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.
Correction link should be: http://discover.itsc.uah.edu/amsutemps/
thepompousgit says:
January 24, 2012 at 9:13 pm
MDR said @ur momisugly 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:
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.(*)
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.”
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.
Joules Verne says:
“WRITE THAT DOWN, PROFESSOR!”
Is “Joules Verne” another screen name for Dave Springer?
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.
What about the ocean? Big potential energy gradient there. What energy gradient balances it?
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
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
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.
http://tallbloke.wordpress.com/2012/01/25/hans-jelbring-an-alternative-derivation-of-the-static-dry-adiabatic-temperature-lapse-rate/
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…
rgb
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…
rgb
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.
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???
What does this even mean? I can just as easily say “This article is right and you are wrong.” But what good does it do?
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.
rgb
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.
rgb
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.
rgb
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.
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.
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”.
rgb
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.
rgb
Robert, you’ve fought an honorable battle. My advice is to disconnect before the maelstrom of gravity creates an event horizon in Raleigh
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.
rgb
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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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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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…
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.
I haven’t read all the comments, so apologies if this point has already been made.
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?
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…