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:
- In static force equilibrium. There is no bulk transport of the gas as buoyancy and gravity are in perfect balance throughout.
- 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.
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.
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.)
Guys, please be aware that many things you try to apply were derived by assuming no external fields.
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?
Silver Ralph says:
January 25, 2012 at 2:57 pm
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.
Eric Atkerson says:
January 25, 2012 at 3:47 pm
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.
Joules Verne says:
January 25, 2012 at 3:16 pm
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.
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
“”””” 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.
“”””” 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.
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.
Joules Verne said @ur momisugly January 25, 2012 at 3:16 pm
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]
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.
For those who seem to have difficulty with why heat flows:
Pressure drives mass flow
Voltage drives current flow
Temperature drives heat flow
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.
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.
@ur momisugly 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.
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.
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.
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?
“”””” Eric Atkerson says:
January 25, 2012 at 6:03 pm
@ur momisugly 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.
Eric Atkerson says:
January 25, 2012 at 6:03 pm
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
@ur momisugly 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)?
@ur momisugly 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.
@ur momisuglyJoules 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.
@ur momisugly 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.