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.
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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“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:
http://pds-atmospheres.nmsu.edu/education_and_outreach/encyclopedia/adiabatic_lapse_rate.htm
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.
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.
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.
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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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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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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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.
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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“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.
Yep. Score is:
skepticism +1
crank science -1
Those coffin nails seem to be bending a lot lately.
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.
DP is right and this article is wrong!
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???
Richard says
Hmmm. Temperature is the integral of the number and energy of particles seen at the measuring surface.
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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.
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!
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.
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.
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.
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.
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?
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.
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.
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.
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!
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