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.
@Willis
But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety [“Open a standard introductory physics textbook. Learn what temperature is. Then return.”] and not of the collegial variety [“If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?”] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?
From Tricks conversation above
Quote
Robert Brown says at 9:07am:
“…in figure 2 above. Which is violated — the heat equation in silver or your absurd assertion that gravity can stably sort out a gas into a hotter temperature and a colder one? One or the other.”
Unquote
Is this not exactly the basis for astrophysics?. gas collects by gravity, warms up, gets denser, then warms enough to become a star!!!!!!
MDR says:
January 24, 2012 at 8:35 pm
@Willis
But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety [“Open a standard introductory physics textbook. Learn what temperature is. Then return.”] and not of the collegial variety [“If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?”] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?
=========
Lots I imagine. The trick is to ignore it, it’s a form of bullying when they can’t answer your questions, for the most part.
Carry on throwing them in every now and then … I’ll enjoy it for one, who’s been on the receiving end rather a lot.
Re: Jupiter giving off more heat than it absorbs.
Just where is the proof that there is not a large radioactive core at its center, similar to what Earth has, but at 10 to 1000 times its size? Everyone making the claim that gas compression is responsible for Jupiter’s IR signature is making the same mistake Lord Kelvin made in estimating the age of the Earth.
To Robert Brown,
Quote “This is a good question for a real climate scientist. I’m not even a Sears climate scientist”.
Hey, I hope you mean Francis Weston Sears. I have only superficially followed this discussion, but I feel your pain.
When temperature decreases with altitude that’s gravity driven lapse rate…
When temperature increases with altitude (very common this time of year where I live), why that’s just weather /sarc
1) if the several km-long tube is horizontal & the perfectly dry air is at a constant temperature throughout & is moved to the vertical, the dry adiabatic gradient will be produced (warm at the bottom, cool at the top w/ approx 8C/1000m gradient in between) due to the ‘work’ of gravity creating a pressure gradient to the compressible gas. Notice, no gradient will be produced if water is used instead of gas because water is non-compressible so no work will be done. If no heat is added or removed to the gas, the column will be in a neutral buoyant state (and will stay that way!!) – if a parcel of air is moved vertically by an outside force, it’s temperature will change to reflect the change in pressure but will still be the same temperature as it’s surroundings.
2) as to the experiment with the thermal conductive wire at the base & top of the tube, the author here is incorrect. If the wire moves heat from the bottom of the tube (the base cools) to the top of the tube ( the top heats), presuming, as the author says, “…save to note that the internal conductivity of the ideal gas is completely neglected.”, the heat from the *local* area of the wire is all that will be moved from the bottom to the top ***and nothing else*** . Why, you ask?? In moving the heat from the bottom of the tube to the top is causing the lapse rate to become **more stable** – cool at the bottom with warm air above is an inversion which inhibits vertical mixing!! THAT is why the engine will not work as it is set up.
Nonsense. I provided a stable isothermal solution, one that is straight out of a textbook. Well, all the textbooks. Why, exactly, is gravity going to further compress any of the fluid, when it is all in static force equilibrium?
You’re thinking of the local heating that you’d get if you dropped a uniform density of air into a column and it settled down into something with a transient lapse rate, because the falling air would indeed heat up. But it isn’t stable! Once it “hits the bottom”, it will gradually conduct heat and adjust pressure and density until it reaches the isothermal distribution that is demonstrably in both force and thermal equilibrium.
As for 2) — you clearly miss the point entirely. I don’t know if you are clueless about fourier’s law or are just being stubborn.
Look, forget gravity. Take two insulated reservoirs filled with anything, one at temperature T_h and one at temperature T_c. Put a wire in between them that can conduct heat. Heat will be conducted from the hot to the cold reservoir. I don’t care if they are uphill, downhill or side to side from each other. Don’t care if one contains air, the other water, or both air, or one a chunk of iron and the other a bucket of feathers. Don’t care if one is at high pressure, the other at low pressure. If you are a “40 year meteorologist”, then presumably you know what the zeroth law of thermodynamics is because otherwise you don’t even know what a thermometer is or how it works or what it does.
The wire in figure 2 doesn’t move heat from “the local area of the wire” and nowhere else. The gas is a conductor of heat. If you cool even a tiny bit at the bottom near the wire, and heat the gas only a tiny bit at the top near the wire, you push the gas away from what you — in 1) claim is the stable equilibrium of the gas. The meaning of stable equilibrium is that if you perturb it away, it comes back. So you can’t make your lapse rate “more stable” by cooling the bottom and heating the top, you either destroy it the lapse rate altogether by heating the top and cooling the bottom until there is no lapse rate or else the system restores the lapse rate, moving the heat from the top back to the bottom.
The former is what happens, because in the second case the second law of thermodynamics is violated. Except that you don’t have to, because:
An Ideal Gas Is Not Really Adiabatic
If you are a meteorologist — which I seriously doubt, at least I doubt that you are a competent one who has actually studied physical climatology since I’ve studied exactly one textbook on it and seem to know more than you do — then you know perfectly well that no gas fails to conduct heat.
The container the gas is in (in our ideal world) might be adiabatic. An parcel of ideal gas moving up or down the air column might be approximately follow an adiabatic expansion curve because air is a relatively poor conductor of air so the error made assuming it is adiabatic is small if the transport time is much shorter than the time for conduction to make secular changes in temperature. But air is not, I repeat not, adiabatic. Once it comes to rest, with no vertical transport, it instantly starts to conduct heat around to bring the system into real thermal equilibrium, which is isothermal.
The silver wire is just a way of hurrying the process up, and letting you see a channel that carries energy. There is absolutely nothing that will restrict heat flow in the wire but the departure of the distribution of heat in the gas from the lapsed distribution that you claim is a stable equilibrium one.
Either you were mistaken (and the system thermalizes to an isothermal state where heat no longer flows) or else heat flows forever as the gas restores equilibrium, permitting more heat to flow in the wire to the top, which the gas moves to the bottom to restore equilibrium, to infinity and beyond.
Because the gas itself conducts heat, you don’t really need the wire. The dry air adiabatic lapse rate isn’t stable because air conducts heat.
rgb
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?
MDR said @ur momisugly January 24, 2012 at 8:35 pm
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.
Doesn’t the silver thread require energy input to keep it at top of atmosphere?
Would not the top of atmosphere have to have tremendous amounts of energy to maintain the same temperature as it is less compressed? Would that energy be great enough to actually break the gravitational bounds of earth? If the molecules escape earth gravity, does that cool the top of atmosphere?
The thing is that the Top of atmosphere is not bound. As energy is increased in the atmosphere, the top of atmosphere moves further away from the earth surface. As energy decreases, it moved closer to the earth surface.
The silver thread does not even need an atmosphere though to move energy away from the earth surface, as it can just simply radiate at beyond the top of atmosphere.
Holding the silver wire at the top of atmosphere ends up requiring the exact same amount of energy to be expended as the energy that the wire can transfer to the top of atmosphere would be my argument. The work required to keep it up there increases the energy at that point. Work is being done.
I do not think the author has convinced me that there would not be a lapse rate in our atmosphere. I can see that there would eventually be equal amounts of energy at each and every place in the atmosphere, but that energy does not translate directly into temperature. The column could come to equilibrium only at the point in which the earth surface is the same temperature as the lapse rate effected temperature of the air immediately above it. At that point, there would be no heat transfer from a steady state temperature surface to the atmosphere that is at the exact same steady state temperature. It would require outside forces at that point to cause turbulence.
Two points.
1. Jelbring is wrong, not because of the adiabatic lapse rate but because he defines the greenhouse effect as the adiabatic temperature difference between two levels. This definition is wrong because the greenhouse effect is purely a radiative effect, not a gravitational effect. You can simulate the radiative greenhouse effect sideways in a lab just as well as vertically.
2. Brown is wrong. The heat flux in a gas depends on the potential temperature gradient, not the temperature gradient. Potential temperature is related to temperature by a function of pressure only. An isentropic atmosphere has uniform potential temperature. An isothermal atmosphere has potential temperature increasing upwards leading to a downward heat flux. An isentropic state is the state of maximum entropy and will not separate into a state with a different potential temperature profile because that would have a lower entropy, given that total potential temperature has to be conserved when integrated over the mass in adiabatic processes. Closely related to potential temperature is dry static energy, cp*T + g*z, where cp is the heat capacity at constant pressure (1004 J/kg/K). This form shows that potential energy is part of the total energy with the other part being an enthalpy or internal energy +PV. This is approximately conserved.
Robert Brown says:
Willis Eschenbach says:
My guess is that if my questions are ignored long enough they will go away. But I will keep asking, in your opinion:
Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?
Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?
A simple answer like – No, no or Yes, No will suffice.
Thank you,
robr
Right. This is why Robert Brown had to invent the perfect insulator design in fig. 2. How’s the patent pending process coming along Robert?
Oh, for Pete’s sake. Have you even read Jelbring’s paper? Of course not. Do you know what the word “adiabatic” means? Obviously not.
Just FYI, since your childish rant is complete lunacy and seems to be nothing but logical fallacy from end to end, Jelbring begins by assuming an entire adiabatic planet. No energy in, no energy out. He surrounds the planet with that “perfect insulator”. He does this to assert that the gas will have an adiabatic lapse rate in stable thermal equilibrium, with no energy in or out. I prove, quite clearly, that no lapse can be thermodynamically stable.
Wait, wait, wait. It’s obvious that I’m wasting my time. You think that the thermal insulator around the gas — present in both Jelbring’s model and mine — matters to the argument. You also think that Joules ravings about the gas collapsing to a supercooled liquid is somehow lucent and relevant.
I gotta ask it. Are you on drugs? I keep reading your “rebuttal” and it is lunacy, utterly incoherent. Do you think that you could maybe go cold turkey for a day or two, maybe drink some coffee, and see if you could actually winnow an argument out of all of the straw men, ad hominem, sarcasm, and so on? I dunno, maybe an actual statement of what the final temperature distribution of the system drawn in figure 2 will look like?
No? Sigh…
rgb
I believe Robert G Brown’s explanation is correct. On the other hand, kdk33 gives us a detailed argument, also apparently correct, that shows why temperatures must follow an adiabatic lapse rate.
The resolution is, I believe, simple; Brown is talking about a thermally isolated (equilibrium) hypothetical atmosphere, whilst kdk33 is talking about a steady state atmosphere with sources of incoming and outgoing energy.
Putting it simply, the ALR is the maximum temperature gradient per unit change of pressure. Greater T gradients are prohibited by convection: A warm air parcel, on rising, will still be less dense than the air around it at the higher altitude, and so will rise even more. Air will keep on rising until the lapse rate is no greater than the ALR. It is just like the slope of the pile of sand in an hourglass: sand falling through the hole piles up in the centre until the critical slope is achieved, and then sand grains roll downhill to maintain the maximum gradient. But once the sand flow stops, there is no longer anything to maintain the gradient: a few jiggles and bumps and the sand evens itself out. In the same way, in an isolated column of air, a few jiggles and bumps (i.e. molecular collisions) will even out the temperature. But in the real atmosphere, there are sources and sinks of energy, and so an active process keeps on ‘topping up’ the imbalance and so all planetary atmospheres are at or close to the ALR. (The fact that they all are is conclusive evidence that there is little or no scope on real planets for changes in ‘greenhouse’ gasses to have significant temperature effects – even if the process worked just the way the AGW theorists claim!)
I refuse to conform to the idea that scientific laws must be obeyed and never questioned.
http://science.kennesaw.edu/~rmatson/3380theory.html
Because that claim —foreseeably (and strictly IMHO) — is going to emerge as the primary fallback position of GHE skeptics.
But who cares? There’s direct observational evidence for the GHE. Maybe I should make that my next article, simply showing the evidence without talking about the details of the mechanism. The IR spectra speak for themselves. Even if Jelbring were right instead of deluded it wouldn’t stop there from being a GHE. You can see it — with IR eyes.
In the meantime, first Jelbring, to clearly demonstrate that DALR is a consequence, not a cause, of differential heating and cooling of surface and atmosphere. Next N&Z because their “miracle” model for planetary temperatures is complete bullshit (and we’ll see what they have to say about DALR after Jelbring isn’t there any more as a crutch).
Then maybe we can start looking at actual skeptical science. Remember, I’m a skeptic, especially of the “C” in CAGW. I just don’t like bullshit arguments and bad science on either side of the issue. Good science, plausible arguments are just fine.
rgb
I don’t believe there can be a lapse rate in a closed system at equilibrium. We observe a lapse rate because a continual flow of energy heats the planet’s surface, which heats the atmosphere above it. The heated gas at the bottom of the column is continually shedding the energy onto the gas just above it, and so on, so that the energy is passed along as if by a bucket brigade. TUrn the sun off, and everything will begin to settle down. As the atmosphere cools, it no longer has the energy that allowed it to extend so far from the planet, and it shrinks, becoming denser and denser as it is pulled down by gravity. At some point it will condense, if the planet’s gravity is sufficient, and then it will freeze, unless there are liquids that do not freeze at 3K. At this point, it is safe to say there is no lapse rate.
What is going to kill these gas giants?
If gravity is constantly maintaining hotter gases at the bottom then convection will move gases around and therefore we seem to have an everlasting living planet.
Screw gas giants in our solar system — they are wussies.
You want gravitational heating, check out:
http://en.wikipedia.org/wiki/Brown_dwarf
A subcritical brown dwarf — one just a bit too light to ignite fusion — heats from gravitational collapse that continues (IIRC from when I taught astronomy) for something like 100 billion years. Brown dwarves will still be gradually releasing heat from gravitational collapse when our own sun isn’t even a faint memory. If the Universe turns out to be closed, some might make it to the next Big Crunch.
Jupiter and the other gas giants are too light (and hence cold) to be considered brown dwarfs, but they are still slowly collapsing and hence give off more radiant heat energy than they absorb from the Sun.
rgb
The reason the silver thingy won’t generate perpetual motion is that the exposed ends will assume whatever the air temp is at that altitude. A temperature difference of 1 degree will not move any heat in a silver rod 100 meters long.
Why not? I could fill the space inside the insulated chamber with insulated rods so that A is huge. Also, it isn’t correct to say that it won’t move any heat. It will just move heat slowly. But I don’t care how fast it carries heat because any heat causes perpetual heat flow. This is a gedanken experiment intended to show that Jelbring’s equally gedanken “adiabatic world” will not have a thermal lapse rate in static thermal equilibrium, nothing more. I don’t care how long it takes to reach equilibrium. Equilibrium has no thermal lapse.
I don’t even need the silver. Air conducts heat all by itself. It’s not a great conductor, but it doesn’t have to be to establish equilibrium.
The point may seem minor, but it transforms “adiabatic lapse” from a sort of “miracle heating” that starts from an outside boundary condition and heats to the surface via lapse into a consequence of forced convection due to the differential delivery of heat to the surface, a dynamic process and not a static one, one that goes away if you stop actively maintaining the surface and some part of the atmosphere overhead at different temperatures. It goes from being the great, noble cause that will replace the GHE and prove that it is all part of the nasty CAGW-IPCC conspiracy and was never true at all to being a possibly important mechanism that helps establish the GHE.
I don’t know why people are so stubborn about this. It could be that an improved understanding of the dynamical transport mechanisms associated with the DALR and convection might help place limits on the climate sensitivity to GH forcing, and that people on this list could be thinking about things like that instead of trying to pretend that the GHE isn’t real. Especially in the face of IR spectroscopy that pretty much directly proves that it is.
rgb
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.
Which does not occur in the real world. That’s why we call it weather. Sorry, no sale. This is just as unacceptable as the nonsense about CO2, a trace gas having more effect than water vapor on the planet’s temperature.
Which is fine, I agree. As I noted at the beginning, I’m specifically addressing Jelbring’s EE paper, EEJ. Read it, and you’ll see what I object to. The nonphysical assumptions in my toy above precisely mirror his, except that I don’t bother making a “round planet” as that has nothing to do with his assertion that an isolated gas in a gravitational field will have a stable thermodynamic equilibrium with a temperature lapse.
If you agree with that, well, that’s all I was trying to sell. I’m not asserting that a DALR doesn’t occur — only that it is a dynamical feature of differential warming on the bottom and cooling on the top. If you do look at where there is a DALR in planets, it is in the convective zone where this differential heating drives atmospheric turbulence and turnover. I’m not sure I would put Jupiter and the gas giants into this particular picture, as they probably have at the very least different mechanisms for differential heating at the “bottom” of their “tropospheres” (whatever that means for planets that don’t really have much of a surface, at least where it is relevant). But none of that is the point of this thread. My purpose is to drive a stake through the heart of the Jelbring paper, once and for all so we can all leave bad, law-of-thermodynamics violating physics behind. The DALR isn’t due to Jelbring, and if you take away his assertion that it is a stable equilibrium in an isolated system there is nothing left.
rgb
In a cylinder with gas at the usual DALR, all that his conducting wire will achieve is a infintesimally thin layer or hotter gas at the top plus an infintesimally thin layer of cooler gas at the bottom.
Both of these would reverse the lapse rate ( inversion) and thus no further heat can be exchanged without adding work to the cylinder (His statement that the system would reorganise itslf into an adiabatic column is wrong)
Piffle. First, the proposed lapse rate is supposedly stable. This means that if one makes a small perturbation — or for that matter a large perturbation — from it, the system will move around to restore the lapse rate. Second, why do you have this fantasy that gas, ideal or not, doesn’t conduct heat? If you cool “an infinitesimal layer” of the gas next to the bottom piece of silver, and warm “an infinitesimal layer” of gas next to the top piece of silver, that is not stable, because that infinitesimal layer of gas is in excellent thermal contact with the next infinitesimal layer over, and that one with the next one, and so on.
Here’s a very, very easy way to see that you are speaking nonsense. The gas in the column doesn’t “know” that it is in a very large column. All it knows is that locally it is supported in static force equilibrium and otherwise is in thermal equilibrium. It is exactly like an ordinary jar of gas at the same pressure and density and temperature. Exactly as in you could not measure any property of the gas in the jar and differentiate it from an identical chunk of gas from the column that isn’t in a jar.
So fill (mentally) the two jars and seal them. Now they are ordinary chunks of air, not unlike chunks of air in any laboratory. Put the two jars next to each other and connect them with a silver wire. Are you seriously suggesting that heat won’t flow between two reservoirs at different temperatures and bring them into equilibrium?
This is, incidentally, yet another excellent way to understand detailed balance. Detailed balance doesn’t depend on the pressure or density of the air in two jars. They can be anything you like. The (adiabatic) jars themselves will always exert exactly the same force on the fluid inside of them that a surrounding fluid would exert on them in equilibrium if we match pressure, density, and temperature in the jars.
So asserting that heat won’t flow in figure 2 above, or will stop flowing before all of the gas reaches thermal equilibrium, is just like saying that heat won’t flow between two ordinary jars of gas at different temperatures in the laboratory, and well over a hundred years of experiments, the entire refrigeration and air conditioning industry, a huge body of technology and engineering, and well understood physical theories all say otherwise.
rgb
Robert Brown – stop before you go mad.
These people here are trolls who don’t want to listen or learn anything.
Leave it… walk away… you won’t ever convince them.
Once upon a time, in places like the Royal Institute, back in the glory days of the 1800’s, physicists were respected, argued with. But they presented to people who wanted to learn. From this, many great discoveries and theories were formed – some of which carry the names of those who discovered them, or who popularised them.
Now instead we have physicists and engineers attacked and torn down by “post normal science” and armchair ignorami who think they know better. What a sad, sad state of affairs. Time to let the ignorami wallow in own cesspool for a while. Imagine a world where the engineers all stopped making things and the physicists stopped helping them with theories – and they all went and played gold for 50 years. What a fun place that’d be.
I’m slightly pissed off – in case you had not gathered.
Enough… I’m off to count the UFO’s at the bottom of the garden.
Not once did I see a proof of the Second Law that did not rely upon circular logic. I’ve seen plenty of empirical proof, that people have been unable to violate it, but no direct proof.
Well, I’ve taken actual statistical mechanics course, and I have seen proofs of the second law that don’t rely on circular logic. Anyone with a child’s understanding of stat mech knows this. If you want a good derivation, look at the general approach of Jaynes, starting from information theory, or if you prefer, from Cox’s algebra of probable inference. The second law is technically a statistical law of large numbers. As Dewitt just pointed out, it can be violated, sure, as long as the violation doesn’t break the first law. It is just very, very, very — (repeat a google to the google power times or so very) unlikely. As in the probability isn’t zero, but it lives right next door, is good friends with zero, their kids go to the same schools, that sort of thing. It is difficult to convey how unlikely it really is, but Dewitt’s example of all of the air in the room bouncing just right and ending up as a drop of liquid air over in a corner leaving you gasping in a vacuum that happens to maintain itself because air molecules just don’t seem to have the right directions to bounce back into the room — that sort of unlikely.
But that hardly matters, does it? All of the laws of physics are empirical, observational laws. I’ve never seen a proof of the law of gravitation, or of energy conservation, or of Newton’s Laws. The more fundamental a physical Law is, the less we are able to prove it, the more the law relies on consistent observation instead of deduction or derivation. I should point out that this is my real interest at the moment — the philosophy of knowledge and the basis of science — and I am happy to cite you chapter and verse.
On that basis, the second law is actually rather derivable, certainly compared to e.g. energy conservation or Maxwell’s Equations. But that isn’t really the point. The point is that the U.S. Patent office will no longer accept patent applications for perpetual motion machines — without a working model. The point is that unless you are a complete idiot you wouldn’t invest a nickel in a company claiming to have one, not even if someone “showed” you that it worked. You’d believe with all of your heart and soul that there was a trick in it, and you’d be right. Yet here, because it contradicts something you want to believe, you choose to doubt it. Are you nuts?
That’s one of the truly amazing things about this list. Doubting the second law of thermodynamics is insane. How can you even seriously propose that?
If somebody claims they can violate it, no they can’t. If somebody claims to build something that they can prove violates it, no it won’t. I’d believe in an antigravity machine before I believed in a machine that does nothing but convert heat into work, or a system where heat moves spontaneously from cold to hot and maintains it there without work and against perturbations — those are all “free lunches”, and most of us old enough to tie our own shoes know that there ain’t no such thing as a free lunch.
Using this rather conservative approach, one might, possibly, conceivably make a mistake. Sure, why not? Magic could be real! People might be able to come back from the dead (one famous second law violation) or walk on water (another) or heal the blind with spit and mud (a third). But don’t bet on it!
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What maintains the lapse rate temperature difference?”
Mostly gravity.
Mostly gravity plus the differential heating and cooling. Move your house to Antarctica and look up mid-July. See all that sky that is warmer than you are?
But generally, I agree with your reply. As I stated, my objection is specific to EEJ — the DALR is not a stable thermal equilibrium, which is precisely what EEJ asserts. I’m not suggesting that there is no ALR, as a general rule, only that a) it isn’t precise, constant, ubiquitous; b) that it depends on differential heating and cooling and active transport in the atmosphere, and goes away when you stop heating the ground underneath it. The layer where the DALR approximately holds is the troposphere, the layer with vertical convective mixing, and it goes away as the ground temperature drops — making it look a whole lot more like an effect, rather than a cause, of warmer ground temperatures.
Personally, I think the DALR is caused by the greenhouse effect and gravity, working together to maintain the heat differentials that drive the troposphere. Heresy, I’m sure, on this blog, but there it is.
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