravity creates a potential energy gradient in an atmosphere. Molecules at higher altitudes have more gravitational potential energy than those at lower altitudes. Therefore, to satisfy 2LoT, there must exist an equal and opposite energy gradient to make up for the gravitational energy gradient. This equal and opposite gradient is a thermal energy gradient. Temperature goes down as altitude goes up in a compressible fluid under the force of gravity. Total energy is equally distributed. No total energy gradient means no work can be accomplished. No harm, no foul, and no perpetual motion.

It’s not wonder that lay people are confused by this when even a Duke physics professor can’t get it right. Academicians are highly overrated. Legends in their own minds, actually. You’re living proof.

298. Smokey says:

Joules Verne says:

“WRITE THAT DOWN, PROFESSOR!”

Is “Joules Verne” another screen name for Dave Springer?

299. Joules Verne says: January 25, 2012 at 4:24 am
“This is exasperating Professor Brown. Gravity CAN NOT maintain an energy gradient. That would be a violation of 2LoT.”

Some people have an infinite capacity for making up stuff about the second law, which they never bother to justify.

300. Not heresy, as nobody would argue that “greenhouse” gases don’t absorb and emit IR and radiate to space. As long as we all understand what we mean by “the greenhouse effect”, then we are all happy here.

“Nobody” and “all” seem to be extravagant based on my tallying of responses on this and other threads, but I’m glad that at least you agree:-).

rgb

301. It is that simple and nothing to do with radiative abilities of molecules of GHG. The so called backradiation from the sky is simply the temperature of the molecules in the air that are directly in front of the sensor.

Or at least it would be if it weren’t for two simple things.

1) For some reason the colder emissions all seem to come from the CO_2 band, and the warmer emissions all seem to come from the ground in the water window band. Clever of those O_2 and N_2 molecules, d’ya think, masquerading as CO_2 by borrowing its spectral structure?

2) Last time I looked, the emissivity of O_2 and N_2 in the entire relevant part of the IR spectrum was pretty much, well, zero. Certainly compared to CO_2 in the CO_2 band.

So it’s just that simple and has everything to do with the radiative abilities of molecules of GHG (in particular CO_2 with a small chunk from the O_3 band in the middle of the water window), as directly demonstrated by the observed IR spectra.

But don’t bother trying to explain the actual data with your explanation, of course. I’m sure there is some other perfectly logical explanation for the IR spectrum, and I’m eager to hear it.

rgb

302. Robert Brown says:
January 24, 2012 at 11:09 pm

“What maintains the lapse rate temperature difference?”

“Mostly gravity.”

Mostly gravity plus the differential heating and cooling. Move your house to Antarctica and look up mid-July. See all that sky that is warmer than you are?

But generally, I agree with your reply. As I stated, my objection is specific to EEJ — the DALR is not a stable thermal equilibrium, which is precisely what EEJ asserts. I’m not suggesting that there is no ALR, as a general rule, only that a) it isn’t precise, constant, ubiquitous; b) that it depends on differential heating and cooling and active transport in the atmosphere, and goes away when you stop heating the ground underneath it. The layer where the DALR approximately holds is the troposphere, the layer with vertical convective mixing, and it goes away as the ground temperature drops — making it look a whole lot more like an effect, rather than a cause, of warmer ground temperatures.

Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere. Heresy, I’m sure, on this blog, but there it is.

rgb

I am pleased to see Robert make this statement. I hope his concerns about Jelbring might be reduced by reference to Hans Jelbring’s new paper, published exclusively at the talkshop.

303. After all your efforts in this thread you have come full circle to that which I told you previously.

Now take one more step. You suggest that the greenhouse effect and gravity work together to MAINTAIN heat differentials.

Look at it slightly differently.

Solar input to the surface together with gravity acting on the atmosphere to cause pressure CREATE the heat differentials (the greenhouse effect) within the atmosphere (primarily the troposphere) which WEATHER and CLIMATE seek to MAINTAIN.

Thus the atmosphere and all the features of it must configure themselves around the lapse rate set by pressure and solar input.

That is the only way that diverse atmospheric compositions can achieve the same outcome on different planets.

To my mind the jigsaw is complete.

Well, it sounds like you are conceding that Jelbring is wrong, and that’s something — or at least the wikipedia page you cite makes it pretty clear that the ALR is due to inhomogeneous heating. That’s my only direct goal at this time in this thread; the rest is mostly just kicking ideas around.

There are only a few things wrong with your “complete” jigsaw puzzle. The first is that you clearly are suffering from serious confirmation bias and cherrypicking disease — the very things we skeptics like to accuse those “warmists” of — when you completely ignore the IR data and its absolutely clear signature of CO_2 causing a roughly 80% reduction of outgoing thermal energy in the CO_2 band specifically. Well, OK, that’s more like trying to pretend that the cherry tree doesn’t even exist, but hopefully you get the point. The second is that it is by no means clear that there would be a DALR in a GHG-free atmosphere, at least one that bore any resemblance to what is observed. There is a strong correspondance between the troposphere/convective zone and the height where the atmosphere becomes transparent to the outgoing CO_2 radiation. Quite a coincidence, you think? Especially where there is a similar correspondance on other planets with greenhouse warming.

What you’d really need to test, or at least support, your assertion is a GHG-free planetary atmosphere, or an atmosphere where GHG emissions don’t seem to define the top of the troposphere. Otherwise you have the embarrassing possibility that a GHG-free atmosphere would simple lower the tropopause to the surface, because there is no mechanism for the atmosphere to cool up there.

That’s the fundamental problem with your argument. You are arguing that it is all adiabatic lapse rate and no actual cooling of the atmosphere needs to occur to maintain it. Yet actual cooling of the atmosphere does occur, right up there at the top of the troposphere, via those miraculous O_2 emissions in the CO_2 band. A not trivial amount of heat leaves through that band. Surely this does, in fact, cool the upper troposphere so the full circulation is not, in fact, adiabatic but is rather convection driven by the absorption of heat one place and its release someplace else.

I’m happy to be convinced that GHG-free atmospheres would establish some sort of equator-poleward major convection rolls that manage to maintain both the lapse rate (at least in the tropics) while only losing heat by moving it from the tropical ground (where it warms) to the arctic ground (where it cools), with both tropics and arctic losing heat only through direct ground-based BB radiation, but I’m a bit shaky on the actual dynamics, because somewhere in there (without cooling that departs from the lapse rate to make the atmosphere unstable) I don’t quite see what is going to force the warm air back down to the ground from any sort of upper troposphere. I have an uncomfortable feeling that the stratosphere would indeed descend almost down to the ground, and most of the circulation would be almost completely lateral convection.

Things that could convince me otherwise — not really any verbal argument, alas. I can do these myself, and just did. I’d have to see some sort of computational model based on good atmospheric convection physics that pops up with the good old DALR to the same old top of troposphere even if there is no actual loss of heat up there.

Doesn’t feel right, does it? It’s not that it couldn’t, but why would it? There is no energetic or entropic advantage to be gained from an isoentropic circulation — the only place you actually increase entropy and irreversibly lose heat (the factor that drives all of those heat transport mechanisms) is where something warms and where it cools, where I mean really cools by irreversibly rejecting heat into a cold reservoir, not just adiabatically moving it around, conserved. There’s nothing that pushes an adiabatic process to occur spontaneously, is there?

So to my mind, your jigsaw puzzle is complete only because you might have, well, forced a few pieces in where maybe they don’t belong…

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304. Some of the long wave from the ground is absorbed in the atmosphere and convection brings this warmer air to the surface thus making the lower level air a little warmer than otherwise. You do not need to invoke “back radiation”.
BTW the prevailing average lapse rate in the troposphere is close to the SALR (Saturated adiabatic lapse rate). That’s because in many parts of the atmosphere, particularly the tropics there’s lots of water vapor which condenses to form clouds.
One more thing – in the stratosphere the lapse rate is decidedly non DALR because solar UV is absorbed at high altitudes which heats that air and causes higher temperatures at higher altitudes. This effectively puts a lid on the convection. So yes, there is a top to the “greenhouse”, it is called the tropopause.

That’s almost exactly the way I understand it as well, so far. I’d argue that the particular mix of things that cause the surface to be hotter is unimportant and might include lots of factors, but the IR spectrum alone tells us that whatever those factors might be, the ground has to be warmer if the CO_2 band is cooler to maintain detailed balance. It’s a strictly empirical conclusion. One can argue about the mechanism later.

As for the tropopause and factors that determine it — UV absorption is good, but one thing that I honestly do not understand is why that happens to correspond to the place where the CO_2 band becomes optically thin. It’s like CO_2 is optically dense all the way up to within a km or so of the tropopause, and then shuts off in the stratosphere. Other planets seem to have a similar structure, top of troposphere coincident with where the GHGs become transparent. I’d love a coherent and physically plausible explanation of why CO_2 more or less “suddenly” becomes transparent and self-consistently stratifies just under the stratosphere. All I’ve heard are question begging things — the stratosphere is where vertical mixing stops (because it is over the troposphere) which is where things still mix but also cool (because it is under the stratosphere and where the GHGs become optically thin). Why doesn’t CO_2 extend up into the stratosphere? Why does water? So much to learn, so little time…

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305. Joe Born says:

Paul Birch and Dewitt Payne:

Perhaps the best way to identify the misapprehension under which you believe I have been laboring in believing that Velasco et al. specify a non-zero lapse rate is to juxtapose the following two passages.

First here is DeWitt’s capsulization: “Nowhere in the paper is there a formula for calculating the magnitude of a non-zero lapse rate in the presence of a gravitational field. This has been pointed out to you in one of the previous threads.”

Then there is the explanatory passage that immediately follows Velasco et al.’s Equation 8, which I have been interpreting as implying a non-zero lapse rate: “i.e., for a finite adiabatically enclosed ideal gas in a gravitational field the average molecular kinetic energy decreases with height.”

Now, I recognize that this does not make Equation 8 “a formula for calculating the magnitude of a non-zero lapse rate in the presence of a gravitational field.” But I had thought that it was an expression for a quantity proportional to the integral of the lapse rate. That is, I would have thought that differentiating that expression for average molecular kinetic energy with respect to altitude would indeed yield a quantity that is proportional to lapse rate. And the result does indeed differ from zero.

Obviously, neither of you agrees. Maybe your telling me why will enable me to see my error.

You cannot break the laws of thermodynamics (there are NO exceptions- the lapse rate article totally misses the point), why does WUWT publish drivel like this to continue to support the failed greenhouse effect??

Again, see the work by the “Dragon slayers” for more info. The sky Dragon is dead, time the world woke up to the fact.

Are you a closet warmist Anthony???

If you want to actually offer a rebuttal of the postulated heat flow in figure 2, play through. The whole point of the article is that any lapse in a closed conductive system does break the second law of thermodynamics. If you agree, then we are good. I don’t really care (at this time) to debate the “failed” greenhouse effect, although I am so very fond of directing people to the satellite IR spectroscopy that as far as I’m concerned is a direct, and I do mean direct, picture of the real live CO_2 mediated GHE. Hard to argue with data so direct it is basically a photograph of the process in action.

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307. The conversation gets pretty dopey when gravitational potential energy is conflated with thermal (kinetic) energy. GPE does not register on a thermometer. Thus in any atmosphere in equilibrium the temperature decreases as height above the ground increases as thermal energy is exchanged for gravitational potential energy. That atmosphere is isoenergetic but it is not isothermal. It would violate conservation of energy if it were isothermal. An isothermal atmosphere is a fictitious entity that is used for first approximations of gas layers where the layer is not thick enough for adiabatic lapse rate to be a significant factor. No real atmosphere is isothermal. WRITE THAT DOWN, PROFESSOR!

The conversation gets very dopey indeed when you steadfastly refuse to address the manifest violation of the second law of thermodynamics illustrated in figure 2 above. But I’m getting tired of asking. I know you can’t do it and — time to move on. If you don’t understand detailed balance and won’t try to understand detailed balance in a system where the mean vertical motion of every gas molecule is zero, there is little that I can do to help you. Gravity cannot do work on a particle unless it goes up or down, and there is zero net transport up or down.

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308. Well, that how I see it. Robert, you almost had me convinced but Venus changed my mind.

Why not just address figure 2? Venus is hardly a closed system, and my article addresses only one thing: Is a lapse rate a stable equilibrium configuration of an isolated ideal gas. The argument that it is not is extremely short and succinct — it is not because a) an isothermal stable equilibrium state exists (proven in the article, although hardly original); b) the arrangement in figure 2 violates the second law of thermodynamics for any vertical thermal lapse. You can’t get much shorter than that.

Venus isn’t even a data point as it isn’t even vaguely isolated. No planet is. The only question before the committee is is Jelbring’s EE paper, which postulates a thermodynamically stable DALR for a completely isolated ideal gas in gravity, correct, or incorrect? The article above proves that it is incorrect. End of story. The DALR itself was hardly Jelbring’s idea, and you haven’t heard me assert that one doesn’t exist. We can argue about its cause later, as long as we agree that Jelbring is wrong now.

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309. Stephen Wilde says:

Robet Brown said:

“What you’d really need to test, or at least support, your assertion is a GHG-free planetary atmosphere, or an atmosphere where GHG emissions don’t seem to define the top of the troposphere. Otherwise you have the embarrassing possibility that a GHG-free atmosphere would simply lower the tropopause to the surface, because there is no mechanism for the atmosphere to cool up there.

That’s the fundamental problem with your argument. You are arguing that it is all adiabatic lapse rate and no actual cooling of the atmosphere needs to occur to maintain it.”

A rotating uneven spherical planet with only non GHGs would radiate very freely from the surface on the night side setting up large temperature differentials and strong winds.

The night side would provide plenty of cooling as the very cold surface sucks energy from the air above via conduction.

It would be a different atmospheric structure to that which we have on Earth but on average globally the solar/pressure induced lapse rate would still prevail. The strength of the winds and the associated turbulence would even out the very steep lapse rate on the day side and the near reversal of the lapse rate on the night side.

In effect that is just what the Earth’s atmosphere does but with the added complications of oceans, water vapour and seasonality.

And a non GHG atmosphere wouldn’t have a true tropopause because on Earth it is a GHG that creates it, namely ozone in the stratosphere.You could say that the tropopause would be on the surface but so what. The surface would still be warmer on average globally than Top Of Atmosphere however defined or identified.The winds would ensure it otherwise the atmosphere would boil away to space or congeal on the ground due to cold.

310. Robert Brown says: January 25, 2012 at 5:33 am

“I’d love a coherent and physically plausible explanation of why CO_2 more or less “suddenly” becomes transparent and self-consistently stratifies just under the stratosphere.”

But does it? Here is a paper which seems to say that there is little variation in mixing ratio up to 33 km.

It seems to me that what happens is that just below the tropopause the optical depth is low enough to allow substantial net emission from CO2 to space. That’s a big heat sink. Above that, UV absorption by ozone is a source. The temperature profile is what you would expect from such a combination.

311. kdk33: The ALR is a necessary result of convection. It seems to me that, even if all GHG were removed, once radiation warms the planet surface, a small amount of condution to the air just above the surface will start convection, which must follow the ALR. The greenhouse effect overlays on that. It seems to me.

Sure, maybe. The question is, where would the tropopause be. 100 meters? 1 km? Without warming below and cooling above, what exactly will make the atmosphere vertically unstable?

Differentially heating a fluid on the bottom (with the top insulated) will, I agree, establish lateral convection. The lateral convection will “pile up” to some extent in order to get enough of a moment arm to drive the flow of heat. But I don’t see any way, or reason, for the vertical convection to reach up to 10 km, or to create anything like the same vertical lapse rate. It might develop a lateral lapse rate, in fact, I rather think that it would.

All of this is very interesting, but irrelevant to my main point above, which is strictly EEJ is thermodynamically wrong and should be ignored. Adiabatic lapse rates are strictly dynamic non-equilibrium phenomena, and IMO at the moment they’d probably nearly disappear without GHGs and upper-atmosphere cooling. At least there I can understand the vertical instability required to drive vertical shear and convection. I’m happy to be schooled otherwise, but it would take a good argument, not a paragraph saying “it is there because I say it is”.

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312. I’ve been up far too long! Will read the response tomorrow.

Yeah, like “all night” for me and it is tomorrow, and I’ve got to go to work. Too bad, but things are winding down anyway and I’m getting pretty wiped out saying the same thing over and over again when people don’t address the actual assertion and proof in the article above and instead redirect to clearly open non-equilibrium systems. Or introduce basic stat mech errors as if they are gospel, while ignoring the more reliable thermodynamics.

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• Anthony Watts says:

Robert, you’ve fought an honorable battle. My advice is to disconnect before the maelstrom of gravity creates an event horizon in Raleigh

313. Gravitational potential energy does not show up on a thermometer. Yet it exists. Molecules that manage to acquire gravitational potential energy do so by trading off thermal energy for it. Follow the joules.

Follow them right around the circle in figure 1 if there is any thermal lapse in equilibrium at all. I can wait all day. I’ve waited all night already.

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314. When physics text books say air is a good insulator, and good insulators are bad conductors of heat and the tutor says they’re both, one has to ask for clarification, perhaps I missed some emphasis or other.

Good, bad, who cares? That’s just setting the timescale for relaxation, which isn’t even close to infinite. The point is that a lapse rate in an atmosphere is thermodynamically unstable. Figure 2 above just makes it easy to see how it violates the second law of thermodynamics.

Maybe you could try, I dunno, explaining how it won’t? Without bullshit assertions like “heat won’t flow up a wire vertically”?

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315. Gravity CAN NOT maintain an energy gradient

I don’t even know what that means, since there are way more particles at the bottom than the top and so on.

Look, I actually gave you a gravitationally stable isothermal solution in the paper above. Why don’t you look at it and explain why the air isn’t in static equilibrium, since I used the condition for static equilibrium and the density of isothermal ideal gas in its derivation?

Then, maybe, you could look at figure 2 and try to wrestly with the thermodynamic instability in the other proposed solution, one with a lapse rate. Personally, I feel pretty strongly about the second law.

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316. ZP says:

While I agree that Jelbring’s assertion for a specific temperature lapse rate is unjustified, I am equally unimpressed by your perpetual motion machine argument to explain why the temperature lapse rate must be zero. From a purely classical thermodynamics point of view, a system is at equilibrium iff dG = 0 (or equivalently dA = 0); dT = 0 or dP = 0 in and of themselves are not the most rigorous definitions of equilibrium.

The criterion for spontaneity is not change in heat nor change in pressure; it is change in free energy. Consider, if the change in heat were sufficient, endothermic reactions would never be spontaneous. Once a system has reached a minimum free energy and dG = 0 (or equivalently dA = 0) throughout, it has reached thermodynamic equilibrium and all macroscopic changes cease. This hypothetical atmospheric system at equilibrium will be described by some T(z) and P(z), but regardless of what the form of these functions take, you simply would not be able to “hook up” a wire and observe anything happening. Hence, failure of your system will not provide proof that the column is isothermal. It only proves that the column is at equilibrium as defined by dG = 0 (or equivalently dA = 0) throughout.

While my gut feeling is that the column would be isothermal, I am not so arrogant as to argue that it must be isothermal. Sans experimentation with accurate measurement of T(z), only a rigorous mathematical analysis of the governing thermodynamic equations will provide a convincing argument. Right now, you have what can best be described a hypothesis based on phenomenological models not subjected to a gravitational field (i.e. dz ~= 0). Therefore, using the most rigorous definition of the equilibrium position (i.e. Gibbs or Helmholtz free energy), please validate your arguments. Clearly demonstrate that the lowest possible value for G (or equivalently A) where dG = 0 (or equivalently dA = 0) occurs iff dT = 0 by clear analysis of the governing differential equation for the equilibrium position. As of right now, you are simply begging the question…

317. Stephen Wilde says:

t”he IR spectrum alone tells us that whatever those factors might be, the ground has to be warmer if the CO_2 band is cooler to maintain detailed balance.”

That ignores the flexibility of the climate system on any planet with any type of atmosphere.

A particular outgoing wavelength my be reduced and admittedly the energy must go somewhere. If it doesn’t warm the surface then there are other ways to deal with it. A faster flow of energy from atmosphere to space would do just fine if it avoids the CO_2 band.

For example, increased conduction to non GHG molecules from GHG molecules would affect the lapse rate of the atmosphere right back to the surface. However there would then be more conduction, convection and on Earth more evaporation from the surface for an increased upward energy flow which would work to maintain the lapse rate set by sun and pressure.

The increase in upward flow would be in wavelengths not ‘blocked’ by CO2.

Atmospheric pressure can only hold back so much energy from leaving to space. Exceed the amount of energy that it can hold back then the surplus just goes straight out by the path of least resistance. The atmosphere has to configure itself accordingly and there can never be any increase or decrease in equilibrium temperature beyond that set by pressure and solar input.

If it were possible for there to be an increase or decrease in equilibrium temperature independently of solar input and pressure then where would it end ?

An infinite number of internal system variables could destabilise the equilibrium temperature to boil off the atmosphere or freeze it on the surface.

That would be the real Perpetuum Mobile.

But virtually every planet we see has an atmsphere of sorts because that hardly ever happens due to the operation of the Gas Laws. Nothing to do with radiative physics at all.

318. DavidB says:

It occurs to me that if Jelbring’s theory were valid, it would apply to liquids as well as gases. (Before anyone replies that liquids are not compressible, (a) they *are* compressible, just not as much as gases, and (b) Jelbring’s argument seems to rely on the existence of a pressure gradient, which can certainly exist in a liquid.)

It is kinda difficult to conduct experiments on a mile-high column of air, but we have known since Torricelli that a 30-foot column of water, or a 30-inch column of mercury, has about the same weight (per unit area of its base) as the Earth’s atmosphere. It would therefore be quite feasible to fill a 30-foot upright tube with water, leave it for a while to allow any heat generated by friction, etc, to dissipate, then measure the temperature at the top and bottom. If Jelbring is correct, it seems, the water should be noticeably hotter at the bottom. Now I can’t claim to have done this experiment with any great precision, but my house happens to contain just such a tube (well, not quite 30 feet), which carries water from the mains supply up to my bathroom. I’ll just check…. Nope, no noticeable difference.

Does anyone disagree with the facts? If they agree with the facts, do they disagree that this (false) hypothesis follows from Jelbring’s theory? If so, what is the relevant difference between gases and liquids?

319. Albert Stienstra says:

Robert Brown’s gas-filled cylinder in a gravity field is identical to a gas-filled cylinder that is constantly being accelerated by a force. The “bottom” of the cylinder, where the force pushes it, is costantly advancing on the gas molecules, like the piston of a bicycle pump, hence increasing the local gas temperature. The top of the cylinder, at the other end, is constantly receding, like a piston that is increasing a volume of gas, thus lowering the local gas temperature. As long as the acceleration is constant, the situation will not change and the temperature difference between top and bottom will exist. Perpetuum mobile? Only when the acceleration remains. Perhaps our time scales are too short to decide what is perpetuus…

320. Richard M says:

As a side note everyone should realize … no matter which side was right it would not change anything relative to the GHE. If there were no radiating gases in a world like this the only place the system could radiate energy is the surface. So, in one case the atmospheric temperature is constant and in the other it cools as you go up. In neither case does it change the surface temperature because the energy in MUST equal the energy out.

The only way to change this is to add radiating gases (and I don’t care if you think N2 and O2 are radiating), and you are left once again with a green house effect.

321. A physicist says:

Robert Brown says: At least some people — primarily the ones that aren’t heavily psychologically invested in there being intrinsic “non-Greenhouse heating” of an isolated atmosphere so they could continue to disbelieve in the GHE altogether — seem to get it.

Robert Brown, your posts so far have served excellently (IMHO) to debunk “gravito-thermal” theories, in large part because your posts have scrupulously adhered to the main principle of The Debunking Handbook (page 5, available free from Richard Dawkins’ website Reason and Science) “Fill the gap with an alternative explanation” … that explanation being:

Nonskeptical Elevator Summary: “Solar heating of the Earth’s surface + GHG heat radiation sustains the nonisothermal / nonequilibrium profile of the Earth’s atmosphere.”

But I think you have to be ready for future skeptical articles that suggest an alternative, more sophisticated non-GHG theory:

Alternative (skeptical) Elevator Summary: “Solar heating of the Earth’s surface + day-night surface temperature cycling sustains the nonisothermal / nonequilibrium profile of the Earth’s atmosphere.”

To my mind this second, skeptical, non-GHG theory cannot be debunked primae facie, and so I will bet anyone a donut that such theories will appear as WUWT posts in the coming weeks and months.

322. Joe Born says:
January 25, 2012 at 5:34 am
“I would have thought that differentiating that expression for average molecular kinetic energy with respect to altitude would indeed yield a quantity that is proportional to lapse rate. And the result does indeed differ from zero.”

You would have thought erroneously – as has already been explained to you repeatedly. You are wilfully taking the extreme and irrelevant sub-thermodynamic case of a minuscule total number of isolated particles – in which regime the macroscopic temperature is increasingly ill-defined and no longer simply proportional to the kinetic energy per particle – and torturing it to produce something that looks a bit like a macroscopic lapse rate, but is really nothing more than a mathematical artefact of absolutely no significance. There is and can be no real lapse rate at all – if there were it would violate the second law.

323. Joules Verne says:

Just to be clear – the adiabatic lapse rate which is caused by gravity does not make the surface any warmer than it would be otherwise. All that happens, as at least one other commenter noted, is that it makes upper layers colder than than they would be otherwise. Nothing happens except that kinetic energy becomes gravitational potential energy with increasing altitude. The kinetic energy of the surface atmosphere is the same regardless. Nikolov et al are still wrong. It just needs to be made clear they aren’t wrong about gravity creating a temperature gradient. They’re just wrong about gravity raising the temperature anywhere in the column. It doesn’t. All it does is change the way total energy at any given altitude is apportioned between kinetic and potential.

324. Joules Verne says:

DavidB says:
January 25, 2012 at 6:45 am

It is kinda difficult to conduct experiments on a mile-high column of air, but we have known since Torricelli that a 30-foot column of water, or a 30-inch column of mercury, has about the same weight (per unit area of its base) as the Earth’s atmosphere. It would therefore be quite feasible to fill a 30-foot upright tube with water, leave it for a while to allow any heat generated by friction, etc, to dissipate, then measure the temperature at the top and bottom. If Jelbring is correct, it seems, the water should be noticeably hotter at the bottom. Now I can’t claim to have done this experiment with any great precision, but my house happens to contain just such a tube (well, not quite 30 feet), which carries water from the mains supply up to my bathroom. I’ll just check…. Nope, no noticeable difference.

Nice. Now consider two equally sized buckets of water. One on the top floor and one on the lower floor. Both buckets are the same temperature. Do they each have an equal amount of energy? No. The bucket on the upper floor has more gravitational potential energy. That energy had to come from somewhere. It came from whatever force was used to lift that water to the higher elevation. If you carried it then that extra energy came from the food you ate.

There’s no such thing as a free lunch. Follow the joules. One MUST account for the source of gravitational potential energy! In reality, despite pleadings to the contrary from sources who should know better, gravity creates the dry adiabatic lapse rate. The gravitational potential energy in the higher layers came from its store of kinetic energy. The Hamiltonian of all horizontal layers is constant but the kinetic energy apart from the potential energy is not.

325. IanH says:

What an interesting perpetual motion machine. We need a solid state physicist. Someone who knows the Debye theory of heat in solids. Someone who thinks that heat is transferred by phonons, and that phonons have a characteristic momentum (mass and velocity). So if a phonon moves uphill against gravity it must loose momentum – and energy because it is, in effect, an upward moving mass. I suggest that the wire too will have an ‘adiabatic lapse rate’ (temperature gradient in a gravity field) because of the nature of heat – and heat transfer – in solids.
Solid state physicists are sensitive creatures and would probably not post here for fear of getting a rhetorical custard pie in the face (even if they made a correct point).

326. DavidB says:

Joules Verne didn’t answer my questions. Does he think the water at the bottom of the pipe is warmer than at the top? If not (and his ‘buckets’ example suggests not) when why does this not follow from Jelbring’s theory? What is the relevant difference between air and water?

327. A. C. Osborn says:

DavidB says:
January 25, 2012 at 8:44 am Why on earth would you think that a 30ft column of incompressible water would react the same as a Miles high atmosphere of compressible GAS???

328. Joules Verne says:

@Robert Brown

I’m not sure what you’re going on about in figure 2. The silver wire is a proxy for thermal conduction in the gas. Thermal conduction is accomplished via collisions. In the absence of gravity there is no preferential direction for collision energy. In a gravity field there is a preference. A molecule travelling upward loses thermal energy as it ascends and gains thermal energy as it descends. A molecule getting whacked from above gets hit harder than one getting whacked from below if everything else is equal.

Let’s take the situation of me throwing a rotten tomato at a Duke physics professor on his lecturn. I might be throwing it from the balcony or I might be throwing it from the orchestra pit. In either case the energy I can add to the tomato with my arm is the same. If I have a choice I’m going to choose to throw from the balcony of course for the obvious reason that gravity is an aid in one direction and a restriction in the other. Thermal conductivity in the gas works the same way. Kinetic energy is preferentially sequestered at the bottom of the gravity well and gravitational potential energy is sequestered at the top.

What part of that do you not understand?

329. Stephen Wilde says:

“They’re just wrong about gravity raising the temperature anywhere in the column. It doesn’t. All it does is change the way total energy at any given altitude is apportioned between kinetic and potential.”

I thought N & Z said that pressure raises the temperature in the denser gases at the bottom of a column when an external energy source is added, not that gravity did it directly.

Gravity just places more energy at the bottom of the column by pulling molecules downward to creater greater density and pressure at the bottom. In the process it does apportion some of the available energy as you say.

I think Jelbring might be suggesting a separate purely gravitationally induced temperature gradient but I’m not convinced that it is significant as yet.

“Does he think the water at the bottom of the pipe is warmer than at the top? ”

As regards water in a column the difference is that water is incompressible and so upward convection dominates and the warm water rises to the top.

The compressibility of a gas results in the higher temperature being at the bottom at all times.

That accounts for the different temperature profiles in oceans and air despite both being affected by pressure.

330. Smokey says:

“Joules Verne” says:

“What part of that do you not understand?”

Is “Joules Verne” another screen name for Dave Springer?

331. IanH says:
January 25, 2012 at 8:28 am

“What an interesting perpetual motion machine. We need a solid state physicist. Someone who knows the Debye theory of heat in solids. Someone who thinks that heat is transferred by phonons, and that phonons have a characteristic momentum (mass and velocity). So if a phonon moves uphill against gravity it must loose momentum – and energy because it is, in effect, an upward moving mass. I suggest that the wire too will have an ‘adiabatic lapse rate’ (temperature gradient in a gravity field) because of the nature of heat – and heat transfer – in solids.”

It wouldn’t matter if it did. So long as the adiabatic lapse rate is not fixed to the same value for every possible material (which we know it isn’t), there will be an exploitable temperature difference somewhere in the system.

Look, if phonons confuse you, forget the solid wire. Just divide the container with a vertical insulating partition. Put a light gas (say, helium) on one side, and a heavy gas (say, argon) on the other. The lapse rate will be less in the former than the latter (in this case by the ratio of molecular weights). Make a short horizontal connection at the top and the bottom, and presto there’s your perpetual motion machine.

332. Joules Verne says:

DavidB says:
January 25, 2012 at 8:44 am

“Joules Verne didn’t answer my questions. Does he think the water at the bottom of the pipe is warmer than at the top?”

It will be warmer at the bottom to the degree that water is compressible. In order for there to be a temperature gradient established there must also be a density gradient. In the water column we have no practically detectable density gradient and hence no practically detectable temperature gradient. If it were water vapor you betcha there’d be a temperature difference we could measure even at 30 feet. It would be about 0.1C warmer at the bottom of the pipe.

333. A. C. Osborn says:

The whole point is that if you could achieve the totally impossible conditions that Dr Brown proposes for his thought experiment, you probably would have a perpetual motion machine. After all to get the conditions proposed would take magic in the first place.
It is an imaginary concept, so is Alice in Wonderland.

334. mkelly says:

DavidB says:
January 25, 2012 at 8:44 am
“What is the relevant difference between air and water?”

Air is compressible and water is not. Air is seen under natural circumstances to flow up hill water has not. Would you rather have a hot water bottle keeping you warm at night or the same volume of warm air trying to do the same thing? There are lots of relevant differences between air and water?

335. Myrrh says:

Joules Verne says:
January 25, 2012 at 4:24 am
This is exasperating Professor Brown. Gravity CAN NOT maintain an energy gradient. That would be a violation of 2LoT. We KNOW for a fact that gravity creates a potential energy gradient in an atmosphere. Molecules at higher altitudes have more gravitational potential energy than those at lower altitudes. Therefore, to satisfy 2LoT, there must exist an equal and opposite energy gradient to make up for the gravitational energy gradient.

Well, I still haven’t worked out what any of you are talking about.., but isn’t the opposite and equal energy gradient to make up for the gravitational energy gradient, pressure? That wot gives buoyancy. More noticeable in the ocean though, but applied to the fluid gas volume of air above us.

“Archimedes’ principle applies to air as well as water: a force equal to the weight of the air displaced buoys up an object surrounded by air.”

“We scarcely think of air at all; it’s just so nebulous and pervasive. But our atmosphere has considerable mass because it towers at least 50 miles (80 km) above Earth’s surface into space. Air provides a buoyant push just as water does. A column of air that extends from sea level to space with a tiny postage-stamp size cross sectional area — one square inch — weighs almost 15 pounds and, consequently, exerts a pressure of 15 pounds per square inch on the bottom of the column.”

“Imagine an air parcel immersed in the ocean of air that is our atmosphere, as shown in the figure. The surrounding air presses in on the air parcel from all directions but the pressure along the sides of the parcel are equal and opposite and thus cancel.

The pressure on the top of the parcel is less than the pressure at the bottom (since pressure decreases with altitude). That pressure difference is the buoyant force — the force that pushes up on the air parcel.

The air parcel, however, has mass and therefore weight. Gravity pulls it down. If gravity’s pull is less than the buoyant upward push, the parcel rises. If gravity’s pull is greater than the buoyant push, it falls.

If the parcel contains light hot air from a flame, then gravity’s pull is less than the buoyant push. That’s why fire goes up.”

336. Joules Verne says:

Smokey says:
January 25, 2012 at 9:10 am

“Is “Joules Verne” another screen name for Dave Springer?”

Presumably the laws of physics would remain the same either way so I’m going to plead the fifth on that question.

337. DeWitt Payne says:

Wayne,
The Venus atmosphere was discussed at length in a couple of threads at Science of Doom. I did find a reference to the solar radiative flux at the surface when the sun is above the horizon on Venus and the peak is about 36 W/m². That was sufficient for Venera 9 (I think) to be able to make visible light photographs of the surface and transmit them back to Earth. I also ran the radiative transfer calculations for the atmosphere and the lapse rate at Spectralcalc and that flux is indeed sufficient to maintain the lapse rate against radiation and conduction. If the atmosphere of Venus became truly opaque to incoming solar radiation at some altitude above the surface, the atmosphere below that point would be isothermal assuming no heat input to the surface from the core of the planet.

338. DeWitt Payne says:

Stephen Wilde and mkelly,

Water is incompressible.

Nope. Water can be compressed, just much less than air. From Wikipedia:

The compressibility of water is a function of pressure and temperature. At 0 °C, at the limit of zero pressure, the compressibility is 5.1×10−10 Pa−1.[27] At the zero-pressure limit, the compressibility reaches a minimum of 4.4×10−10 Pa−1 around 45 °C before increasing again with increasing temperature. As the pressure is increased, the compressibility decreases, being 3.9×10−10 Pa−1 at 0 °C and 100 MPa.

The bulk modulus of water is 2.2 GPa.[28] The low compressibility of non-gases, and of water in particular, leads to their often being assumed as incompressible. The low compressibility of water means that even in the deep oceans at 4 km depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume.[28]

But not no decrease in volume. That means a water column has a potential temperature just like air.

339. Bryan says:

Paul Birch says
“Look, if phonons confuse you, forget the solid wire. Just divide the container with a vertical insulating partition. Put a light gas (say, helium) on one side, and a heavy gas (say, argon) on the other. The lapse rate will be less in the former than the latter (in this case by the ratio of molecular weights). Make a short horizontal connection at the top and the bottom, and presto there’s your perpetual motion machine.”

Does it not give you pause to think why none of these seemingly very simple methods have been tried?
Robert Brown towards the end of the previous thread said that he wished he could demonstrate his conjecture by an experiment.
He is thinking along the lines of a centrifuge.

340. Paul Bahlin says:

Everyone assumes an ideal gas as a starting point in these treatments , based I presume, on the correct assumption that nitrogen, oxygen, and even CO2 closely approximate the definition of an ideal gas, duh. Here’s the thing though. This is an argument about the gas, in an of itself, i.e. it ignores the gas’ context.

Here’s my dilemma. One of the premises made regarding an ideal gas is that there are no inter-molecular collisions in an ideal gas and this is done so as not to introduce a ‘wall bias’ where molecules near a wall experience (inter-molecular) vector forces that tend to pull them away from the wall. The problem is that a gas constrained by gravity is unavoidably subjected to a ‘gravity bias’, irrespective of how ideal it is, as a function of its container.

With gravity as your container, any gas no matter how ideal, is being subjected to a force (gravity) that biases collisions and (i would think) completely invalidates any assumption of ideal behavior, doesn’t it?

341. Joules Verne says:

The centrifuged cylinder of gas is a great example that someone brought up.

As the centrifuge spins up a pressure gradient is set up. What does the ideal gas law demand will happen to temperature as the pressure increases at one end of the cylinder and decreases at the other?

As the centrifuge spins down the gas at one end of the cylinder expands and at the other end it contracts. What does the ideal gas law demand must happen in this case?

It’s a given that no one here is willing to cast aside the ideal gas law we should all agree that spinning up and spinning down the centrifuge will create at least a temporary temperature/pressure gradient predicted by the ideal gas law.

So the question boils down to what happens when the centrifuge is left running indefinitely. Does the column temperature equalize? I say no because for conduction to equalize the temperature there has to be equal freedom of motion in any direction and this clearly isn’t the case. Freedom of motion is restricted going against the centrifugal force and is aided going in the direction of the force. The temperature will not equalize if we discount conduction through the solid walls of the cylinder. If we stuck a silver wire down the center of our cylinder as in Brown’s figure 2 the temperature would equalize because the thermal conductivity of the silver wire has no preferential direction due to centrifugal force.

I’m trying as many ways as I can think of to explain what I know must happen and how. So now I’m trying it via illustrating that thermal conductivity coefficient changes in a compressible fluid with greater conductivity going with gravity and lesser conductivity going against gravity. This does not happen with incompressible fluids.

Does that help? It should certainly help to explain to Brown why his silver wire is not a valid proxy for thermal conduction in a compressible gas in a gravity field.

342. DeWitt Payne says:

Robert Brown,

The way to think about the difference between the stratosphere and the troposphere is to use the slab gray atmosphere toy model ( see 7.3.2 here, for example. Petty goes into more depth). In the troposphere, the atmosphere is more transparent to SW radiation and less transparent to LW radiation so the surface temperature is warmer than the slab. The opposite is true in the stratosphere. The stratosphere is less transparent to SW radiation because of absorption of UV by oxygen and ozone and more transparent to LW radiation. That makes the ‘surface’, i.e. the tropopause, colder than the slab.

343. Tim Folkerts says:

Paul Birch says

So long as the adiabatic lapse rate is not fixed to the same value for every possible material (which we know it isn’t), there will be an exploitable temperature difference somewhere in the system.

AMEN, BROTHER!

344. Myrrh says:

Robert Brown says: “At least some people — primarily the ones that aren’t heavily psychologically invested in there being intrinsic “non-Greenhouse heating” of an isolated atmosphere so they could continue to disbelieve in the GHE altogether — seem to get it. ”

Shrug, industry figures give 67°C for our atmosphere without greenhouse gases. The mass/weight/gravity/pressure/ play of the fluid gaseous ocean of nitrogen and oxygen above us is the greenhouse/thermal blanket around the Earth. Adding some fibres of water vapour in the Water Cycle cools that by 52°C to bring it down to the 15°C we have. Carbon dioxide fully part of the water cycle, all pure clean rain is carbonic acid, can only aid the main greenhouse gas water vapour in its role of cooling.

For goodness sake, just step out into a desert to get some grasp on this.

345. DavidB says:

I’m well aware that air is more compressible than water (though not incompressible), which is why I mentioned it when I introduced the example, to anticipate an obvious objection. But is that a relevant difference in the context of Jelbring’s theory? I thought that depended on a pressure gradient, which does exist in the case of water.

But at least we have made progress if it is accepted that the Jelbring theory depends on compression. Of course, it is true that a gas can be heated by compression, as I mentioned in an earlier comment on this thread. If you take a long horizontal cylinder of air and then raise it to vertical, the gas at the (new) bottom of the cylinder will be compressed and heated, while the gas at the top will be rarified and cooled. A temperature gradient will thus arise. But that is a one-time effect which fades as heat flows from hotter to colder areas, in accordance with the Second Law. It does not explain how a permanent gradient is maintained in a planetary atmosphere.

346. @joules >>>>It’s a given that no one here is willing to cast aside the ideal gas law we should all agree that spinning up and spinning down the centrifuge will create at least a temporary temperature/pressure gradient predicted by the ideal gas law.

I would hazard a guess that by now, millions of hours of gases being spun in gas centrifuges have been completed over the past decades, all around the world. Uranium hexafluoride used U-235 / U-238 separation processing. There is probably data on gas temperature profiles available somewhere.

347. A physicist says:

Bryan says: Does it not give you pause to think why none of these seemingly very simple methods have been tried? Robert Brown towards the end of the previous thread said that he wished he could demonstrate his conjecture by an experiment. He is thinking along the lines of a centrifuge.

Just to reiterate, this experiment is being conducted, tens of thousands of times every day, in the gas centrifuges used for uranium isotope separation, which generate g-forces sufficiently large that the on-axis pressure is a near-vacuum, which the outer-rim pressure is many atomospheres — precisely the conditions of interest.

These gas centrifuge “experiments” concretely affirm Brown’s theoretical arguments: the observed equilibrium temperature distribution is isothermal. Indeed, the multibillion-$isotope separation industry would fail otherwise. For more theoretical and experimental details than most folks want to know, see @article{Kemp:2009lr, Author = {R. Scott Kemp}, Journal = {Science and Global Security}, Number = {1}, Pages = {1–19}, Title = {Gas Centrifuge Theory and Development: a Review of US Programs}, Volume = {17}, Year = {2009}} and references therein (a Google search will find it). Elevator Summary: “Gravito-thermal” theories are just plain wrong. 348. Joe Born says: Paul Birch: Thank you for your recent posts. I apologize for not having acknowledged them in my most recent one; I somehow failed to see yours before I sent mine. I believe I now understand your position, and, as you say, it is entirely possible that I am “trying to read far too much into a mathematical subtlety [I] don’t understand,” although I see no evidence so far from which to conclude that. However that may be, I’ll give some feedback in case any lurkers find the issue of interest. First to your contention that we are not talking about the microcanonical ensemble. Here a little context is in order. Recall that both Robert Brown in this thread and Willis Eschenbach in the previous one were addressing themselves to refuting the Jelbring paper. That paper began with a hypothetical ideal gas G disposed between concentric spherical surfaces A and S. Jelbring said that “A and S are thermally insulated preventing heat from entering into G and infrared radiation to reach space.” It is no doubt to parallel this condition that Robert Brown says of his thought experiment that it involves an “adiabatically isolated column of an ideal gas.” In short, heat can flow neither into nor out of the gas, so by definition it is indeed a microcanonical ensemble. Next I consider your statement that “for any reasonable number of particles, it makes no difference” whether we’re dealing with the microcanonical ensemble or not. I agree with you that as a practical matter any lapse rate as small as I’m saying Equation 8 implies would be too small to measure. But, again, the context needs to be considered. What Robert Brown and Willis Eschenbach are both saying is that any non-zero lapse rate at all would violate the First Law because there would be a perpetual heat flow through the external wire. Had they instead based their proofs on a lapse rate of the magnitude for which Jelbring contends, then I would agree with them that they had proved their case. But they insisted that they needed no such limitation. So any non-zero lapse rate is relevant, no matter what its magnitude is. So the microcanonical ensemble is indeed relevant to the issue under consideration. You make two further points that at base are not technical arguments so much as statements of your point of view. You say, “However, even in this extreme case, the temperature at equilibrium will still be the same throughout the entire height, in the crucial sense that no net work could be extracted from the gas by connecting different levels, by any means whatsoever.” Essentially you’re saying that even if a difference in mean translational kinetic energy is non-zero, it doesn’t qualify as a lapse rate in your view if it’s exhibited by a maximum-entropy configuration and therefore results in no net heat flow. Okay, I understand your redefinition. You additionally observe that I am “taking the extreme and irrelevant sub-thermodynamic case of a minuscule total number of isolated particles – in which regime the macroscopic temperature is increasingly ill-defined and no longer simply proportional to the kinetic energy per particle.” Let’s set aside what exactly you may mean by imprecise terms like “sub-thermodynamic,” “macroscopic,” and “increasingly ill-defined.” And let’s concede that the case I discussed was an extreme case. That case nonetheless remains relevant, because it illustrates by exaggeration something that remains true independently of how large the number of molecules gets: the mean molecular translational kinetic energy decreases with height, and it does so at a rate that is finite and non-zero, albeit negligible for most purposes. In any event, I think these on-line interchanges have the potential to be enlightening, and, although I can’t profess to have made any great strides in this case, I do appreciate your making the effort. 349. Crispin in Waterloo says: @Robert “In figure 1 above, an adiabatically isolated column of an ideal gas is illustrated.” It has been a great week to review the basics of physical phemonena. I have been serially convinced by many contributions in opposite directions. I agree that there is a conduction issue as you have pointed out, Robert, but a guy named Kevin and I agree that it is not going to create an isothermal condition. If the atmosphere does not conduct heat (which seems to be Jelbring’s assumption) it is an unreasonable experiment. But you can’t have lots of conduction just because it is convenient. It has to be realistic. If the atmosphere was warmer at the top than the bottom, it would have stable and unequal temperature distribution. The reason is that gases are really lousy conductors of heat, especially downwards, meaning downwards in a gravity field. Bouyancy can override conduction in this theoretical atmosphere in some cases. In your example above, the gas is treated as if it was a solid at certain times, which it clearly is not. It has to be discussed as a gas at all times. You have mentioned several times that if the gas moves it has to have a driver (some work going on). But gas is always in motion – perpetual motion as far as we know – and also we know that individual molecules contain more energy than their neighbours. Many energetic molecules of gas are literally hotter than the others. There are gazillions of molecules in continuous motion with no energy input from outside the column. At any time that on average a group of molecules is slight hotter and lighter than a neighbouring group, they separate with the hotter ones rising slightly because of bouyancy. This is gravitational separation that is not caused by the density of the molecule, but by the well known convection principle applied at the molecular level. Will conduction overwhelm this? I am raising that question. Left alone, there are two forces opposing each other: the tendency of hot gases to rise and cool gases to fall, opposed by conduction that tends to average the temperature in the system. If on average the temperature of a gas is some fixed value, we know that is an average. If molecules of gases and even water behaved like the average, water would not evaporate from a pot at 80 Deg C. The isolated, undisturbed column would tend to separate the more from the less energetic. Also, it is known that as the gas pressure tends to zero, conduction reduces faster than the tendency of hotter molecules to rise. This creates a bias in favour of thermal segregation, assisted by gravity. At some point either in the entire column, or near the top, it will be hotter above and cooler below and this condition will be permanent on condition that the bouyancy exceeds the thermal conduction at that pressure (and gas characteristics). A silver wire conducting heat from the top to a point where it is cooler will indeed see heat flowing continuously (and slowly). That is not perpetual motion any more than the vibrating and moving gas molecule is perpetual motion (as we normally mean it). For heavens sake, people, do not interpret this heat flow as being able to ‘do work’ unless the system is cooled as a whole. There is no free lunch! The movement of heat through the silver wire is not perpetual motion and thus ‘ruled impossible’. Yes the heat will flow continuously, as fast as the hotter molecules can rise in the gravitational field. Heat transfers from one molecule to another continuously and we do not call that transfer of heat ‘perpetual motion’ capable of being tapped for ‘doing work without an input of energy’. It is just a characteristic of gases. Energy flows all the time in stable conditions we view (on average) as unchanging. As far as I understand adibatic cooling, it will not prevent the more energetic molecules from rising. If it does for some reason I can’t see, then a different temperature profile will prevail (possibly a different one foreach unique gas). Save in special cases, not all of the column can be isothermal. 350. The whole point is that if you could achieve the totally impossible conditions that Dr Brown proposes for his thought experiment, you probably would have a perpetual motion machine. After all to get the conditions proposed would take magic in the first place. It is an imaginary concept, so is Alice in Wonderland. The totally impossible conditions like the adiabatic planet discussed in EEJ. Have you even read the paper that this whole discussion refers to? Besides, these aren’t “totally impossible conditions” at all, not for discussing whether or not an adiabatic lapse rate is a stable equilibrium. The point isn’t that I’ve designed a perpetual motion machine — the point is that a stable thermal equilibrium of an isolated ideal gas with a lapse rate violates the second law of thermodynamics. The proof, my friend, is by contradiction — if one postulates that an isolated ideal gas is in a stable equilibrium with a lapse rate, I’ve shown that it enables a perpetual motion machine to be built. That is a sufficient thermodynamic proof that the postulate is untrue, as it leads to an impossible conclusion. I did it this way because it avoids arguing about the details of straightforward (but far more difficult) textbook calculations that directly show that the equilibrium is the isothermal state I describe above, or the much more difficult calculation in stat mech that directly shows that the equilibrium is the isothermal state that I describe above. I’ll probably eventually put the detailed balance demonstration up that the equilibrium is the isothermal state that I describe above. This is entirely relevant to the laboratory. After all, if you take an empty thermos bottle and set it on a desk, it either has a stable adiabatic lapse rate (after a reasonably long time) or it is isothermal equilibrium precisely like I describe above. The difference would be difficult to measure, but the implications are profound. One of the first things almost any intro book on stat mech or thermodynamics does is demonstrate that thermal equilibrium is isothermal — the zeroth law of thermodynamics. If I stick a thermometer in at the top of static, isolated air column, and it reads some temperature, and I stick it in somewhere else and it reads another temperature, the zeroth law clearly states that the two locations (with different temperatures) are not in thermal equilibrium. It clearly states that connecting them with any sort of conducting pathway will cause heat to flow — it is really pretty trivial to look at the distribution of microstates and show that equilibrium will have the same temperature. The gas itself is always such a conducting pathway. Asserting that a thermal equilibrium exists in some straightforward, isolated, thermally connected system that has sat around for many thermal relaxation times that has a macroscopic distribution of local temperatures isn’t trivial. It is a complete and utter disaster for all of thermodynamics. The second law is only the first consequence. Which one is more likely: All basic thermodynamics and stat mech textbooks are wrong, including the ones that make showing that there is no lapse rate a homework problem or that do it in the actual text, or some people who have a really hard time understanding what a degree of freedom is or how to do an integral or mess with logarithmic expansions have made a mistake, the biggest of which is assuming that the DALR worked out in climate systems is stable in the absence of a driving thermal gradient and that air is locally truly “adiabatic”, instead of just having a thermal conductivity that is slower than convection? Anyone who can’t understand this simple presentation is going to have enormous difficulties with the more complex ones. Sorry about that, but that’s the way it goes. 351. Sorry about the accidental italics inversion too. Truly wish for edit and preview, I do. rgb 352. Trick says: Robert Brown says 1/25 at 12:09am: “Turn to page 36. Read section 2.17. Work through it carefully…” Thank you Robert, now you are engaging in calm scientific discourse. This is interesting progress. I have worked thru Caballero sec. 2.17 page 36 very s-l-o-w-l-y & carefully. I return. I note that in section 2.17 to develop the temperature field eqn., Caballero refers us to Fig. 2.3 for the gas in a pipe where it is assumed to quote Caballero: “…consider a pipe of cross-sectional area A containing an ideal gas with an isotropic velocity distribution (Figure 2.3).” Isotropic velocity! So there is NO gravity field used to develop the temperature field in Caballero 2.17. There is no g in temperature field equations 2.74 or 2.75 by inspection. They are pretty obviously not dependent on the g field in z direction. Caballero in 2.17 writes for no gravity & I quote: “Thus, heat flows down the temperature gradient (from hot to cold) and ceases to flow when temperature is uniform, exactly as required by the Second Law. A more precise calculation using the full apparatus of kinetic theory gives the same qualitative result.” This proof you have referred me to is for the isotropic velocity/temperature field ideal gas NOT in gravity field. Yes, I grok this previously & agree w/o gravity: the temperature field will be isothermic from 1st law b/c the velocity hence KE from top to bottom does not vary – no g temperature field is indeed uniform as this isothermal derivation shows. Caballero here in 2.17 is NOT talking about hydrostatic equilibrium temperature with dp/dz non-zero in a gravity field where the velocity and KE of the molecules vary. In fact, for gravity field acting, Caballero agrees the temperature field is non-isothermal as the mean velocities vary from top to bottom of the air column in sec. 2.3 where he does add the gravity field: “…this time we’ll add the effect of gravity….the effect is quite interesting:… Mean velocities will be greater near the bottom of the box than near, the top…” Read that slowly again, the temperature field in the presence of gravity Caballero shows it is non-isothermal in the up/down direction. You cannot refute a non-isothermal science paper based on sending me to isothermal examples. Robert continues: “Then be sure to do exercise 2.17. I quote: Exercise 2.17: Extend the argument above to show that (2.75) also applies to a vertical column of air in hydrostatic equilibrium.” Eqn. 2.75 just shows the “net rightward flux” where even in hydrostatic equilibrium, dp/dx =0 which is what it takes to derive 2.75 in the isothermal case. This is trivial for hydrostatic case, since we are really interested in temperature field z variance with non-zero dp/dz. I could agree air column temperature is isothermal horizontally even in the presence of gravity. Robert Brown has not yet shown how temperature could possibly be isothermal in the air column z direction in the presence of gravity to refute any science paper esp. when Caballero relying on “Bohren and Albrecht’s excellent Atmospheric Thermodynamics” tells us above in sec. 2.3 the z temperature field in the presence of gravity is non-isothermal. Robert Brown continues: “Goodness, could Caballero be saying that thermal equilibrium is isothermal, regardless of whether you move up or down in a static air column? Even in Climate Science? Do you think? Is he asking you to (gasp) actually prove it? Well heck, it ought to keep you out of trouble for a while. Give it a shot. In the meantime, meditate upon that “exactly as required by the Second Law” bit. It’s important!” Yes, Caballero in velocity isotropic pressure sec. 2.17 is saying thermal equilibrium is isothermal regardless whether I move up or down in a static air column with no gravity field. Yes, I think that’s obvious even in climate science; I gave it my shot. It did indeed keep me out of trouble for awhile and I did meditate some more on the 2nd law, it is really pretty interesting. However, Robert Brown still has to find a refuting ref. to cite in order to support Robert Brown’s refuting theory that temperature is isothermal in the gas column of interest in the presence of gravity where M-B cannot be invoked due to M-B applying only to the special case of no gravity. Otherwise proper application of 0th, 1st,2nd & Caballero does refutes top post. Cabellero teaches: an adiabatically isolated column of gas in a gravitational field CAN have a thermal gradient maintained by gravity. Robert Brown’s thermal law inconsistent conclusion in top post is hereby still refuted (my cap.s): “an adiabatically isolated column of gas in a gravitational field CANNOT have a thermal gradient maintained by gravity.” 353. Alan Millar says: Joules Verne says: January 25, 2012 at 9:49 am Why do you not just think about this in as simple terms as possible. Forget about any mechanisms that causes it, what are you saying is the outcome? You are saying that Gravity can cause an everlasting temperature gradient in a column of gas in a closed system with no possible energy input. Right now think about just one inevitable consequence. Convection. Convection must occur because we have hotter gases at the bottom and there will be constant particle movement up and down the gravity well as particles heat up and cool down and are affected by the gravity well. Ok what is needed to move a particle up a gravity well………work! Or explain how you move a particle up a gravity well without performing work. What happens when work takes place? Well the 2nd Law of Thermodynamics says that entropy must increase and that entropy can never decrease in a closed system without the creation of energy. So how do you maintain an everlasting temperature gradiant in this column of gas? Well the 2nd Law says you can’t. Entropy increase will eventually lead to the ‘heat death’ of the system as temperatures equalise accoss it. To do it, you have to create energy and the Laws of Thermodynamics says you can’t do this either. So tell me how you maintain an everlasting temperature gradient without breaching the Laws? Alan 354. Myrrh said @ January 25, 2012 at 4:19 am But what we have here is tutorials in which the tutors fall short, discovered when students go away to do their own research, and when said students raise this and ask for explanations they are bombarded with ad homs and told to go read physics text books, which they’ve just done to be able to point out the tutors are saying something different.., and then the tutors arrogantly announce they don’t answer stupid questions hoping they’ll go away when it’s the stupid answers they’ve given that are being questioned. Examples: Willis Eschenbach says: January 24, 2012 at 7:07 pm George Turner says: January 24, 2012 at 2:40 pm George, if you do not know from the context that we are talking about net heat flow through the wire, and not freakin’ brownian movement of electrons, you are not paying enough attention. I His bold. I asked for clarification: “What has Brownian motion got to do with electrons?” “And by “net heat”, do you mean the photons from colder to hotter thing?” Because, I want to know what electrons have to do with Brownian motion, which is about movement of particles in fluids. Because I discovered this when I went away to research this term a couple of years ago having been given this as a reason carbon dioxide gets thorougly mixed in the atmosphere and finding that carbon dioxide was itself part of the fluid etc. Because, I want to know if Willis is referring to the “heat flows from hotter to colder and colder to hotter to give net flow from hotter to colder” – because if so, I’ve already concluded, from going away and doing my own research, that there’s a missing link in this reworking of the 2nd law.(*) Brownian motion has nothing whatsoever to do with electrons; it’s the motion of small particles of matter (originally pollen grains) being jostled by the random movement of molecules in a fluid. Heat is one form of energy among many: chemical, kinetic etc. Photons are packets of energy being exchanged between atoms. They are not heat so they don’t care about the temperature of those atoms. Heat flows from hot to cold only. Physics is divided into Classical and Quantum descriptions of the world. They describe the same world in different ways. From your questions, and there’s nothing wrong with your questions, it’s clear that these two views are conflated in your mind. You definitely need to learn some basic physics. Mine came from Resnick, Halliday & Walker in 1969. While the papers being discussed are recent, the physics isn’t. An ad hominem BTW is when you claim that what someone claims is false by virtue of who they are. Insulting someone is not an ad hominem. The first is a logical fallacy, the second is being rude and not a logical fallacy. And now we have the main tutor tell us: “Because the gas itself conducts heat, you don’t really need the wire. The dry air adiabatic lapse rate isn’t stable because air conducts heat.” when earlier he said air was a lousy conductor of heat. When physics text books say air is a good insulator, and good insulators are bad conductors of heat and the tutor says they’re both, one has to ask for clarification, perhaps I missed some emphasis or other. So my question is, what do you mean here? It’s not lack of willingness on my part to go away and do my own homework. A good insulator is one that conducts heat slowly. A bad insulator is one that conducts heat quickly. All matter conducts heat, but the rate at which it conducts depends on the state (solid/liquid/gas) and chemical composition. Air conducts heat very slowly, but perforce will reach an equilibrium temperature very slowly in the absence of convection. In any real atmosphere, convection will predominate over conduction. Not having science formally beyond ‘high school’ level and what I have learned generally since including reading such range as Lederman, Hawkings and Dawkins, and without easy knowledge of mathematics as bandied about here, I have to rely on the willingness of tutors to engage in English. I’ve been sadly disappointed. I was quite excited to find these discussions and thought I would at last have the pleasure of getting some science education I’d missed out on in having the opportunity to follow such discussions and in having any, I thought, my simplistic, questions answered. Seems these are so simple they’re now avoided altogether by some who claim they are science experts. So, I don’t know what Robert is saying in any of his replies any more because one moment he is saying that “air is a lousy conductor of heat” and the next “Because the gas itself conducts heat, you don’t really need the wire. The dry air adiabatic lapse rate isn’t stable because air conducts heat.” Unfortunately Myrrh you have chosen the wrong classroom in which to learn the basics. There’s not just basic thermodynamics and quantum physics, there’s basic boundary layer climatology being discussed here. A lot of the discussion is frankly a display of ignorance. There’s nothing at all wrong about ignorance per se, but wilful ignorance is a different matter. This muddies the water and makes learning extraordinarily difficult for those who have yet to grasp the fundamentals. This saddens me; I experienced this in a cosmology class I took; our lecturer/tutor had a very difficult time keeping to the arguments he wanted us to focus on because of students who lacked the underpinning knowledge required to understand those arguments. It was very frustrating. Bottom line is: get that basic physics under your belt. If you can find a friend who wants to do the same, you will make much more rapid progress. To teach is to learn twice. And please forgive Willis. Unfortunately, his mother neglected to put a warning notice on him: Handle with Care. He’s been a reforming cowboy ever since I first came across him nearly a decade ago and I have learnt heaps from him. Live long and prosper Myrrh. Your questions are not stupid. The answers you have received are not stupid, either. Confusing you, yes, but not stupid. • Bryan says: thepompousgit says ” Live long and prosper Myrrh. Your questions are not stupid. The answers you have received are not stupid, either. Confusing you, yes, but not stupid.” Myrrh states up front that he has no formal science training. Sometimes this shows through in his questions. However this sometimes has its advantages as he is not soaked in a particular paradigm. Quite often he is the boy who spots the ‘Emperor has no clothes’. I think he made a valuable contribution when he noticed that the NASA educational pages were being reinterpreted to blur the differences between light and infra red radiation. Some would think that this was done to make IPCC science more believable. 355. mkelly says: Ken Finney says: January 25, 2012 at 10:03 am Thanks for the links. I think you know what I was getting at. 356. kdk33 said “if the atmosphere was heated from the top there would be no convection, hence no lapse rate. The lapse rate doesn’t apply to the ocean because water is incompressible. Hot water doesn’t expand as it rises, hence does not do work on the surroundings, hence does not change temperaure, hence no lapse rate.” Sound is the alternating compression & decompression of a fluid. A practical experiment for you: Partially fill a bathtub with water. Take a portable radio, or CD player into the bathroom and turn on. Your choice of music. Lie in the bath and submerge your head in the water. If you still believe in the incompressibility of water, please keep your head there. 357. gbaikie says: January 25, 2012 at 3:15 am I know of no data that indicates DALR “going away”- arctic regions with lack of humidity tend to have around 9 K per 1000- a larger change compared to regions with more humidity. That is not correct. The lapse rate is almost always 6.5 K/km. High humidity makes the tropopause higher, but does not change the lapse rate. The one exception is when clouds form and the lapse rate is variable between 4 and 6.5 K/km. A greenhouse effect generally is about “trapping warm gases” Actually, it is not – it is about cooling the atmosphere. A fraction of that heat returns to the surface (back radiation) and makes it a bit warmer. To be perfectly clear, because some of the heat comes from conduction/convection, greenhouse gases emit more energy than they trap. 358. mkelly says: thepompousgit says: January 25, 2012 at 10:55 am Sir your responce to Myrrh was a very nice display of kindness oft lacking by some. You are to be commended. As we used to day in the Navy, BZ (bravo zulu). 359. wayne says: January 25, 2012 at 4:05 am How can .. Venus have the huge thermal gradient removed by merely making [sure] there [is] no thermal input at all at the base (remove the 5W/m2 at the surface) and that is then supposed to cause the entire column over time to be isothermal. The atmosphere becomes isothermal when the cooling is removed from the top. The amount of energy arriving at the bottom really does not matter. It merely sets the final temperature, not the lapse rate. 360. A. C. Osborn says: A physicist says: January 25, 2012 at 10:23 am “For more theoretical and experimental details than most folks want to know, see @article{Kemp:2009lr, Author = {R. Scott Kemp}, Journal = {Science and Global Security}, Number = {1}, Pages = {1–19}, Title = {Gas Centrifuge Theory and Development: a Review of US Programs}, Volume = {17}, Year = {2009}} and references therein (a Google search will find it).” I think you need to re-read the Article. It talks about “assuming a linear-thermal-gradient profiles” and “reate a dynamic equilibrium”, not thermal equilibrium. The word “Isothermal” does not appear anywhere in the available text whatsoever. 361. Nullius in Verba says: My admiration to Professor Brown. It was an elegant demonstration and a tenacious defence. You asked about convection on a world with no GHGs I think it would work a bit like the convection pattern of the thermohaline circulation, inverted. The oceans are warmed at the equator and cooled at the poles. The cold water at the poles sinks, flows equatorwards across the ocean deeps. Water at the equator is warmed, rises and spreads out polewards. Because the deep oceans receive no heat input, at least not on the scale of the circulation time, they are fairly uniformly at the temperature of the descending polar waters, even below the equator. There is in fact a lapse rate in the deep oceans of about 0.1 C/km. With GHG-free atmosphere, you have to swap warm for cold and up for down, and equator for pole. Thus, air is warmed at the equator, rises, and spreads polewards. Its potential temperature (adjusted for lapse rate) remains constant then, and most of the atmosphere is equatorially hot, even at the poles. The thin layer in contact with the ground there cools, and flows back to the equator over the surface. There would be a lapse rate, as there is in the oceans, and I think it could extend high up, as the ocean circulation goes deep. While you might think that polar waters need only sink below the thermocline and could then flow back equatorwards only a few hundred metres down, analogous to the low tropopause, it doesn’t work that way. Pressure is exerted omnidirectionally, and unless channelled/diverted by some external force, an upward force on air at the equator will push all the air above upwards until forced sideways by the top of the atmosphere. The upwards push can’t be changed entirely to a sideways push 100 m up unless there is somethere there to actively resist it. And since all the atmosphere far above the surface is at the same potential temperature, and neutrally buoyant, I don’t see how or why this could happen. The idea that you can get convection cycles driven by temperature differences from the top sounds odd, but I find it helps to think of it as cooling of the fluid over one area giving the fluid negative buoyancy, and driving the fluid down – this being analogous to heating from the bottom causing positive buoyancy and a drive up. It helps as well to remember convection is about the whole cycle – what goes up must come down – not just hot air rising. (There are complications, of course. On a rotating planet, air converging on the poles would spiral into a cyclostrophic vortex. You’d get multiple Hadley cells and jet streams and so on. I’m not claiming it would really be that simple.) It’s a controversial idea – I know several people have objected vociferously when I’ve mentioned it – but that doesn’t mean it’s therefore incorrect. If you can see anything obviously wrong with it I’d be grateful. 362. Bryan said @ January 25, 2012 at 11:15 am Myrrh states up front that he has no formal science training. Sometimes this shows through in his questions. However this sometimes has its advantages as he is not soaked in a particular paradigm. Quite often he is the boy who spots the ‘Emperor has no clothes’. I think he made a valuable contribution when he noticed that the NASA educational pages were being reinterpreted to blur the differences between light and infra red radiation. Some would think that this was done to make IPCC science more believable. Yes, I noticed. That’s why I went to the trouble of answering his questions at length. Robert’s been doing most of the heavy lifting around these parts and I thought I’d lend a hand. 363. Ralph says: . Just a thought, for you all. There are (I think) two main ways of reducing heat-loss from a planet (resulting in warmer surface temperatures): a. LW absorption and emission (greenhouse gasses and effect). b. Conduction-convection (atmospheric effects). Let me explain what I mean. We have three types of planet: a. Airless planet. Cooling via LW, and no ‘insulator’ to reduce LW cooling. (An insulator being any method of preventing cooling.) b. Atmospheric planet, with no greenhouse gasses. Cooling via LW. Reduced cooling via conduction-convection to the atmosphere. Initially, this process simply warms the atmosphere, until the atmosphere is so warm it absorbs little more surface temperature. Now this warm atmosphere cannot cool itself via LW emission, but it can cool itself via conduction to areas of the planet in shadow. Thus the atmosphere is ‘warming’ (or reducing cooling) areas of the planet in shadow. This will surely make the average surface temperature of the planet higher, than if there was no atmosphere (because the cold shadow areas are now warmer, resulting in a higher average temperatures.) As an aside, this means that the effective surface LW cooling area of a hilly planet like the Earth is much greater than a simple sphere would lead us to believe. Up to 20% greater surface area. I presume this greatly effects the w/m2 calculations that have been tossed around. (The incomming SW radiation only sees the area of a smooth sphere, but the outgoing LW radiation sees a much higher surface area than a normal sphere.) c. Planet with greenhouse gasses. Cooling via LW Reduced cooling via conduction-convection (as explained above). Reduced cooling via gasseous absorption and reemission (greenhouse gasses). In a similar fashion to conduction (above), the re-radiation of LW from H2O and CO2 towards the surface delays and reduces the coolling of the surface, resulting in higher average temperatures than if there were no such gasses in the atmosphere. Thus (in my opinion) both the greenhouse gasses and the atmosphere itself act in partnership to reduce the cooling of the surface (erroniously called warming, but you know what I mean). . 364. A physicist says: A physicist says: “For more theoretical and experimental details than most folks want to know, see @article{Kemp:2009lr, Author = {R. Scott Kemp}, Journal = {Science and Global Security}, Number = {1}, Pages = {1–19}, Title = {Gas Centrifuge Theory and Development: a Review of US Programs}, Volume = {17}, Year = {2009}} and references therein (a Google search will find it).” A. C. Osborn says: I think you need to re-read the article. It talks about “assuming a linear-thermal-gradient profiles” and “reate a dynamic equilibrium”, not thermal equilibrium. The word “Isothermal” does not appear anywhere in the available text whatsoever. A. C. Osborn, the isothermal assumption is build into Dirac’s starting theory (equation 1 of page 5), which assigns a single uniform temperature $T$ to the entire body of gas in the centrifuge. Yes, that’s “the Dirac”, who (as it turns out) did seminal research on both isotope separation and quantum theory . While temperature gradients are discussed appear later on in the article, they appear in the context of gentle along-axis temperature gradients that are externally generated (with heating coils), not as radial gradients that appear spontaneously by the “gravito-thermal” mechanisms. Physically speaking, it turns out that the centrifuge separation gains in efficiency when the centrifuge column stands vertically, and gentle heat is applied to the bottom of the centrifuge, so as to to induce a slow floor-to-ceiling circulation, as illustrated here. For the present purposes, the bottom-line doesn’t change: Gravito-thermal theories of temperature gradients are just plain wrong. 365. kdk33 says: OK, For all the smarties that want to point out that water is actually compresible. Yes you are right. But relative to a gas? Not so much. A lapse rate in the ocean? Sure maybe a tad. But relative to the atmosphere? Not so much. Happy now? 366. DeWitt Payne says: Robert Brown, Truly wish for edit and preview. I can’t help with edit, but you can get preview. CA Assistant works just fine here. Go to: http://climateaudit.org/ca-assistant/ and follow the instructions. It does require that you use Firefox as your browser. I’ve never found a place where the subscript/superscript HTML quicktags work, though. 367. Robert Brown says: January 25, 2012 at 5:33 am It’s like CO_2 is optically dense all the way up to within a km or so of the tropopause, and then shuts off in the stratosphere. Actually, it is water vapor (not CO2) that becomes optically thin at the tropopause. It is about 200 ppm below the tropopause and 5 ppm above. In the tropics, where there is more water vapor, the tropopause is higher. In the stratosphere, CO2 is the main greenhouse gas, more than 100 times more abundant than water and more than 1,000 times more abundant than ozone. I have seen the TOA spectra you have referred to, I still can’t explain the CO2 emission that appears to come from the tropopause, but I am certain that that is not the correct explanation. It is possible that the feature originates from (and perhaps causes) the thermal anomaly at 32 km, in the mid-stratosphere. One problem is that the resolution of space borne instruments is not quite good enough to know how to interpret that feature. To be very clear, at the tropopause, water vapor and CO2 emit the same amount of energy. However, CO2 is emitting energy from the stratosphere toward the tropopause and water vapor is emitting the same amount of energy toward space. At that level of the atmosphere, the CO2 and water spectra no longer overlap by much. 368. George E. Smith; says: “”””” Joe Born says: January 24, 2012 at 8:21 am That Dr. Brown has it wrong is readily demonstrated by a thought experiment nearly any layman can perform. If an ideal monatomic gas subjected to gravity in a thermally isolated container consists of only a single molecule, its kinetic energy K–and thus the mean translational kinetic energy–at any altitude z is given by K = mg(z_max -z), where m is molecular mass, g is the acceleration of gravity, and mgz_max is the total (kinetic + potential) energy of the gas. “”””” Well Joe, I DON’T agree that Professor Brown has it wrong; but I DO agree that nearly any layman can perform your thought experiment; that’s how they earn the prestigious title of “Layman” rather than “Professor.” So to your layman thought experiment. you state:- “”””” If an ideal monatomic gas subjected to gravity in a thermally isolated container consists of only a single molecule, “”””” There you just shot your self in the head. A gas, ideal or not, cannot consist of a single molecule. when in a thought experiment you say “”””” any altitude “”””” that is taken to mean “”””” any altitude “””””, tha’ts the terrific advantage of a thought experiment; an infinifte sized container is easy to get by declaration; and your container must be infinite in size for your molecule to be able to be at any altitude. Therefore your single molecule never hits the wall of the container, and there is nothing else present to hit either, so no collisions occur, so your molecule has no Temperature. It’s energy is indeterminate since according to Einstein there is no absolute frame of reference, and your molecule is simply in free flight. it also clearly doesn’t have any Maxwell-Boltmann energy distribution either since only one molecule is present; further proof that it has no Temperature; or at least it has no Temperature different from zero Kelvins. Maybe if you listen a bit more closely to Professor Brown, you could eventuall discard your layman’s mortarboard, and tassel. 369. Ralph says: . Dr Bown. With regards to your thought experiment with the silver wire, you say that: “””Heat will flow from the bottom to the top until they are at the same temperature. At this point the top and the bottom are indeed in thermal equilibrium.””””” Sorry, I am only an aviator and meteorologist, but are you not confusing ‘heat’ and ‘temperature’ here? The individual molecules in the upper atmosphere can indeed be very hot (high kinetic energy), but there are so few of them, their total temperature on any thermometer is very low. Thus the top of your silver wire can be as hot as it likes (say 35oc), and yet the individual molecules at 50,000 feet are not going to accept any of that heat because they are already (individually) quite hot themselves. (But because there are so few of them, the atmosphere at this level feels very cold). Does not your thought experiment fail, because most of the molecules in the atmosphere are all at the same heat (kinetic energy), while the difference in temperature with altitude (on a thermometer) is simply an effect of the number of molecules you meet (pressure and density). . I am not denying greenhouse effect here – any meteorologist will know this is a real effect. But it is surely also true that an atmosphere warmed at its base by conduction will transmit that heat throughout the atmospheric column, maintaining its temperature and lapse rate, yet with most of the molecules in that column having the same kinetic energy (the same heat, but not the same temperature). Where Tallbloke et al seem to fall down, is believing that conduction-convection is the sole method of decreasing LW heatloss from a planet (thus deriving a warmer surface). It is not. The absorption and reemission of LW by clouds and certain gasses (the greenhouse effect) is a much more potent effect. . 370. DeWitt Payne says: Paul Bahlin says: January 25, 2012 at 9:47 am One of the premises made regarding an ideal gas is that there are no inter-molecular collisions in an ideal gas and this is done so as not to introduce a ‘wall bias’ where molecules near a wall experience (inter-molecular) vector forces that tend to pull them away from the wall. Nope. The premise is that all collisions are elastic, both with each other and with the container walls. See for example the Wikipedia article on Kinetic Theory: The rapidly moving particles constantly collide among themselves and with the walls of the container. All these collisions are perfectly elastic. This means, the molecules are considered to be perfectly spherical in shape, and elastic in nature. The particles must also be small so that the total volume of the particles is much smaller than the volume of the container. 371. DeWitt Payne says: Robert Clemenzi says: January 25, 2012 at 12:42 pm Actually, it is water vapor (not CO2) that becomes optically thin at the tropopause. It is about 200 ppm below the tropopause and 5 ppm above. In the tropics, where there is more water vapor, the tropopause is higher. Water vapor becomes optically thin far below the tropopause. Look at the IR emission spectrum of the atmosphere from space. The water vapor lines and bands are far more intense than the CO2 band. That’s because water vapor, which has a scale height about 1/4 that of the noncondensable gases (2km compared to 8km) becomes optically thin (optical density < 1) at lower altitudes where its warmer. At 17 km for a tropical atmosphere the amount of water vapor in a given volume is less than 1% as much as the amount of CO2. 372. DeWitt Payne says: Ralph says: January 25, 2012 at 12:54 pm The individual molecules in the upper atmosphere can indeed be very hot (high kinetic energy), but there are so few of them, their total temperature on any thermometer is very low. This piece of misinformation seems to be even harder to kill than a gravity maintained adiabatic lapse rate. Temperature, as long as the pressure is high enough it can be defined, is a function of the average kinetic energy of the gas only. What happens at low pressure is that it takes longer for a thermometer to equilibrate with the gas. If the thermometer has a large thermal mass, on the order of the heat content of the volume of interest, it will perturb the actual temperature. 373. Joules Verne says: “On the influence of gravity on the thermal conductivity” M. Tij (1), V. Garzó (2), A. Santos (2) ((1) Départment de Physique, Université Moulay Ismaïl, Meknès, Morocco; (2) Departamento de Física, Universidad de Extremadura, Badajoz, Spain) (Submitted on 25 Feb 2000) In this paper we evaluate the corrections to the Navier-Stokes constitutive equations induced by the action of a gravitational field in a gas subjected to a thermal gradient parallel to the field with no convection. The analysis is performed from an exact perturbation solution of the BGK kinetic model for Maxwell molecules through sixth order in the field. The reference state (zeroth order approximation) corresponds to the exact solution in the pure planar Fourier flow, which holds for arbitrary values of the thermal gradient. The results show that the pressure tensor becomes anisotropic, so that the momentum flux along the field direction is enhanced. In addition, the heat flux increases (decreases) with respect to its Navier-Stokes value when the gas is heated from above (below). full text: http://arxiv.org/pdf/cond-mat/0002397v1.pdf These authors said the same thing I did in a lot more detail and precision numbers. snip: The main results concerning the transport of momentum and energy are that the external field induces (i) anisotropy in the pressure tensor, (Pzz−p)/p ≃ 84 5 ǫ2g∗2, and (ii) deviations from the Fourier law, qz/q(0) z − 1 ≃ 58 5 ǫg∗. While the first effect is of second order, the correction to the heat flux is of first order, so that it depends on the sign of the thermal gradient. As a consequence, the heat transport is inhibited when the gas is heated from below (ǫ 0). So there. A gravity field introduces a first order effect that causes coefficient of thermal conductivity to be asymetric in direction of flow. Maxwell’s Demon in other words sorting out molecules by kinetic energy content. I’m afraid you boys are going to have to come to grips with this. There’s no violation of thermodyanmics. The Demon creates a thermal gradient at the expense of an equal and opposite potential energy gradient. You can’t make a perpetual motion machine out of this. Every attempt at finding a way for the Demon to get a free lunch has failed. This is no exception. 374. IanH says: Gravity-Induced Electric Fields in Metals Canadian Journal of Physics, 1971, 49:(22) 2754-2767, 10.1139/p71-334 Just to muddy the waters further. There’s an electric field on that wire due to gravity – what if the hypothetical gas can conduct electricity – won’t it warm up because of the current flowing between the ends of the wire?. (I have become confused – I thought I ‘got’ lapse rates.) A good argument : http://www.youtube.com/watch?v=RDjCqjzbvJY 375. Joules Verne says: Let’s try that quote from the paper again. Somehow the last few words in the paragraph I clipped didn’t come through and they were important (my bold). “The main results concerning the transport of momentum and energy are that the external field induces (i) anisotropy in the pressure tensor, (Pzz−p)/p ≃ 845 ǫ2g∗2, and (ii) deviations from the Fourier law, qz/q(0)z − 1 ≃ 58 5 ǫg∗. While the first effect is of second order, the correction to the heat flux is of first order, so that it depends on the sign of the thermal gradient. As a consequence, the heat transport is inhibited when the gas is heated from below (ǫ 0). Again, the source: On the Influence of Gravity on the Thermal Conductivity http://arxiv.org/pdf/cond-mat/0002397v1.pdf 376. Well, I still haven’t worked out what any of you are talking about.., but isn’t the opposite and equal energy gradient to make up for the gravitational energy gradient, pressure? Gold star for Myrrh. Some fun for everybody: http://phet.colorado.edu/en/simulation/gas-properties A final exam you all might want to look at, especially problem 1. Would you flunk? http://www.physics.sc.edu/~yar/phys706_2011/…/final_solutions.pdf I know, I know, those of you who are devoted to the idea of a lapse rate at true equilibrium to the extent that you ignore the fact that the solution openly violates the second law won’t be swayed by a little thing like the fully worked out solution — which is the one I have in the article at the top, but this exam goes ahead and computes various quantities of interest and shows that they do the right asymptotic things. If the debate continues, I have a lovely contribution from a list-lurker that does the textbook exercise of showing that isothermal is indeed the maximum entropy solution. And on the list today it was verified (not by me) that the full stat mech computation is isothermal. Finally, Caballero has it as a homework exercise (2.17). Is this starting to look like a conspiracy of some sort? A nefarious plot by evil warmists, who’ve managed to corrupt every thermo and stat mech textbook in the country? Who are brutally grading students incorrectly on their final exams, all to keep them from questioning Greenhouse Warming by hiding the True Solution from them? If so, you might want to ask yourself — is it just barely possible that all of these Ph.D. physicists who teach and do research and all that stuff in the general field of thermal physics are all right, and it is me that is wrong? It truly would be lovely if, with all of these guns brought to bear to back up what was already a perfectly adequate proof by contradiction above, we could all just agree that Jelbring’s EE paper is categorically incorrect, because the state with a DALR that he asserts as the stable thermal equilibrium of an isolated ideal gas violates the second law of thermodynamics, fails of detailed balance, is not (in fact) the maximum entropy solution, and doesn’t make sense as no air parcels are being moved around in an atmosphere in static equilibrium. Just a thought. A foolish one, I know — a mad, mad, dream. But y’know, I’ve gotta lay it out there. rgb 377. Joules Verne says: Darn it. It was still cut off. While the first effect is of second order, the correction to the heat flux is of first order, so that it depends on the sign of the thermal gradient. As a consequence, the heat transport is inhibited when the gas is heated from below, while the opposite happens when the gas is heated from above. I really needed that last bit where it is specified that heat transport is accelerated when heated from above in addition to being inhibited when heated from below. I highly recommend reading the whole paper. This corrects both Brown AND Nikolov neither of whom have characterized the situation correctly either conceptually or with mathematical rigor. 378. Joules Verne says: DeWitt Payne says: January 25, 2012 at 1:15 pm Ralph says: January 25, 2012 at 12:54 pm “This piece of misinformation seems to be even harder to kill than a gravity maintained adiabatic lapse rate. Temperature, as long as the pressure is high enough it can be defined, is a function of the average kinetic energy of the gas only. What happens at low pressure is that it takes longer for a thermometer to equilibrate with the gas. If the thermometer has a large thermal mass, on the order of the heat content of the volume of interest, it will perturb the actual temperature.” It’s harder to kill because it’s correct. All matter above absolute zero has a temperature. There is no constraint on some minimum amount of mass involved. Any amount will do. The problem you are struggling to understand is that there is a Bolztman distribution of kinetic energy such that you cannot obtain a reliable temperature for an ensemble by measuring one individual molecule’s temperature. It’s sort of like trying to figure out the average intelligence quotient here based on measuring one individual. It does not follow that only groups have an IQ. Every molecule has a temperature. 379. The way to think about the difference between the stratosphere and the troposphere is to use the slab gray atmosphere toy model ( see 7.3.2 here, for example. Petty goes into more depth). Thanks, looks very useful. I do so hate the toy model with downwelling radiation, but the general idea looks good and I’ll see what I can make of it. rgb 380. DeWitt: You asked elsewhere about why a laser can cut metal even when the metal gets very hot. But Claes Johnson’s paper is only about spontaneous blackbody emission, not induced emission as in a laser. Induced emission does not have a frequency proportional to the absolute temperature of the source, as does spontaneous blackbody emission in accord with Wien’s Displacement Law. (When lasers are used to cut steel there is also a blowing process helping to cool the metal.) You yourself quoted empirical proof of what Claes has proven computationally when you talked about a gas not absorbing radiation from a cooler emitter, but doing so when the emitter got warmer than the gas. I would very much appreciate the reference for this experiment if you could oblige. 381. Trick says: Robert Brown says at 10:40am: “…the point is that a stable thermal equilibrium of an isolated ideal gas with a lapse rate violates the second law of thermodynamics…the zeroth law clearly states that the two locations (with different temperatures) are not in thermal equilibrium.” Well, the top post does tell us: “Those same textbooks carefully demonstrate that there is no lapse rate in an ideal gas in a gravitational field in thermal equilibrium because, as is well known, thermal equilibrium is an isothermal state; nothing as simple as gravity can function like a “Maxwell’s Demon” to cause the spontaneous stable equilibrium separation of gas molecules into hotter and colder reservoirs. Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics…” Why is that last true? I agree, it should be so but it flies in the face of hydrostatic equilibrium actually being in “temp. equilibrium” in Caballero. I noted that the 1st time you sent me there last week. Seems so long ago now…ha. I am truly curious. So far as I can see in the top post this is just announced, 2nd law violation is not irrefutably proven up there. In the gas ideal gas column of interest, no process is irreversible in there. The molecules bounce around elastically with everything, entropy does not go down. Couldn’t entropy just stay the same in this idealization & therefore pass the 2nd law test? In real world, of course entropy goes up due to real inelastic collisions. But then , in sec. 2.3 Caballero writes being non-isothermal is acceptable for hydrostatic equilibrium. Stunning. Caballero even goes so far in Sec. 2.3.1 to write: “Overall, it can safely be stated that atmospheric motions with horizontal scales > 10 km are always in hydrostatic equilibrium.” Meaning non-isothermal. That is a stunningly tall column & long wire to insert but it works in reality, no perpetuum, no 2nd law violation. Why? Maybe I am about to be directed to another text book deep dive but that would be ok & progress. Robert, the teach-a-holic – Thank you for an enjoyable renewed science discourse. 382. DeWitt Payne said @ January 25, 2012 at 1:15 pm Ralph says: January 25, 2012 at 12:54 pm The individual molecules in the upper atmosphere can indeed be very hot (high kinetic energy), but there are so few of them, their total temperature on any thermometer is very low. This piece of misinformation seems to be even harder to kill than a gravity maintained adiabatic lapse rate. Ain’t that the truth? Temperature, as long as the pressure is high enough it can be defined, is a function of the average kinetic energy of the gas only. What happens at low pressure is that it takes longer for a thermometer to equilibrate with the gas. If the thermometer has a large thermal mass, on the order of the heat content of the volume of interest, it will perturb the actual temperature. More accurately, measuring temperature with a thermometer always changes the temperature. Most often that can be neglected because the change is trivial, but there’s many a researcher come unstuck from not realising that they are changing what they measure.[/nitpick] 383. Joules Verne says: George E. Smith; says: January 25, 2012 at 12:52 pm “There you just shot your self in the head. A gas, ideal or not, cannot consist of a single molecule.” Ummm… I think it can’t exist as a liquid or solid because that requires proximal arrangement with neighboring molecules. A molecule is a gas generally when it is very isolated from neighbors so that it can flit about traversing a great number of molecular radii without hitting anything else. There’s probably a better definition but in general a gas is a gas because the individual molecules are a great distance from neighboring molecules compared to liquids and solids. 384. Myrrh says: thepompousgit says: January 25, 2012 at 10:55 am Myrrh said @ January 25, 2012 at 4:19 am Brownian motion has nothing whatsoever to do with electrons; it’s the motion of small particles of matter (originally pollen grains) being jostled by the random movement of molecules in a fluid. That was my point. Not only does it not have anything to do with electrons, it has eff all do mixing carbon dioxide thoroughly in the atmosphere… …though idiotically given as proof is a typical non-experiment from the AGWSF department, by opening a bottle of scent in a classroom saying it proves the scent is spread by Brownian motion, that’s when it’s not being not being idiotically explained by using ideal gas properties of elastic collisions in empty space as if ideal gas, but more often than not, claiming both these processes happening at the same time – seemingly as unconcerned as Willis about context. Photons are packets of energy being exchanged between atoms. They are not heat so they don’t care about the temperature of those atoms. Heat flows from hot to cold only. Physics is divided into Classical and Quantum descriptions of the world. They describe the same world in different ways. From your questions, and there’s nothing wrong with your questions, it’s clear that these two views are conflated in your mind. You definitely need to learn some basic physics. Mine came from Resnick, Halliday & Walker in 1969. While the papers being discussed are recent, the physics isn’t. Not conflated in my mind, conflated in minds that can’t separate contexts one from another. As I showed in the link to an exchange I had about ‘net heat flow including heating flowing from cold to hot’ Visible light is not a radio wave, for example, it has distinct properties in its own right and these properties act in distinct ways on meeting matter, to reduce this to some as yet unproven idea of photons and claim that all photons in transferring energy heat matter oblivious to other uses of energy while claiming to be discussing science of the physical world around us we can see and taste and hear and which we do understand empirically well how it impinges on us and we on it, is frankly pathetic coming from those claiming themselves educated in this. It’s not I who needs to learn some basic physics.. An ad hominem BTW is when you claim that what someone claims is false by virtue of who they are. Insulting someone is not an ad hominem. The first is a logical fallacy, the second is being rude and not a logical fallacy. I know the difference. I meant the ad hom the like which you’ve repeated, “You definitely need to learn some basic physics” and “Bottom line is: get that basic physics under your belt” … I suggest some return to the real physical world around us and stop blinding themselves with their own imagined quantum brilliance, which may or may not yet have arrived from the future carried by a non-existant photon.. A good insulator is one that conducts heat slowly. A bad insulator is one that conducts heat quickly. All matter conducts heat, but the rate at which it conducts depends on the state (solid/liquid/gas) and chemical composition. Air conducts heat very slowly, but perforce will reach an equilibrium temperature very slowly in the absence of convection. In any real atmosphere, convection will predominate over conduction. Thank you, I hope that helps Professor Brown to better articulate what he meant. Unfortunately Myrrh you have chosen the wrong classroom in which to learn the basics. There’s not just basic thermodynamics and quantum physics, there’s basic boundary layer climatology being discussed here. A lot of the discussion is frankly a display of ignorance. There’s nothing at all wrong about ignorance per se, but wilful ignorance is a different matter. This muddies the water and makes learning extraordinarily difficult for those who have yet to grasp the fundamentals. You err, I have grasped the fundamentals well enough to see that many hide the fact they don’t know the basics by playing the ‘superior because so very well educated in science card’ and worse, refusing to engage and distracting from this by the use of the ad hom technique that those questioning them have nothing worth listening to because they don’t have science phd’s coming out of their arses. I call bullshit on the lot of it. To teach is to learn twice. And what are you learning twice if teaching nonsense imaginary physics about a fictional world? When some confuse photons with discrete packets of visible light and conclude that visible light must therefore be heating water when real physics says water is transparent to it? And when having given the properties of one thing to another by claiming visible and short wave heat land and oceans they junk the real great thermal energy coming to us direct from the Sun, because they can’t find a role for it in their so called ‘energy budget’..? From which they have also expunged the great cooling role of the greenhouse gas water vapour, simply by ignoring it and sticking their fingers in their ears whenever it’s mentioned? I call bullshit on the lot of it. Live long and prosper Myrrh. Your questions are not stupid. The answers you have received are not stupid, either. Confusing you, yes, but not stupid. Thank you, I add be happy to you. The answers I have received as explanations for ‘greenhouse gases warm the Earth’ are most definitely stupid, I’m not the one confused here, as I’m still trying to point out.. 385. Perhaps this will settle things, for anyone still listening that thinks that Jelbring’s paper is correct: http://www.physics.sc.edu/~yar/phys706_2011/…/final_solutions.pdf I have waiting in the wings a user-contributed textbook demonstration that isothermal is maximum entropy with gravity, as well. Then there is Caballero’s detailed balance assignment (2.17). There is Paul Birch’s analysis of Velasco, which seems to be a full stat mech computation that arrives at the same conclusion. And finally, there is the clear violation of the second law the article above makes very clear. Are we done yet? Tallbloke, from much earlier: Since Robert Brown is setting a refutation of Hans Jelbring’s 2003 paper, it would be a common courtesy to provide a link to that paper in the headline post. This is my bad, Tallbloke. My only excuse is that I wrote the paper in latex and submitted it to Anthony to format the equations, and while I did put the reference in I forgot the link (and had no way to add it afterwards). I appreciate your doing so. For everybody: We’re quickly getting to where there are three or four complete algebraic demonstrations that the equilibrium state of a thermally isolated ideal gas in a gravitational field is isothermal that have been linked, directly indicated in replies, or posted and discussed. Stat-Mech and Thermo textbooks are more or less unanimous about isothermal equilibrium, of course — it is derived in stat mech very early in the process, in a way that is more or less independent of the details of the system in question. In Thermo, it is the zeroth law and the second law — any time one has a proposed system with a non-isothermal equilibrium one can trivially violate Kelvin-Planck and Clausius with it, unless it is a very odd system indeed. A column of ideal gas isn’t odd, it is textbook. It would be nice to lay this to rest soon. Sure, anyone who wishes to can claim to be smarter than all of the authors of all of the standard physics texts on thermo, but it looks pretty unanimous out there. There are more interesting and useful things to discuss than a paper that is really pretty obviously wrong, however well intentioned. If anybody has a serious argument — one that can stand up to e.g. the exam question and solution above, for example — I’d still be happy to address it as soon as I have time again, but it might be a day or so. rgb 386. Joe Born says: January 25, 2012 at 10:24 am “First to your contention that we are not talking about the microcanonical ensemble. Here a little context is in order. Recall that both Robert Brown in this thread and Willis Eschenbach in the previous one were addressing themselves to refuting the Jelbring paper. That paper began with a hypothetical ideal gas G disposed between concentric spherical surfaces A and S. Jelbring said that “A and S are thermally insulated preventing heat from entering into G and infrared radiation to reach space.” It is no doubt to parallel this condition that Robert Brown says of his thought experiment that it involves an “adiabatically isolated column of an ideal gas.” In short, heat can flow neither into nor out of the gas, so by definition it is indeed a microcanonical ensemble.” They are isolated with respect to heat flow to and from the outside universe. Not from the walls of the container, or at any rate, the floor – the planetary surface – with which they are in thermal equilibrium. So, except in the ludicrously pedantic sense in which no ensemble is truly canonical unless it includes every single particle in the entire universe, the canonic limit applies. None of which actually matters, so long as you don’t insist on filling the volume with a hard vacuum orders of magnitude more rarefied than even intergalactic space! Jelbring explicitly states that his shell is no higher than the 100mbar level. Robert Brown has also indicated somewhere (I think in one of the previous threads) that he is not considering cases in which the gas is so thin that the concept of temperature goes pear-shaped. Joe: “Next I consider your statement that “for any reasonable number of particles, it makes no difference” whether we’re dealing with the microcanonical ensemble or not. I agree with you that as a practical matter any lapse rate as small as I’m saying Equation 8 implies would be too small to measure.” No, that’s not what I’m saying. It is a general principle of statistical mechanics that the microcanonical converges to the canonical, as Velasco et al themselves point out. Equation 8 does not imply any lapse rate at all. All it implies is that the details of statistical mechanics calculations are messy for small numbers. Joe: “You make two further points that at base are not technical arguments so much as statements of your point of view. You say, “However, even in this extreme case, the temperature at equilibrium will still be the same throughout the entire height, in the crucial sense that no net work could be extracted from the gas by connecting different levels, by any means whatsoever.” On the contrary, this is an utterly fundamental technical argument. The very definition of “same temperature” for connected regions is “no net flow of thermal energy”. Hence “no net work” can be done by the gas. Joe: “You additionally observe that I am “taking the extreme and irrelevant sub-thermodynamic case of a minuscule total number of isolated particles – in which regime the macroscopic temperature is increasingly ill-defined and no longer simply proportional to the kinetic energy per particle.” Let’s set aside what exactly you may mean by imprecise terms like “sub-thermodynamic,” “macroscopic,” and “increasingly ill-defined.”” Let’s not. Let’s face up to it instead. If we have a large number N of monatomic particles we say that the thermodynamic temperature is T, where the total kinetic energy is 3/2 NkT. If there is only one isolated particle it doesn’t have a temperature at all! In a thermal system the motion of the particles is isotropic; there is no directional bias; and this is not possible for a single isolated particle. It’s kinetic energy, not thermal energy; we cannot put T=(mv**2)/3k. If anything, T=0. What about N=2 or 3 then? Somehow we have to cobble a fit across the middle between these two contradictory extremes. In statistical mechanics, this is possible, but messy, if you are very, very careful about your definitions, your scenario, your boundary conditions, and the limits on your sums and integrals. Even then you are quite likely to get it wrong. Whether Velasco et al have got it right I don’t know. What I do know is that if your results purport to show any non-zero temperature gradient in a state of thermal equilibrium, then somewhere or other you’ve made a boo-boo. That result cannot be correct. I am enormously more certain of that than I ever could be of any piece of statistical mechanics, and so would just about every other physicist I know. Joe: “And let’s concede that the case I discussed was an extreme case. That case nonetheless remains relevant, because it illustrates by exaggeration something that remains true …” Fine, but you’ve chosen the wrong extreme to illustrate this problem. It doesn’t illuminate the solution, it obscures it. It’s as if you were discussing the tendency of buses to come in threes, and spent all your time trying to analyse the behaviour of two buses setting off from the terminus 100Gyr apart. 387. separation science, especially that surounding the separation of uranium gases in centrifuges, give you all the evidence you need to that this is a load of crap. blog comments dont overturn working engineering. • Steven Mosher, “separation science, especially that surounding the separation of uranium gases in centrifuges, give you all the evidence you need to that this is a load of crap. ” Yup separation science. that means centripetal force, separates things of different density I believe. Lemme see, what in our atmosphere is different temperature and where do they end up?? Oh yeah, gas particles are different temps and are generally separated, or stratified, by their density!!! What does it? Well, my barely HS education tells me GRAVITY!!!! What were you saying again?? 388. DeWitt Payne said @ January 25, 2012 at 12:31 pm Robert Brown, Truly wish for edit and preview. I can’t help with edit, but you can get preview. CA Assistant works just fine here. Go to: http://climateaudit.org/ca-assistant/ and follow the instructions. It does require that you use Firefox as your browser. I’ve never found a place where the subscript/superscript HTML quicktags work, though. Thank you your majesty :-) 389. Robert Brown: You invited “a serious argument” so I put one: Empirical evidence using spectroscopy proves that a gas does not absorb spontaneous emission from a body which is significantly cooler than it, but it does absorb (and spectral lines thus appear) when the same body is made warmer than the gas. Q.1: Why? Q.2: Does this extend to the oceans and/or land surfaces and thus imply that a warmer solid or liquid surface does not absorb radiation from a cooler atmosphere? Q.3: Can you refer me to any experiment proving empirically that backradiation from a cooler atmosphere can warm the surface and/or slow its rate of cooling, as claimed by the IPCC? 390. Silver Ralph says: DeWitt Payne says: January 25, 2012 at 1:15 pm This piece of misinformation seems to be even harder to kill than a gravity maintained adiabatic lapse rate. Temperature, as long as the pressure is high enough it can be defined, is a function of the average kinetic energy of the gas only. What happens at low pressure is that it takes longer for a thermometer to equilibrate with the gas. If the thermometer has a large thermal mass, on the order of the heat content of the volume of interest, it will perturb the actual temperature. ——————————————————————————— But that is the whole point, isn’t it. just what is Dr Brown supposed to be measuring? He says ‘temperature’, which is a wooly term unworthy of a scientist. Does he mean the individual the temperature of individual molecules (molecular kinetic energy), or does he mean the temperature of the total airmass? (See my earlier post, a few scrolls up.) If he means the temperature of individual molecules, then thermal equilibrium in the ‘silver wire experiment’ has already been achieved (between the top and bottom of the air column). The individual molecules at altitude have about the same temperature (kinetic energy) as those at sea level. Thus the warm wire at the top of the collumn (at say +30 oc ) cannot ‘heat the air’ at high altitude, because the individual molecules at altitude are already at something like +30oc (in terms of their individual kinetic energy).. If, on the other hand, he means the temperature of the total airmass, as measured by a standard thermometer, then he should know that you could never get the air at 50,000 ft to be +30oc. Just not possible. Never going to happen. Crazy suggestion. So Dr Brown cannot mean this. So when DR Brown says: “”””Heat will flow from the bottom to the top until they are at the same temperature. At this point the top and the bottom are indeed in thermal equilibrium.”””” He cannot be referring to the total airmass temperature, as measured by a thermometer, as you could never get the air at 50,000 ft to be +30oc. So he must be referring to individual molecular temperatures (molecular kinetic energy). But these molecules at altitude are already at something like +35oc (individually) already. So there will be no heat flow in the wire, because the molecules at altitude are already at the same temperature as those a sea level and the same temperature as the top of the wire. In short, I fail to see what this thought experiment is supposed to prove !! There could never be any flow of temperature in the silver wire. If there were, then there would already be a massive flow of energy through the atmosphere itself, through conduction and convection. And while there IS a certain amount of heat transfer through the atmosphere from surface to tropopause (as we know), this heat transfer has never made the upper atmosphere +35 oc — not even in several hundred million years of heat transfer between surface and upper atmosphere (with or without a silver wire). Again, I must ask, what is this thought experiment supposed to prove? Please see my previous posts at: Ralph says: January 25, 2012 at 12:27 pm and Ralph says: January 25, 2012 at 12:54 pm . 391. Nullius in Verba says: January 25, 2012 at 12:05 pm “… convection on a world with no GHGs … I think it would work a bit like the convection pattern of the thermohaline circulation, inverted. … With GHG-free atmosphere, you have to swap warm for cold and up for down, and equator for pole. Thus, air is warmed at the equator, rises, and spreads polewards. Its potential temperature (adjusted for lapse rate) remains constant then, and most of the atmosphere is equatorially hot, even at the poles. The thin layer in contact with the ground there cools, and flows back to the equator over the surface. … ” I agree with the overall scenario (and was actually thinking of posting something similar), except that I suspect that instabilities and the Earth’s rotation would cause the pattern to break up into relatively narrow latitudinal bands perhaps as little as a few tens of kilometres wide, with a sort of helical circulation in each (like a rope). The bands would probably meander a bit, depending on the local topography, and also wander up and down in latitude with the weather. The bands would sometimes break up further into strings of cyclones and anticyclones. We’d still have a troposphere and tropopause, and, as now, the temperature in the convective cells and at the top of the troposphere would fall fairly gradually from equator to pole. The lapse rate in the active parts of the cells would be more-or-less adiabatic; in between it would be smaller (with temperature inversions common at night). 392. Hey Myrrh you are not stupid. Since last year I’ve been chasing up your statement that visible light does not create heat and believe me the info has not been easy to find and even when I find some it always conflicts with the one I found before. Anyway I’ve come to the conclusion that you are correct. IR radiation is what warns the atmosphere and not visible radiation. Thank you. 393. Joules Verne says: Another paper backing me up. http://adsabs.harvard.edu/abs/1997PhRvE..56.6729T “Nonlinear heat transport in a dilute gas in the presence of gravitation” Looky here boys. If heat is transported more easily in one direction than another then heat will flow in the direction of least resistance. This is what happens in a non-convecting atmosphere. Heat flows preferentially towards the ground until there is enough back pressure from the higher kinetic energy to prevent further flow in that direction. Pressure and gravity come to a stalemate (except in a black hole) and the treaty that ends the war is called the adiabatic lapse rate. Some of you boys would come up with some really interesting kinds of stars with your misunderstanding of the asymmetric directional effect of gravity on heat transport. Or rather your denial that gravity HAS an asymmetric effect on heat transport… I’ll look around for more papers. Given this is a first order effect from first principles in classical thermodynamics I find it hard to believe it wasn’t first described in the 19th century. 394. A physicist says: January 25, 2012 at 10:23 am “These gas centrifuge “experiments” concretely affirm Brown’s theoretical arguments: the observed equilibrium temperature distribution is isothermal. Indeed, the multibillion-$ isotope separation industry would fail otherwise.”

While I would agree that such centrifuges could in principle provide an experimental test of the hypothesis, it is not clear to me that their actual operation necessarily provides conclusive data on this question. They may not be sufficiently well insulated, or isolated from thermal and other energy flows, say – because there is no particular engineering requirement to do so. There might, for example, be some net warming at the top and net cooling at the bottom (the former due to waste heat from the centrifuge machinery, the latter due to air cooling enhanced by the spin).

(I apologise if the reference you gave – which is not accessible to me – already answers these points.)

395. Somebody says:

Guys, please be aware that many things you try to apply were derived by assuming no external fields.

396. Eric Atkerson says:

Dr. Brown,

Thank you for this post. It has encouraged me to think more deeply about the gravitation based temerature theories that I have kind of ignored. I want to do more background reading to get up to speed (I’m a tax lawyer with some undergrad physics, so I’m slow digesting this stuff), but there is one thing in your write-up that I’m having trouble with on a conceptual level.

You seem to have a problem with something as simple as gravity causing an isolated gas to be in an equilibrium state of different temperatures in different regions. But ignoring the semantics of general relativity vs Newtonian gravity, gravity is a force and causes objects with mass to accelerate. So, I don’t quite understand why gravity couldn’t provide the force to run the heat engine.

And aren’t there examples of gravity giving rise to a perpetual motion machine? It is the gravity of the earth (causing the constant acceleration of the moon and resulting in an orbit) combined with gravity of the moon that causes the tides which we can harness to produce work.

And I believe there are examples of gravity applied to a gas in uniform thermal equilibrium with significant consequences. In particular, I’m thinking of an interstellar gas cloud that comes in contact with gravity. The gravity causes the gas cloud to condense, and the condensing gas increases in temperature and pressure. If the mass is sufficient, a star is born.

Have I misinterpreted your concern or am I missing something?

397. DeWitt Payne says:

Silver Ralph says:
January 25, 2012 at 2:57 pm

If, on the other hand, he means the temperature of the total airmass, as measured by a standard thermometer, then he should know that you could never get the air at 50,000 ft to be +30oc. Just not possible. Never going to happen. Crazy suggestion. So Dr Brown cannot mean this.

Not on Earth. But on a hypothetical planet with an isothermal surface and a transparent atmosphere or a very tall insulated cylinder, sure. You just need a surface temperature of 30C (the degree symbol is unnecessary) and a lot of time. Temperature in thermodynamics has a very precise definition. By that definition, a single molecule or atom does not have a temperature. You can plug its kinetic energy into the Boltzmann equation, but the result is meaningless. A cloud of gas moving at nearly the speed of light could have a temperature close to absolute zero because the frame of reference would be the center of mass of the cloud and the temperature of the gas would be the related to the rms velocity with respect to that reference frame. Or think of a meteor coming in from deep space. It would have a very high kinetic energy with reference to the center of the Earth, but if you stuck a thermometer in it before it hit the atmosphere, it would be very cold.

So a thermometer reads according to the average kinetic energy of the molecules that hit it, not the rate that the molecules hit it.

398. DeWitt Payne says:

Eric Atkerson says:
January 25, 2012 at 3:47 pm

So, I don’t quite understand why gravity couldn’t provide the force to run the heat engine.

Energy has units of force (mass times acceleration) times distance or kg m²/s². Gravity is a force, but it has to move something or there is no energy. But at thermodynamic equilibrium, nothing is moving. If something did move, it would only do it once. Some source of energy would then be needed to lift it back up again.

399. DeWitt Payne says:

Joules Verne says:
January 25, 2012 at 3:16 pm

Another paper backing me up.

“Nonlinear heat transport in a dilute gas in the presence of gravitation”

Looky here boys. If heat is transported more easily in one direction than another then heat will flow in the direction of least resistance.

No. Heat always flows from hot to cold. It may flow faster when the temperature gradient is negative than when it is positive, but it still flows only from hot to cold.

400. Joules Verne says:

My bold…

http://www.theweatherprediction.com/basic/equations/

9. The dry adiabatic lapse rate

The change in temperature with height of a parcel of air if relative humidity is less than 100%
dT/dz = g/cp
Units = ms^-2J^-1kgK = ms^-2kg^-1m^-1s^2m^-1kgK = Km^-1
g = gravity 9.81 ms^-2
cp = 1004 Jkg^-1K^-1

Interpretation: The dry adiabatic lapse rate is a direct function of gravity. Since gravity is basically a constant, the dry adiabatic lapse rate is basically a constant.

Example problem: What is the dry adiabatic lapse rate on the planet Venus? How does this compare to the dry adiabatic lapse rate on Earth? The gravity on Venus is 0.904 that of earth. Assume the atmosphere of Venus is pure CO2 (it is actually 96%). The cp of C02 is 840 Jkg^-1K^-1.

Answer: First find gravity on Venus = 9.8ms^-2(0.904) = 8.87ms^-2
dT/dz = 8.87ms^-2/840 Jkg^-1K^-1 = 10.6 ° K/km = 10.6° C/km
A rising parcel of dry air on Venus cools at about the same rate as on Earth

401. George E. Smith; says:

“”””” Eric Atkerson says:

January 25, 2012 at 3:47 pm

Dr. Brown,

Thank you for this post. It has encouraged me to think more deeply about the gravitation based temerature theories that I have kind of ignored. I want to do more background reading to get up to speed (I’m a tax lawyer with some undergrad physics, so I’m slow digesting this stuff), but there is one thing in your write-up that I’m having trouble with on a conceptual level. “””””

Stick to the tax law Eric.
1/ In equilibrium, macroscopic state variables do not vary with time.
2/ Thermodynamic state variables are only measurable and only defined in equilibrium.
In particular your condensing gas cloud system is NOT in equilibrium.
Zero’th law of thermodynamics:- Systems that are in thermal equilibrium with a given system are in thermal equilibrium with each other. Professor Brown’s column of gas is in thermal equilibrium (throughout), and in particular the top is in thermal equilibrium with the bottom; ergo both are in (simultaneous) thermal equilibrium with each other, and also with some third system to which we might attach the label; THERMOMETER. Ergo the whole system MUST BE ISO-THERMAL.
As has been said on several occasions, and I believe Prof Brown said the same thing, a system like your condensing gas cloud, which is collapsing under the effect of gravitational attraction, is having WORK done on it, as a consequence of the gravitational FORCE acting over a DISTANCE; the distance travelled by the molecules during the collapse, and as those molecules close on each other and begin to have collisions with each other, which will turn the pre-collision molecular trajectories into a chaotic set of trajectories in all directions which is exactly what constitutes the Temperature of the gas. It is this conversion of an earlier orderly set of trajectories (towards the common center of mass of the gas cloud) into a chaotic set is why we call it “heat”. It can no longer return itself to the previous orderly motions before the molecules began to collide with each other and it is the work done by the force of gravity as it collects up the molecules that is getting “wasted” in the form of heat, and can only partially be converted back to work, and is why the Temperature is increasing.

Brown is quite correct in stating that if the posited system DOES maintain a permanent Temperature differential from top to bottom, then a thermal conductor would continually convey “heat” from the hotter bottom, to the colder top. I would use Type II-A diamond instead of silver, to pump the “heat” faster.

Sorry, a system in Thermal equilibrium is isothermal, and the much discussed star lit system is NOT in thermal equilibrium, since the star is continually supplying energy to the bottom of the gas.

402. George E. Smith; says:

“”””” Joules Verne says:

January 25, 2012 at 2:00 pm

George E. Smith; says:
January 25, 2012 at 12:52 pm

“There you just shot your self in the head. A gas, ideal or not, cannot consist of a single molecule.”

Ummm… I think it can’t exist as a liquid or solid because that requires proximal arrangement with neighboring molecules. A molecule is a gas generally when it is very isolated from neighbors so that it can flit about traversing a great number of molecular radii without hitting anything else. “””””

I have a simple rule; I never get between someone, and a cliff they are determined to jump off; so go ahead and jump. Perhaps I can hold your wallet for you while you jump.
There are plenty of people willing and able to learn; wasting energy and time on those determined to not learn, is not something I do.

403. Yes, Joules. In a gravity, on a rotating planet that is illuminated on only one side that possesses and night and a day then temperatures differences will cause weather that will move the gassious atmosphere into some kind lapse rate. The actual lapse rate will be a mix of dry and wet lapse rate if humidity is involved.

Now, climate scientists are repeatingly making an assumption to take solar insolation received by the sun on a disk that equals the cross section of a planet (i.e. the earth at 1364 +/- 3 w/m^2), then taking that face-on power and dividing by 4 to make average insolation, steady state, 24 hours/day, without night and day. They do this so that the math is easier. But, as has been shown by me, Willis, Dr. Brown and may others, a constant insolation, constant temperature ground must lead to an isothermal atmosphere.

BOTH ARE CORRECT! BUT THEY ARE INCOMPATIBLE.

If you want to work with a lapse rate, don’t divide solar insolation by 4 !!! Do not start with 240 W/m^2 after the albedo, or even 342 W/m^2 average incoming. Don’t start with a dead planet. You have already committed the error in initial conditions. Average insolation cannot create a lapse rate. It must be an isothermal atmosphere, whatever it’s composition. “It’s Dead, Jim”. But it is only a fiction, a Toy Model, that has no reality. 240 W/m2 might be mathematically correct, but it has no basis reality.

If you want a lapse rate, you must choose a insolation model with a day and night.
One that warms the ground in the day and cools at night.
One in which heat is expressed in temperature – OR is stored as heat of fusion, latent heat, heat of vaporization, heat capacity and conduction into the ground and water.

The lesson I have learned this month is that any scientific paper or theory that divides solar insolation by four and then works with a lapse rate should be marked as untrustworthy. It is founded on false, if not conflicting, physical assumptions.

404. Joules Verne said @ January 25, 2012 at 3:16 pm

Heat flows preferentially towards the ground until there is enough back pressure from the higher kinetic energy to prevent further flow in that direction.

Blimey! And I always thought the flow of heat was from hot to cold. Time to start burning those physics textbooks folks. Send everyone with a PhD, or BSc in physics back to uni to re-earn their degrees… [/sarc]

405. Robert Brown, it is really quite amusing how many here aren’t even considering your little experiment but something else entirely. They’d fail an exam through not reading the question and not answering it but answering something else.

You however, are getting hung up on CO2. H2O vapor is the main greenhouse gas by far in Planet Earth’s atmosphere. It is a very effective IR absorbing gas present in concentrations 25 to 100 times that of CO2 and overlaps the CO2 absorption band and has a significant band where CO2 doesn’t absorb(this is why 35% extra CO2 has no measurable effect). It also exists as ice crystals and liquid droplets with their own CO2 emission characteristics. It seems to me that the tropopause is the average altitude at which the water has essentially all precipitated out. This is the end of the cooling effect of greenhouse gases. Which I consider to be good evidence that CO2 as a greenhouse gas is a bit player. Above that the stratosphere is isothermal as convection mostly cannot operate and then you also get at slightly higher altitudes the solar UV absoprtion which seems to overwhelm the effect of radiating CO2 causing cooling.

406. For those who seem to have difficulty with why heat flows:

Pressure drives mass flow
Voltage drives current flow
Temperature drives heat flow

407. Joules Verne says:

DeWitt Payne says:
January 25, 2012 at 4:25 pm

“No. Heat always flows from hot to cold. ”

Due to Boltzman distribution there will always be some flow in both directions. Net flow is from hot to cold. This is the basic misunderstanding with people who deny the mechanism by which greenhouses gases raise surface equilibrium temperature. They somehow believe that a warm object prevents a colder object from radiating. No such thing happens of course. Radiation flows in both directions with a greater flow from the warmer to the colder. The warmer object can’t stop the colder from emitting photons. All it can do is throw more photons at the colder object than the colder object is emitting.

The same principle of two way flow applies to energy transport by conduction. A few hot molecules in a net cooler ensemble will hop on over to the warmer side. There’s just more frequent hopping in the other direction. Maxwell’s Demon is a hypothetical little guy that sits at a gate between two gas reservoirs at equal temperature. When he sees a hotter than average molecule heading across the divide in one direction he opens the gate. When he sees colder than average molecule going in the opposite direction he opens the gate. He keeps to gate closed to all others. Thus the hotter molecules are sequestered on one side and the cooler molecules on the other.

The age old question is whether or not Maxwell’s Demon can operate the gate with less work than he can extract from the temperature gradient he creates. If he can do that it constitutes a perpetual motion machine.

Gravity is Maxwell’s Demon. Brown thinks gravity isn’t complex enough to be a demon but he’s quite clearly wrong. Maxwell’s Demon is not constrained by complexity. The Demon only requires a differential coefficient of conduction distinguished by direction. In this case gravity does exactly that and the gate sits between higher and lower elevations.

Brown is quite justifiably reluctant to believe that Maxwell’s Demon in this case needs less work to operate the gate than he can get out of the gradient he creates. I agree. There is no perpetual motion machine to be had here. Brown just can’t seem to understand the forces that are powering the demon. He works by using gravitational energy to open the gate in one direction and he uses kinetic energy to open it in the other direction. The net result is a wash because he is sorting the molecules not by total energy but rather by form of energy. Entropy is about total energy on either side of a boundary not about the specific forms of energy. If there’s no difference in total energy across the boundary then there’s nothing to equalize and it’s already sitting in a state of maximum entropy.

A simple pendulum is an example of something that (discounting friction) will swing back and forth endlessly translating kinetic energy to gravitional and back again. There is no energy expended in the translation. But if you try to extract energy you’ll damp the motion of the pendulum and gravity won’t start it swinging again just as gravity won’t add energy back into the atmosphere if you remove some by leveraging the adiabatic lapse rate. You’ll just end up with a colder atmosphere like you’ll end up with slower pendulum in the classic case.

408. Joules Verne says:

A physicist says:
January 25, 2012 at 10:23 am

“These gas centrifuge “experiments” concretely affirm Brown’s theoretical arguments: the observed equilibrium temperature distribution is isothermal. Indeed, the multibillion-\$ isotope separation industry would fail otherwise.”

Isotope separation in centrifuges is by molecular weight. A temperature gradient would have no effect one way or another on that. A physicist should know that. A fifth grader should know that.

409. Eric Atkerson says:

@ Payne

Not sure why you say nothing is moving in thermodynamic equilibrium. The gas molecules are moving and they have a mass that can be acted upon.

410. Joe Born says:

Robert Brown: “There is Paul Birch’s analysis of Velasco, which seems to be a full stat mech computation that arrives at the same conclusion.”

It’s true that Velasco et al. is a statistical-mechanical analysis. But it’s not true that “arrives at the same conclusion.” Quite the contrary. In connection with their Equation 8, what Velasco et al. say is, “i.e., for a finite adiabatically enclosed ideal gas in a gravitational field the average molecular kinetic energy decreases with height.”

So, if you think for yourself and you believe that temperature is mean molecular translational kinetic energy, and if you believe that lapse rate is a change of this quantity with altitude, then you will not “arrive at the same conclusion.” And, if you can read Equation 8, you’ll conclude that it specifies a non-zero lapse rate at equilibrium no matter how may molecules are in the column.

On the other hand, you can accept Paul Birch’s analysis, which in my view is nothing more than so redefining lapse rate as to exclude anything exhibited by a maximum-entropy configuration. I don’t find his reasoning compelling. But decide for yourself whether you find it comes within shouting distance of rigorous.

Also, none of this really matters to the original issue, which is Jelbring’s theory, because the lapse rate Velasco et al. dictate is so small as to be undetectable: if they’re right, too, Jelbring is wrong. It merely means that “the correct static equilibrium distribution of gas in the system is the usual isothermal distribution” is not strictly true.

411. DeWitt Payne says:

Joules Verne says:
January 25, 2012 at 5:08 pm

Regarding your link to Phys. Rev. E 56, 6729–6734 (1997) Nonlinear heat transport in a dilute gas in the presence of gravitation, did you read the article or even scan the abstract? The abstract refers to Navier-Stokes. That’s the equations for fluid flow. It looks to me like the temperature, and thus the pressure, gradient is perpendicular to the gravitational field, thus inducing horizontal flow. But there is no flow in this experiment. I fail to see the relevance.

412. Joules:

No. Your statement “They somehow believe that a warm object prevents a colder object from radiating” is incorrect. Go and read what they do believe: http://climate-change-theory.com/RadiationAbsorption.html

Briefly, the warmer body (Earth’s surface) is not affected by radiation from the cooler one (the atmosphere) because that radiation does not have enough energy (high enough frequency) to bring about the conversion of its energy into thermal energy.

Now, if you don’t accept that, then explain these two observed facts ….

(1) A gas does not absorb spontaneous radiation from an emitter that is cooler than itself, but does do so when the same emitter becomes warmer than itself.

(2) Dew on the ground (shaded from direct Sunlight) can remain there all day (even when ground and air are above 0 deg.C) so why doesn’t backradiation melt it?

413. George E. Smith; says:

“”””” Eric Atkerson says:

January 25, 2012 at 6:03 pm

@ Payne

Not sure why you say nothing is moving in thermodynamic equilibrium. The gas molecules are moving and they have a mass that can be acted upon. “””””

Thermodynamic equilibrium is a MACROSCOPIC PROPERTY of systems; the average velocity (a VECTOR) is precisely zero when the system is in equilbrium. The system is not exchanging energy or matter with anything else.

414. DeWitt Payne says:

Eric Atkerson says:
January 25, 2012 at 6:03 pm

@ Payne

Not sure why you say nothing is moving in thermodynamic equilibrium. The gas molecules are moving and they have a mass that can be acted upon.

There is no organized bulk movement. The molecular movement is isotropic and random with an average velocity over all molecules of zero. That’s why you have to take the root mean square of the velocities

415. Eric Atkerson says:

@ George Smith

But tax gets boring at times so it is good to have a diversion…

My only thought on the gas cloud example is that gravity can act as a heater (maybe a literal pressure cooker) of sorts.

I want to think about Dr Brown’s argument and your response to me a little more, but it would be helpful if you wouldn’t mind clarifying one thing just to make sure we’re not talking past one another. Putting Jelbring’s paper and Prof Brown’s exact example to the side do you think that we could extract work from a gas that is isolated from external heat sources, but is not isolated from gravity (can we use gravity as a replacement bunsen burner)?

416. Eric Atkerson says:

@ Payne

To get temperature, yes. But that doesn’t mean that gravity won’t have any effect on the molecules. And it seems to me that the molecules closest to the source of gravity will end up with a higher average velocity than the molecules further away. After a while I would expect the system to reach a steady state under the influence of gravity that would be similar to an open system that is exposed to a constant heat source at the bottom.

417. Crispin in Waterloo says:

@Joules Verne

I have greatly enjoyed each of your posts. Iwill read the linked article DeWitt doesn’t see as relevant – might agree, might not. I am still of two minds because there are several ways for an isothermal column to be disrupted vertically: Is it hotter on top when there is no radiation into space or at the bottom where teh gas is compressed? The Lettered above cannot even agree on what ‘temperature’ is. Everyone seems to be building models of convenience, leaving out parts here and there. This silly part of this is that the scenario is arbitrary and unreal and ultimately of no value at all.

@ Ye who have Names to be wise: Stop appealing to your own authority. My version of Feynmann: If you can’t explain it to each other, you do not understand it. 40% of Fortune 500 companies are run by CEO’s with no post-secondary education. Schools are filled with examples of sense-dulling and closure. Science degrees have been devalued by the sheer number of ‘scientists’ who have greedily participated in the largest, most expensive sky-is-falling scam ever perpetrated on humanity known as catastrophic anthropogenic global warming. We plebs don’t trust you any more. You gotta explain it from now on.

Even on this little blog it has been mentioned (above) that the narrow CO2 emission band is basically blank at the TOA (because of CO2 saturation at only 390 ppm). Read Prof Lu, 2010 on the implications of recent high resolution IR frequency distribution. Critical thinking is the oxygen of the educated if unschooled mind. Some kings have no clothes.

Willis, can we move on to real atmospheres? This is Angels dancing on a pin head.

418. Correction: That should read …

“FROST on the ground (shaded from direct Sunlight) can remain there all day (even when ground and air are above 0 deg.C) so why doesn’t backradiation melt it?”

Note (in the link* below) that both the ground beneath and the air just above the frost were each just above freezing point, so there should be some conduction into the frost, but no radiation out of it. However, if the backradiation really does have about a quarter of the power of the Sun at noon and the backradiation from a cooler atmosphere really is able to impart thermal energy into the frost, then that frost should have melted at least as quickly as it would have in the Sun for a couple of hours. After all, water molecules should absorb IR radiation, shouldn’t they?

Well Prof Claes Johnson has shown why they don’t when they are warmer than the source.

And if backradiation all day long can’t even melt a bit of frost, how much warming will it cause in the oceans?

419. Crispin: Whilst I trust you know my position on all this, I do not like pushing the “CO2 saturation” concept. Firstly, bands only appear blank at TOA because CO2 scatters radiation and hence, when you point an instrument at some place on Earth, very little appears to come directly towards you from that point. Warmists will argue that the bands just get wider,

None of this matters anyway, because the energy will be mostly converted to thermal energy which can then transfer to other molecules (by collision) and end up being emitted by water vapour for example. Any emission to the surface will not be absorbed and converted to thermal energy (because it comes from a cooler source) and so all radiation from the atmosphere eventually ends up going to space. Hence carbon dioxide molecules have a cooling role radiating away that thermal energy which they acquire from oxygen and nitrogen molecules that cannot radiate themselves. It also absorbs and sends back to space some of the Sun’s incident radiation which is in the IR spectrum, hence also having a cooling effect in this manner.

420. eyesonu says:

Dr. Brown, George E. Smith, Willis, and a couple of others, Thank You.

I want to thank you for this educational opportunity. I have read all the comments that have been presented on this thread as well as other threads. Thank you for explaining the physics as I learned it. Now I feel much better that I could not fully grasp the gravitational temperature effect.

If one can’t follow the thought experiment presented by Dr. Brown, then an understanding will likely be very difficult, a tough nut to crack. Some who like myself are the slowest to grasp something may be most likely to become the greatest supporters of if when we do because we fought tooth and nail not to believe in it. Hence my learning process, quite skeptical with regards to anything concerning ‘climate related’. WUWT and the open discussion here is the greatest venue to acheive that type of learning experience. When every conceivable argument is presented as well as the facts, I feel confident with my knowledge when I walk away. Thanks to all.

421. Willis Eschenbach says:

robr says:
January 24, 2012 at 9:32 pm

… Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?

The DALR is defined as g / Cp, where g is gravity and Cp is the specific heat of the atmosphere at constant pressure. Since I see no pressure term in there, I’m gonna say no.

(Bear in mind, however, that if you double the gravity, you’ll double surface pressure more or less. And so both pressure and “g” will change, and also DALR will change … but DALR will change because of the “g” term, not because of the pressure.)

Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?

A simple answer like – No, no or Yes, No will suffice.

Unfortunately, there is no simple answer to that one, as you are talking about a complete planetary climate system on an imaginary planet, and the pressure would have a host of different effects on winds, evaporation, all kinds of things.

So if anyone gives you a yes or no answer to the second question, they’re blowing smoke.

All the best,

w.

422. Willis Eschenbach says:

don penman says:
January 24, 2012 at 9:42 pm

I refuse to conform to the idea that scientific laws must be obeyed and never questioned.

Cool. Step out of a window, and tell gravity you’ve decided not to obey the law. There’s big money in it … selling tickets. Like getting energy from gravity, however, it’s a one-time thing.

w.

423. Bill Hunter says:

The problem outlined by Dr. Brown is interesting but largely irrelevant to the issue of whether the surface would be warmer in the absence of greenhouse gases.

Here is my reasoning on that.
It’s the analogy to the passive solar water heating system. First lets get a few things clear on that.
A good passive solar system does not need a greenhouse for the collectors to operate well. Often they use just plain black piping. It works nearly as well as pipes in a greenhouse because the 1,000 plus watts of solar radiation far exceeds radiation losses without the greenhouse. The pipes do not ever get warm enough due to the convection occurring in the water system bringing constant cooler water to the inside of the pipes.

Greenhousing the pipes only adds a few degrees to the system and is often not done as that’s the most expensive part of the system. (convection also ensures the surface does not equilibriate to the average daily temperature reading above the surface. Error is greatest at night.)

The heat you get in a passive system is far in excess of the daily average temperature.

Its important to understand this as well. We are looking at incremental warming not warming from the greenhouse effect itself which is already incorporated in the ambient local temperatures.

Finally, we should note that a favorite tactic of folks arguing this point is they want to simplify it by applying uniform radiation. These are analogies like Willis was using to argue against the gravitational effect. But uniform radiation would cause our passive water heating system to fail. All we would have would be water at the ambient local temperature.

The passive system uses gravity and convection but it entirely depends upon a diurnal cycle to obtain a higher average and in no depends upon the radiative effect of the medium in the storage system.

Thus it doesn’t matter a whit if after we invent an atmosphere isolated from any external interactions what it does in those states. The world of Jelbring is only relevant for ruling out external effects from explaining the actual state of the atmosphere at the moment the world is imagined. Thus what it does afterwards is truly irrelevant. It is relevant to how gravity does it but not to whether gravity does it or not.

The AGW advocates would like for us to believe that convection is caused by a radiative atmosphere but the atmosphere inside the pipes of the water system is not radiating, yet it warms and it warms purely by convection and acceptance of radiation at the surface (the collector level)

So what are the results? Well if Jelbring’s conclusions are correct that the adiabatic lapse rate is stable and it probably has a 50% chance of being so (or 49% if you really want to argue it) then gravity causes the surface all by itself to be warmer than it would be without an atmosphere.

And what would be the case if it weren’t stable like Dr Brown claims? Well then it would be like the passive solar hot water system that does not have a defined lapse rate but does convect under a varying heat source and averages a greater temperature than the ambient local temperature (which has the GHG effect included already). Indeed the system would equilibriate as soon as you either turn off the sun or set it at a uniform level of radiation.

So the conclusion is there is 1) Jelbring’s lapse rate is not stable so some great portion of the ATE (redefined GHE) comes from gravity enabled by the variability of downward surface radiation.
Or 2)
Jelbring’s lapse rate is stable so the ATE comes from gravity and variability of the downward surface radiation can be averaged and you get the same result.

What will be interesting is in the details of how this is being correlated to other worlds. And of course Dr. Brown and crew are certainly welcome and encouraged to do the same as one should be able to tease out the differences implied by the two different theories.

Better get that space program back on steroids is all I can say.

• Bryan says:

Bill Hunter says
“First lets get a few things clear on that. A good passive solar system does not need a greenhouse for the collectors to operate well. Often they use just plain black piping. It works nearly as well as pipes in a greenhouse because the 1,000 plus watts of solar radiation far exceeds radiation losses without the greenhouse. The pipes do not ever get warm enough due to the convection occurring in the water system bringing constant cooler water to the inside of the pipes. Greenhousing the pipes only adds a few degrees to the system and is often not done as that’s the most expensive part of the system. (convection also ensures the surface does not equilibriate to the average daily temperature reading above the surface. Error is greatest at night.) ”
Thanks for this practical information it backs up another practical investigation from Penn State Uni on ethylene polytunnel greenhouse.
Basically the project was to find if it made any sense to add Infra Red absorbers to polyethylene plastic for use in agricultural plastic greenhouses.

Polyethylene is IR transparent like the Rocksalt used in Woods Experiment.

The addition of IR absorbers to the plastic made it equivalent to “glass”

The results of the study show that( Page2 )

…”IR blocking films may occasionally raise night temperatures” (by less than 1.5C) “the trend does not seem to be consistent over time”

424. Bill Illis says:

When matter heats up due to compression or from falling into a gravity field, where does the extra thermal energy come from?

What standard model particle delivers the additional energy?

The matter heats up but where does the energy come from.

We know photons or EM radiation can deliver energy through the Electro-Magnetic Force. We know energy is added from the Weak Force in nuclear reactions according to E=M*C^2, the Strong Force does not operate unless Neutron Stars are Black Holes are involved. The Gravitational Force may compress space-time so the molecules themselves may just be more energetic in a space compressed 3-D environment.

But I have never seen an explanation of where the extra energy comes from when matter is heated up due to compression or when matter falls into a gravity well.

It IS coming from somewhere. It is already there, it is just a question of what is the ultimate source of this thermal energy.

• Bryan says:

Bill Illis says

“When matter heats up due to compression or from falling into a gravity field, where does the extra thermal energy come from? ”

If the falling is at constant speed it comes from the work done by atmosphere at that level (PdV work).
Its the opposite of the work done by a rising expanding parcel of air which does PdV work ON its surrounding atmosphere.

425. Silver Ralph says:

DeWitt Payne says: January 25, 2012 at 4:13 pm

Silver Ralph says:January 25, 2012 at 2:57 pm
If, on the other hand, he means the temperature of the total airmass, as measured by a standard thermometer, then he should know that you could never get the air at 50,000 ft to be +30oc. Just not possible. Never going to happen. So Dr Brown cannot mean this.

Not on Earth. But on a hypothetical planet with an isothermal surface and a transparent atmosphere or a very tall insulated cylinder, sure. You just need a surface temperature of 30C (the degree symbol is unnecessary) and a lot of time.

__________________________________________________________

Thank you for the scientific definition of temperature.

However, this is hardly explaining our atmosphere. We have a surface that is sort of isothermal (within a band of, say, +40 to -40oc); we have a fairly transparent atmosphere; and we have had a lot of time to run the experiment (several million years).

Yet the average temperature at 50,000 ft is around -80 oc. And there is no chance of the ‘temperature’ at 50,000 ft ever equalling the suposed average surface temperature of +15oc (ISA defined atmosphere), no matter how sensitive your thermometer. So if your explanation is correct, then why is the Earth so unlike the idealised system?

In short, I still cannot see the difference between the silver wire experiment, and the normal atmosphere. Ok, so the silver wire has greater conductivity to transport het to the upper atmosphere, but the less conductive real atmosphere has had several million years to transport surface heat to the top of the atmosphere and it would appear that it has still not achieved anything like equilibrium temperature.

Some basic explanations without the math is required, I feel.

PS In science you may use ‘c’ as opposed to ‘oc’, but in the rest of the world ‘c’ means ‘cents’ (dollars and….).

.

426. Bill:

One component of total thermal energy is gravitational potential energy. Thus a portion of total thermal energy can interchange with potential energy.

The assumption is that the compression occurs when the body of gas is physically lowered closer to the Earth and thus loses PE. That loss of PE transfers into a gain of KE which contibutes to thermal energy raising the temperature. (Compare the interchange between PE and KE with a pendulum, or when you car starts to roll down a hill.) The opposite occurs when warm air rises.

PS As you probably know, this is a reason for using the term “thermal energy” rather than “(ocean) heat content” as used by you-know-who. There is no fixed thing which is “heat content” and heat is energy in transit as distinct from energy itself.

427. Cal says:

As a “layman” I find this very interesting.

Fig 2 doesn’t really convince me of anything. I like the analogy of the spinning wheel. Let’s say we have a spinning ring in a vacuum with no gravity. The ring will spin forever right? Now imagine we attach a couple gears and a shaft from a fixed point. The gears will simply connect the shaft to the inner ring causing it to spin. If the gears are all frictionless the shaft will rotate forever.

I know the analogy doesn’t fit but it’s close. Obviously if we apply any friction to the shaft (a generator) the ring will stop spinning. Saying any heat runnin through the wire is a perpetual motion machine just doesnt ring true.

Having said all that I think the temperature will equalize in the cylinder and no heat will flow through the wire.

Applying this to our atmosphere is the hard part for me. So we have an atmosphere with a hot side and a cold side. This seems to easily explain the temperature gradient.

What I wonder about is the effect of doubling or tripling the nitrogen thereby increasing pressure. I can’t see this making the hot aide hotter. I imagine the cold side will just move farther out. The atmosphere would be a greater reservoir of heat but the temp wouldn’t be higher.

Taking into account day/night, the rate of conduction at the surface and the differences between surface and atmospheric temperatures oh and GHGs all make things more confusing!

428. Joules Verne says:

As I suspected this notion that gravity produces a lapse rate goes WAY back. James Clerk Maxwell hisself proposed it in 1866. If I’m wrong I’m in very good company. Here’s a nice writeup on the history. Many physicists to the present day have carried Maxwell’s torch. It is not settled science. Maxwell himself collaborated with Boltzman to formulate the Maxwell-Boltzman distribution law that made the column isothermal. Maxwell continued to question its validity though and many since then have also questioned it. At least Maxwell was a good scientist skeptical of his own work his entire life.

http://philosophyfaculty.ucsd.edu/faculty/ccallender/index_files/maxwell.doc

Who’s Afraid of Maxwell’s Demon—and Which One?
Craig Callender
Department of Philosophy, UCSD, La Jolla, CA 92130, USA
Abstract. Beginning with Popper, philosophers have found the literature surrounding Maxwell’s demon deeply problematic. This paper explains why, summarizing various philosophical complaints and adding to them. The first part of the paper critically evaluates attempts to exorcise Maxwell’s demon; the second part raises foundational questions about some of the putative demons to be summoned at this conference.
INTRODUCTION
In 1866 J.C. Maxwell thought he had discovered a Maxwellian demon—though not under that description, of course [1]. He thought that the temperature of a gas under gravity would vary inversely with the height of the column. From this he saw that it would then be possible to obtain energy for work from a cooling gas, a clear violation of Thompson’s statement of the second law of thermodynamics. This upsetting conclusion made him worry that “there remains as far as I can see a collision between Dynamics and thermodynamics.” Later, he derived the Maxwell-Boltzmann distribution law that made the temperature the same throughout the column. However, he continued to think about the relationship between dynamics and thermodynamics, and in 1867, he sent Tait a note with a puzzle for him to ponder. The puzzle was his famous “neat-fingered being” who could make a hot system hotter and a cold system colder without any work being done. Thompson in 1874 christened this being a “demon”; Maxwell unsuccessfully tried to rename it “valve.” However named, the demon’s point was to “show that the second law of thermodynamics has only a statistical validity.” Since that time a large physics literature has arisen that asks a question similar to that asked in theology, namely, does the devil exist?

429. George E. Smith; says:

“”””” Bill Illis says:

January 25, 2012 at 8:22 pm

When matter heats up due to compression or from falling into a gravity field, where does the extra thermal energy come from?

What standard model particle delivers the additional energy?

The matter heats up but where does the energy come from “””””

Bill there really is not much to it. Imagine a humungous cloud of gas but assume the individual moelcules are separated far enough in space. that they basically never (or extremely seldom) ever see each other, so there ar no collisions. Jeans showed that any such cloud no matter how uniform in properties, if the total mass exceeds some threshold value, becomes unstable, and a region of slightly higher density appears. That becomes a gravitational “magnet” attracting every molecule towards that region, which will simply increase the density inhomogeneity.
So your “gravity field”, is the mutual self attraction of all of those molecules to each other, and each molecule will start to move in the direction of the center of mass of all the molecules. So every molecule will be headed towards the same point. Now it is also possible even likely, that the initial velocity vector for each molecule is not directedf exactly at the CM point, but to slightly off center points; and this will result in a rotary momentum, in addition to the linear momentum towards the CM.
Initially there are basically no collisions, so the Temperature is essentially zero (kelvins).
As the molecules move towards each other the density increases, and the inverse sqare law causes the gravity to increase, so the molecules are accelerating towards the CM, ever faster, andf also starting to show signs of a net cloud rotation, depending on the initial state.
Eventually the density will get high enough, and the initial directional non uniformity sufficient to allow molecules to start banging into each other. These collisions are random events, and so they start to change the directed collapse towards a common focal point, into a more chaotic pattern, and the directed acceleration starts to get attenuated by the chaotic scattering of the colliding particles. This is the first sign of both pressure (change in momentum of particles in collision) and also Temperature. The Temperature represents the statistical distribution of individual molecular motions; relative to the common center of mass of the collapsiong cloud. The conversion from an orderly directed collapse to a more chaotic structure, represents the appearance of waste “heat” as the original work done by the force of gravity operating over the distance the molecule moves.

So the source of the energy is simply the work done by gravity forcr times distance. The potential energy of the molecules far removed from the CM of the entire cloud, is slowly being converted into kinetic energy of the onrushing molecular mass, but once collisions start occurring to disturb the uniform collapse, some of that kinetic energy gets converted to “heat” represented by the random distribution of the kinetic energies relative to the CM space co-ordinate frame. The density will continue to increase without limit, as the gravitational force increases due to the inverse square law of gravity, and the rotation will speed up, to conserve the angular momentum of the initial state, as the size decreases, so the moment of inertia continues to decline, and angular velocity increases to keep I. omega^2 constant.

It is the original potential energy of the distantly spaced gravitationally attracted molecules, that first converts to a directed kionetic energy and angular momentum, and finally start so dissipate as heat, once the molecules start to collide.
So the Temperature will increase without limit, until hydrogen thermo-nuclear “burning” starts. The energy released now heats the gas till it becomes an ionised plasma due to the high Temperature, the escape of this centraally generated energy to the suface of the “cloud” , now a proto star will eventually stop the collapse as the outer layers also heat, and the outer plasma will become opaque to the EM radiation generted at the million degree buring interface. So long as the hydrogen keeps converting to helium, the star will shine as a”main sequence star” and thr gravitational collapse will have been halted by the thermo-nuclear energy released.

The problem with the earth’s atmosphere is that there isn’t near enough gas to reach the density and Temperature to start hydrogen conversion, so the collapse stops when the pressure generated by gravitymatches the gravity force. The heating that occurs during collapse due to the work done by gravity, is eventually radiated away assuming no star is nearby, to supply new energy.

We hqppen to have such a star that delivers EM energy to the bottom of the transparent atmosphere, and that energy warms the bottom of the atmosphere by all the well known thermal processes, until the energy loss rate, eventually limited by radiation, matches the supply rate from the star. It is the heating of the atmosphere bottom, by the star light, that creates the outgoing Temperature lapse rate. It is NOT gravity that creates the Temperature gradient.

430. Silver Ralph and others:

I confess I have not read many posts on this thread, so I may be repeating something said by others. NASA data shows mean temperatures going down to around -60 deg.C in the troposphere, then back up by about 40 degrees in the stratosphere. Then I understand they go back down to around -100 deg.C at the mesopause, but then can be much warmer than the surface (even over +100 deg.C) in the thermosphere.

Any experiments in glass jars, cardboard boxes etc (including those of Arrhenius, Wood and Nahle) can never emulate an open atmosphere. One reason is that the inside surfaces of the containers absorb (and transmit) thermal energy, and can contribute to overall warming or cooling. Also pressure is nearly uniform, so downward conduction occurs and the Second Law applies. However, one “result” of the Second Law (see Wikipedia) is uniform pressure, and obviously that doesn’t apply in the atmosphere.

Hence, adiabatic temperature variations are a fact of life in the atmosphere. Furthermore, there will never be a stable state due to weather conditions. Energy is continually entering the atmosphere (probably more than 50% at the surface) and then of course it takes a finite time for warm air to rise by convection, cooling as it does so. In fact I understand that its motion is more cyclic, rising in equatorial regions and falling at the poles where inversion can prevail.

Then there are further complications when incident solar radiation causes some warming, and evaporation and radiation “springboard” some of the energy from the surface to somewhat higher altitudes.

The lapse rate is far from constant, there being a fall of roughly twice as much in the first 14,000 feet as in the next 11,000 feet for example, according to NASA data. This may be due to the springboarding of latent energy in evaporated water going up to cloud levels.

No one really has a hope of modelling it all accurately – ever.

Pick a good spot to live on this planet – and enjoy your weather!

431. @Bill Hunter. Thank you for that example where the diurnal day-night pumping is so essential for a passive solar hot-water system.

As I wrote earlier in the tread, the “average insolation” concept so often used to explain the climate energy balance misses so much. You have given us a great example: Solar Heaters don’t work without a night and day.

432. George E. Smith; says:

“”””” Eric Atkerson says:

January 25, 2012 at 7:02 pm

@ George Smith

But tax gets boring at times so it is good to have a diversion… “””””

The short answer Eric is yes; but only for a short period of time.
Gravity provides a FORCE, that attracts the gas towards the ground. That force is m.g, where m is the mass of the molecule, and g is the acceleration due to gravity, so m.g is literally the WEIGHT in the gravity field of that molecule.
When that force pulls the molecule down some distance, the WORK done is the force times the DISTANCE moved . WORK is FORCE times DISTANCE (moved). ENERGY is the CAPACITY for DOING WORK.. Now of course the gravity will change with distance so you would have to do a calculus integration to get the correct answer.

As the gas drops under gravity and work is done by gravity compressing that gas; that work gets converted into heat as the molecular collisions increase at the higher density and the pressure goes up. The compression WORK gets converted to heat; BUT, once the collapse stops when teh pressure builds up enough to stop the fall, then the gas starts to lose energy and cool, by radiation, and eventually the whole thing would settle at a fixed Temperature. That assumes no other source of energy such as a nearby star. So yes gravity can create heat in compressing the gas but it is a transient event.

433. Silver Ralph says:

DeWitt Payne says: January 25, 2012 at 4:13 pm
So a thermometer reads according to the average kinetic energy of the molecules that hit it, not the rate that the molecules hit it.

_________________________________________________________

Sounds counter-intuitive, to me.

So an aircraft travelling at the normal TAS of 450kts (say, 900kph) at 40,000 ft, increases the measured temperature of the air by, say 30oc (-30oc TAT, as opposed to -60oc OAT). Are you saying that this measured temperature increase is solely due to an increase in the (relative) speed of each molecule hitting the probe, rather than the increased number of molecules hitting the probe? (The number of collisions with the temperature probe increases dramatically with increasing speed, as you might expect.)

I always thought that the surface warming of an aircraft (several hundred degrees-worth on Concorde), was due to the increased number of molecules hitting the airfame, and not the individual molecule’s increased velocity..

.

434. I don’t understand what all this commotion is about, this is not a novel problem!

This is not an appropriate application of thermodynamics, vis analysis of the atmospheric temperature lapse rate. The ideal gas atmosphere, or also the real atmosphere, isn’t isothermic. There is no “thermodynamic equilibrium” in the real atmosphere or even in an ideal gas atmosphere. There is no “heat flow”. There is no actual “heat”, anywhere at all, in this argument.

The atmospheric temperature lapse rate is a very simple statistical mechanical problem; it is energy partition, elastic molecules colliding in a gravitational field. A simple one dimensional model demonstrates it. Contrary to Dr Browns arguments, there are no Maxwell’s demons in the adiabatic lapse rate, and no other thermodynamic shibboleths. No “heat” is necessary, or even actually exists. There is no “perpetual motion” anywhere in the atmospheric temperature lapse rate, any more than the Laplacian elliptic operator, energy partition, and orbiting planets are “perpetual motion”. Gravity applies to molecules as well as to planets. Absent planetary gravitons, the atmospheric temperature lapse rate would still exist if little elastic strings were used to tie all the air molecules to the Earth.

435. addendum: The atmosphere temperature profile is described by bulk gas properties (ideal gas law) up to the tropopause, and gas radiative transport properties in and above the stratosphere.

436. addendum: The formalizations of the arguments here are very confusing; “heat”, “work”,
“equilibrium”, etc. The only real things involved here are electrons, photons and gravity (and extra inert mass proportional to electrons). This isn’t difficult!

437. Jordan says:

You have been tenacious and your “temperature” was never raised. You have approached the issue from numerous angles to explain your reasoning and helped to improve my appreciation of all of the relevant points.

Others have presented their arguments forcefully too. But – despite it being described as a textbook case (an appeal to authority), I remain unconvinced by the arguments at the top of this thread.

438. wayne says:

This point about openness is perhaps also of relevance to the gravity demons. It is not clear that classical thermodynamics operates very well outside the idealization that there are no significant long-range forces present. Pippard [22], for example, states that the notion of adiabatic isolation is applicable only when gravity is excluded. So if the second law is restricted to adiabatically isolated systems, as Clausius assumed, and if Pippard is right, then it’s not clear that a gravity demon meets the strict requirements of a closed isolated system. Further discussion of this and related questions regarding the range of the Maxwell-Boltzmann distribution is needed.

http://philosophyfaculty.ucsd.edu/faculty/ccallender/index_files/maxwell.doc

439. Silver Ralph wrote “Sounds counter-intuitive, to me”

You should trust your intuition a little less it would seem. The plane warms by friction. The thermometer measures temperature, not the amount of friction. Temperature has nothing to do with the density of molecules. If it did, consider a near vacuum such as between the walls of a vacuum flask – does that have a temperature of near absolute zero? Hardly!

440. George E. Smith; Jan 25, 2012 at 9:23 pm

“It is the heating of the atmosphere bottom, by the star light, that creates the outgoing Temperature lapse rate. It is NOT gravity that creates the Temperature gradient.”

This simplistic summation really does not take into account all processes involved. For a start you ignore energy transfer by phase change. You appear to disregard the physical rate at which warm air rises by convection. When the warm air rises, I’m not even sure that you take into account the conversion of the change in gravitational potential energy to thermal energy, do you? If so, why isn’t gravity in your result?

What, may I ask, is wrong with this computation which gives a very different result?

441. George, Robert G Brown (and others)

Of course I realise that this is leading to a very different result, but it is one which agrees quantitatively with reality and, in this case, I go with Professor Claes Johnson’s computations and obviously much more comprehensive coverage of the various processes in the atmosphere.

442. Bill Hunter said @ January 25, 2012 at 7:48 pm

The problem outlined by Dr. Brown is interesting but largely irrelevant to the issue of whether the surface would be warmer in the absence of greenhouse gases.

Here is my reasoning on that.
It’s the analogy to the passive solar water heating system. First lets get a few things clear on that.
A good passive solar system does not need a greenhouse for the collectors to operate well. Often they use just plain black piping. It works nearly as well as pipes in a greenhouse because the 1,000 plus watts of solar radiation far exceeds radiation losses without the greenhouse. The pipes do not ever get warm enough due to the convection occurring in the water system bringing constant cooler water to the inside of the pipes.

Greenhousing the pipes only adds a few degrees to the system and is often not done as that’s the most expensive part of the system. (convection also ensures the surface does not equilibriate to the average daily temperature reading above the surface. Error is greatest at night.)

The heat you get in a passive system is far in excess of the daily average temperature.

Gosh! I’ve been wasting money on putting greenhouse film on my greenhouse when I didn’t really need any. Whoda thunkit? People who use greenhouse film to raise the temperature around their crops are all idiots wasting their money? Don’t think so Bill…

• Pompous said:

“Gosh! I’ve been wasting money on putting greenhouse film on my greenhouse when I didn’t really need any. Whoda thunkit? People who use greenhouse film to raise the temperature around their crops are all idiots wasting their money? Don’t think so Bill…”

Check and see if your fancy IR film is also moisture resistant. Reducing the thickness of the moisture layer on the inside of the cover has more effect than the IR coating.

443. Joe Born says:
January 25, 2012 at 6:04 pm

“It’s true that Velasco et al. is a statistical-mechanical analysis. But it’s not true that “arrives at the same conclusion.” Quite the contrary. In connection with their Equation 8, what Velasco et al. say is, “i.e., for a finite adiabatically enclosed ideal gas in a gravitational field the average molecular kinetic energy decreases with height.””

They do come to the same conclusion; they quite clearly show – and state – that, for any macroscopic system, canonic or microcanonic – the sort of system we are actually interested in here – the result is isothermal, as it should be. You keep refusing to accept – or even adequately acknowledge – that their Equation 8 doesn’t mean what you want it to mean, because temperature itself doesn’t mean what you think it means in that isolated small-number regime.

Joe: ” … if … you believe that temperature is mean molecular translational kinetic energy … ”

But that’s the point. For small isolated systems it isn’t. The limiting case of the single isolated particle, which has no thermodynamic temperature, proves this.

Velasco et al do not calculate a thermodynamic lapse rate in the small-number microcanonic regime at all. They do not prove it to be isothermal; nor do they prove the contrary. What they do show is that their statistical mechanics confirms the thermodynamic conclusion that – for ensembles large enough to apply said thermodynamics to – the answer is indeed isothermal.

Joe: “On the other hand, you can accept Paul Birch’s analysis, which in my view is nothing more than so redefining lapse rate as to exclude anything exhibited by a maximum-entropy configuration.”

Please stop misquoting me. I said nothing whatsoever about “maximum entropy”. I didn’t even mention entropy. I didn’t need to. My “redefinition” (not actually a redefinition at all, but the utterly bog-standard original definition) is simply the statement that things in thermal equilibrium are at the same temperature; that’s what “same temperature” means.

444. Doug Cotton said @ January 26, 2012 at 1:15 am

Temperature has nothing to do with the density of molecules. If it did, consider a near vacuum such as between the walls of a vacuum flask – does that have a temperature of near absolute zero? Hardly!

No. It lacks a defined temperature because temperature does depend on density of molecules. Consider a universe in which there is exactly one molecule. What temperature is it? Consider a universe in which there are two molecules and we know the exact distance between them. What is their temperature? Rinse and repeat…

• Pompous said:

“Consider a universe in which there are two molecules and we know the exact distance between them. What is their temperature? Rinse and repeat…”

Come on, you sound more intelligent than that. You have just described an instant in time when you know the distance between two particles. You have not indicated mass, velocity, acceleration, vectors…

Rinse and repeat…

445. kwik says:

robr says:
January 24, 2012 at 9:32 pm

“Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?”

Willis Eschenbach says:
January 25, 2012 at 7:40 pm

“The DALR is defined as g / Cp, where g is gravity and Cp is the specific heat of the atmosphere at constant pressure. Since I see no pressure term in there, I’m gonna say no. ”

Hmmm. Interesting.

What is Cp, or “specific heat”, really?

http://en.wikipedia.org/wiki/Heat_capacity

I am just trying to repeat all this again (25 years since my school-days);

If Cp had been “molar heat capacity” in that formula, then pressure wouldnt matter IMO.

But, since Cp is “Geat Capacity per unit mass” of a material….that means that if you increase the mass…then Cp increase. Right? Or am I misunderstanding this sentence?

So, how can you increase the mass? Well, increased pressure is really just that the number of molcules per volume unit has increased. Right? Hence, the mass has increased. And therefore Cp increase.

So, In my opinion , yes, increased pressure => increased mass => increased Cp.