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.
Meaning Robert Brown is allowed only one heat reservoir to demonstrate his proposed isothermal gas column where the wire stays in thermal contact with the white colored gas everywhere – no U-turns as here to a 2nd thermal reservoir. Trick’s view is Robert will be unable to do so – the gas column will not be isothermal – there will be a temperature lapse rate.
Excuse me? I have no idea what you could possibly be talking about. Look, grab a copper wire by one end. Hold the other end in the flame of your stove. I don’t care what shape it has, you will burn the hell out of your fingers (and keep burning them until your fingers are at the same temperature as the flame).
My picture shows a wire insulated on the sides so that any heat that goes into the wire can’t come out anywhere but the end. It just makes the wire a one dimensional conductor of heat. Put the damn wire (insulated on the sides) right into the container, perfectly straight if you like. As long as the bottom UNinsulated end is in contact with the gas at the bottom at T_b, and the top UNinsulated end is in contact with the gas at the top at T_t, and T_b > T_t, heat will flow in the wire from the bottom to the top.
The point is that heat will flow in this system forever if you postulate that gravity will maintain a lapse between the bottom and the top stably. That means that any small packet of heat that is moved around in the gas has to eventually settle back down into equilibrium, and you are asserting that equilibrium has a lapse. So when the wire carries heat from the bottom to the top — which it will — gravity has to sort it back down to the bottom, because you assert that a lapse is the stable equilibrium.
Only it won’t. If it did, the second law wouldn’t be satisfied, heat would flow forever.
The real point is that you don’t need the silver wire to make this argument. The gas itself conducts heat from the bottom to the top as long as the temperatures are different. It’s what systems do. Conduct heat from hotter places to colder places, unless you do work to prevent it. Gravity does no work in this problem, not in steady state. So what makes the heat go round and round?
It doesn’t.
Of course.
It evolves to the isothermal state where no heat flows.
rgb
I am not a scientist and never claimed to be so, could someone explain why the gas, or atmosphere in this case, should be colder on top than on the bottom assuming convection works in all cases (cold air falls while hot air rises) Yes, I can figure, as air gets closer to outer space (in really simple terms) it would get mighty cold but, cold air is more dense and as such it should fall more rapidly. Exactly where does gravity enter the picture? It is exerted equally on all temperature states of air, right?
Or should I up my meds? 😉
RGB
thank you for this elegant demonstration that a gas in a gravitational field is isothermal when in equilibrium. I lost count of how many times I pointed this out on Willis Eschenbach’s original thread (the one that caused all the controversy). Even Willis didn’t get it at the time. I hope he does so now.
[REPLY: Indeed you did, Paul, and you were right and I was wrong. Thanks for your contribution in fighting my ignorance. I mean this quite seriously. That’s how I learn. –w.]
Robert, it seems that you have completely missed the fact that gravity causes a pressure and density gradient in your air column.
Your equilibrium air column is NOT isothermic, as you assert–that could only happen in the absence of gravity. Because the density and pressure decrease with altitude, the temperature at the top is much lower than at the bottom. The bulk of the mass and heat energy of the air column is at the bottom.
Remember what heat energy is: it’s defined by the kinetic energy of the individual air molecules. Temperature is defined by both that molecular kinetic energy and by the density of the atmosphere. The pressure gradient leads to a sorting; the more energetic molecules tend to be at the top of the air column–more space to allow a longer mean free path above than below. However, because the density and pressure decreases with altitude faster than the thermal energy of individual molecules increases, total temperature decreases with altitude.
Your thesis may indeed be correct, but you can’t prove it by considering only temperature and convection without considering density and pressure and conduction as well. It’s the pressure and density gradient that is alleged to cause gravitational heating of the lower atmosphere.
This is a much more complex problem than a quick, partial recitation of a freshman physics text can handle.
The device in figure 2 doesn’t work because it’s a closed system and the work extracted will reduce the total energy of the column until eventually there’s no more energy to extract at which point the gas reaches a temperature of absolute zero and has presumably vanished from this universe being totally converted to kinetic energy in the extracted useful work. In the real world the gas will collapse to the surface as a liquid before it gets to absolute zero and this will shut off further extraction of energy because the cold side of the thermocouple no longer has any cold gas to cool it.
Work? What work? Are you crazy? Collapse to a liquid?
Let’s try again. I-s-o-l-a-t-e-d S-y-s-t-e-m means that no energy enters or leaves. No mass transport means no work is being done In the real world, the system will evolve to an isothermal state precisely as I described it because it is in equilibrium. In any imaginary world where gravity acts on “heat” or does “work” on a gas that is in static force equilibrium and not moving, you can make it come out any way that you like, but please understand that it is nothing but a fantasy on your part.
The point is that heat will not cycle indefinitely — you can see that that makes no sense. No work is done. No energy enters or leaves — where would it go? How would it get there? That’s what the adiabatic walls around the gas and wire prevent. If gravity maintains a constant lapse rate in steady state, the second law and common sense are massively violated by the enternal heat flow. All other solutions mean that equilibrium is isothermal.
rgb
Heat is Energy is mass by M=E/c^2 so said Einstein.
So what force causes Mass to rise up the silver conductor against gravity ie work has to be done?
The silver conductor is little different from the gas in a column in this respect. The top will be colder than the bottom and heat will not flow up the silver conductor unless a heat source (work) is supplied from the bottom..
If the atmosphere was heated from the top there would be no convection, hence no lapse rate.
The lapse rate doesn’t apply to the ocean because water is incompressible. Hot water doesn’t expand as it rises, hence does not do work on the surroundings, hence does not change temperaure, hence no lapse rate.
I conclude that a thermally isolated container of gas in zero gravity and at uniform temperature, will not see any temperature change if some other demon could switch a gravitational field on at will. Merely the creation or a density gradient. Is that right?
Not quite. “Turning on the field” is like “a collision” and the gas will rearrange, releasing a bit of gravitational potential energy as heat. But then it will “thermalize” to an isothermal temperature, one a tiny (and I do mean tiny, generally speaking) higher than before.
This is not unlike the mechanism that heats protostars as the gas they are made up of falls inward and stops (on average) converting their infalling KE into heat. Or what happens when a big asteroid hits the earth and stops
The key elements are movement and inelastic stopping.
rgb
I have been following these threads, lurking from the sideline, for a while. Well, the time has come to add my $.02 worth. I have been studying meteorology for 40 some-odd years now & I shake my head in seeing some of the most common properties of the atmosphere being missed in these threads as it applies to these ‘thought experiments’.
1) if the several km-long tube is horizontal & the perfectly dry air is at a constant temperature throughout & is moved to the vertical, the dry adiabatic gradient will be produced (warm at the bottom, cool at the top w/ approx 8C/1000m gradient in between) due to the ‘work’ of gravity creating a pressure gradient to the compressible gas. Notice, no gradient will be produced if water is used instead of gas because water is non-compressible so no work will be done. If no heat is added or removed to the gas, the column will be in a neutral buoyant state (and will stay that way!!) – if a parcel of air is moved vertically by an outside force, it’s temperature will change to reflect the change in pressure but will still be the same temperature as it’s surroundings.
2) as to the experiment with the thermal conductive wire at the base & top of the tube, the author here is incorrect. If the wire moves heat from the bottom of the tube (the base cools) to the top of the tube ( the top heats), presuming, as the author says, “…save to note that the internal conductivity of the ideal gas is completely neglected.”, the heat from the *local* area of the wire is all that will be moved from the bottom to the top ***and nothing else*** . Why, you ask?? In moving the heat from the bottom of the tube to the top is causing the lapse rate to become **more stable** – cool at the bottom with warm air above is an inversion which inhibits vertical mixing!! THAT is why the engine will not work as it is set up.
Just a few thoughts…
Jeff
@Robert Brown: To do LaTeX in WordPress, do $\latex n^2$ (except leave out the backslash in front of “latex”. It’s just like going into math mode in LaTeX, except that you add the word “latex ” after the opening dollar sign.
nothing as simple as gravity can function like a “Maxwell’s Demon”
There is nothing simple about gravity. it is the least understood force in the universe with many unresolved questions.
Professor Brown: To some extent, two of your arguments start by assuming what you want to prove.
You and the introductory textbooks start by assuming a isothermal column of gas. The situation is far more complicated if you consider a column with a temperature gradient. For a thin layer of gas in a non-isothermal cylinder, the pressure difference across that layer is produced (at a molecular level) by differences in the vertical impulse provided by the gas molecules at the top and bottom of the layer. The density of molecules and pressure in an isothermal column both change following the same exponential, -mgh/kT. This means that the difference in impulse between the top and bottom of a layer is due only to the difference in density and the average speed of the molecules moving up and down must be the same. This is consistent with the original postulate that the column is isothermal. In a non-isothermal column, however, the density of molecules and pressure don’t change in parallel. In this case, the speed of the molecules at the top and bottom of a thin layer will not be the same and energy will flow up or down. Which way is the flux? If the flux reduces the temperature gradient (and I presume that it will), does the flux persist until isothermal or are other stationary states possible?
To prove that heat flow in a cylinder of gas is unaffected by a gravitational field, you assume that heat flow in the silver conductor is also unaffected by the same gravitational field. IF exchanging kinetic for potential energy were important to energy flux in a gas, it would probably also be important in a solid. In a sense, you are assuming what you want to prove. You can use the 2LoT to eliminate the possibility that a lapse rate of g/Cp develops spontaneous. If you have two equally tall columns in thermal contact with the ground which are filled with gases with different Cp’s, you could use the temperature difference which would develop spontaneous at a given height in the gravitational field to produce perpetual motion. However, this argument doesn’t work when the lapse rate that hypothetically forms spontaneously in a gravitational field is independent of composition and only depends on height.
I feel for you Robert.
It seems the more challenging and subtle the physics, the more experts there are. And the more sure they are that they are right. It is a lot like playing whack-a-mole — every time you think you have explained something so well that it couldn’t be clearer, someone will find a new objection (or more likely, recycle an old objection). For example, the “it loses KE on the way up so the temperature must go down” is convincing unless you have a subtle understanding of thermodynamics. And we have seen it rear its head a dozen times in the last few days in these threads.
I hate to admit that I, like Willis, even fell for this argument for a brief time until the obvious flaws were pointed out. But we both quickly reformed.
I wish you patience and persistence in your efforts to bring correct science to WUWT. You will need it!
As an aside, it’s trivial to design a machine that seems to violate the Second Law and pumps heat from cold to hot with no input of work.
On a sheet of paper draw two horizontal lines, one at the top and one at the bottom, that represent radiating surfaces at temperatures Ttop and Tbottom. Then draw a cute little flight of stairs ascending from left to right, with a smooth bottom and the usual treads on top. Cover the stairs with mylar and let them sweep from right to left at nearly the speed of light. (You can also make the stairs steeper and sweep them slower). There are a very large number of flights of stairs, looking in 3-dimensions like a venician blind with treads on one side.
Assume the top and bottom emitting surfaces are very distant and finite, so photons are traveling between them in a roughly vertical direction. Photons from the bottom don’t hit the stairs because the stairs are moving out of the way as fast as the photons are traveling upward. (The stairs dodge upward moving photons). Photons moving downward cannot find a clear path between flights of stairs and always slam into a tread, getting reflected back towards the top.
So photons emitted from the top surface return to the top surface, and photons emitted from the bottom surface travel freely to the top surface, regardless of temperature. The bottom surface cools and the top surface warms, even if the bottom is already cooler than the top, and the stairs aren’t doing anything but freely moving along between.
At most, the stairs might extract a little work from the momentum of the photons being reflected from the top, but this would happen regardless of the difference between the top and bottom temperatures.
The problem here is that heat is not temperature. Heat is energy, temperature is average kinetic motion, which is one -type- of energy. A glass of water and a bathtub full of water can have the same temperature, but the bathtub has more heat than the glass of water, as more heat is required to bring the tub up to the same temperature as the glass.
Moreover, heat can be added to a system without temperature changing. When ice melts, continuous heat is required to continue the melting, yet the temperature will remain the same until a significant amount of the ice has melted. Still, the system has far more heat content now as a liquid, even at the same temperature, than it did as a solid.
For instance: “This heat in turn may lift mountains, via plate tectonics and orogenesis. This slow lifting of terrain thus represents a kind of gravitational potential energy storage of the heat energy. The stored potential energy may be released to active kinetic energy in landslides, after a triggering event. Earthquakes also release stored elastic potential energy in rocks, a kind of mechanical potential energy which has been produced ultimately from the same radioactive heat sources. Thus, according to present understanding, familiar events such as landslides and earthquakes release energy which has been stored as potential energy in the Earth’s gravitational field, or elastic strain (mechanical potential energy) in rocks.” So, this action of heat pushing against a gravity well and from kinetic to potential energy is part of what drives plate tectonics itself.
Here we see heat being transformed from kinetic (TEMPERATURE) energy to potential energy by moving against a gravity field. The resulting raised land mass has lower temperature as it as lower kinetic energy, but it contains similar amounts of heat.
This effect of changing kinetic energy to potential energy (E = mgh) won’t be seen measurably in a gas over a small distance, but over the miles of the atmosphere?
This is why it’s hard for me to understand your explanation, which doesn’t mean you aren’t correct, Dr. Brown. But it seems like your equations are all missing the big picture: potential energy. When h (height) is very big, even though gasses have low m (mass), you’re going to have a transfer of energy into potential energy that is considerable. The only source of energy that can go into the potential energy (since conservation of energy demands transformation not creation) is the kinetic energy of the molecules. Just like bouncing balls. And if kinetic energy drops, -so too does apparent temperature-. Again, -temperature is not energy-. Temperature is not heat. Temperature is just our observation of heat in the form of -kinetic energy-. And kinetic energy can be changed to potential energy while keeping the total energy of the system -the same-. Like a bouncing ball, or a stone rolling up hill a ways. Or plate tectonics!
You’re looking at far too small a case. An ideal, not realistic, case. Or maybe i just don’t get it.
Robert Brown: “There is no question that the silver will conduct heat between reservoirs at different heights exactly the same way it does any other time.”
In my post above, where I disputed Dr. Brown’s isothermality conclusion, I was silent about his proof; I concentrated on mine. For the sake of completeness, though, I’ll mention that, if the Velasco et al. paper that I’ve been evangelizing is correct, the silver actually will not conduct heat once the temperature difference that Velasco et al. specify is imposed across it. This is a result of the fact that, according to Velasco et al., entropy is maximized, not by an isothermal configuration, but by a configuration whose (again, quite small) temperature lapse rate is the one that Velasco et al.’s paper prescribes.
If you think of heat transfer in the silver as a diffusion phenomenon and recognize that concentration gradients prevail all the time when maintained by forces from, e.g., electric fields, this is not as hard a proposition to swallow as it may at first sound.
Greg Elliott says: “But what about the energy absorbed by the N2 some might ask. Indeed and what about the energy intercepted by the CO2? Both must either heat the atmosphere or be returned to the surface and thus are indistinguishable in their effects.”
But this is the flaw in your thinking. N2 can only transfer energy to the surface or the atmosphere, as you say. But CO2 can ALSO transfer energy to space via IR photons. That is ultimately the cause of the greenhouse effect.
Oh, I should point out you cannot -generate heat- with gravity, but over a very large distance, gravity should maintain a -temperature- gradient if the heat is in equilibrium by necessity due to the change of kinetic to potential energy as one moves far enough up a gravity well. Notice that the energy of the gas column will be in equilibrium, but temperature is only the measure of kineitc not potential energy.
That fact is why I can’t wrap my head around such a small case explanation as yours, which is correct on the small scale, when applied to the entire planet.
Again, maybe I’m completely wrong. But I feel we’re missing out on one entire half of the equation. Gasses are still subject to potential energy as far as I know!
I think one reason that some people are taken in by Jelbring’s theory is that they are vaguely aware that if a gas is compressed, e.g. the air in a tire being compressed by a pump, its temperature goes up, so in their minds they form the vague association ‘higher pressure = higher temperature’. But the increase in temperature is a temporary effect, due to the transfer of kinetic energy from the piston of the pump to the air molecules. If you stop pumping, the tire will cool down to the ambient temperature, as it loses heat by conduction and radiation. As the air in the tire cools, it will also reduce in pressure, but not to the orginal level (otherwise there would be no point in pumping up a tire!) There is no necessary connection between high pressure and high temperature; a hot gas can have low pressure and a cold gas can have high pressure (unless it is so cold as to liquify).
Incidentally, I wonder if someone could explain the opening quote from Jelbring:
“An adiabatically moving air parcel has no energy loss or gain to the surroundings. For example, when an air parcel ascends the temperature has to decrease because of internal energy exchange due to the work against the gravity field”.
I don’t understand the second sentence of this. If an air parcel ascends, it is surely because it has first expanded due to heating (usually from the sun). As it expands, it does work against the surrounding or covering air, compressing or displacing it, and loses some kinetic energy (heat) in the process, but it does not immediately cool to the ambient temperature. (If it did, it would not ascend at all, contrary to experience.) The expanded parcel of air is less dense, and therefore less heavy, than the surrounding air, and the entire column of air above the parcel (including the parcel itself) is lighter than the surrounding columns. At this point the parcel begins to rise as the heavier surrounding air forces it up. During the ascent the air parcel itself is not ‘doing work against the gravity field’, it is having work done on it by the surrounding air, which is ‘repaying’ the work done on it during the initial phase of heating and expansion. Does Jelbring suppose that a hot-air balloon would rise in a vacuum? I really can’t make sense of his second sentence at all.
You’ve very coyly avoided answering the objections raised by Dr Brown’s Gedankenexperiment. So according to you, we could take a perfectly insulated container several miles high in a gravitational field under a hard vacuum, fill it with gas and that gas will self-organize so that it’s warmer at the bottom and colder at the top. Now I can construct a heat engine which extracts useful work based on the temperature gradient and gravity will continue to organize the air column forever and my heat engine will never run out of “fuel”? Really??
To Joules,
According to Newton, gravitational force is expressed as F=m1*m2/R^2 where m1 and m2 are the mass of two attracting bodies and R is the distance between the centers of mass. The molecules at TOA have less gravitational energy than molecules at sea level but not by much because the change in R is relatively small. So the pressure at sea level is essentially the mass of the earth times the sum of the mass of all those molecules in the atmosphere divided by the radius of the earth. In a steady state condition, the pressure at sea level will be constant and the number of molecules causing that pressure will be constant. Pressure decreases with altitude because the number of molecules per volume decreases. Now apply this knowledge to the perfect gas law expressed as pv/nt= constant by integrating from TOA to the surface and see what happens to temperature as a function of altitude.
Joules Verne says:
January 24, 2012 at 7:04 am
“Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics. It is a direct, literal violation of the refrigerator statement of the second law of thermodynamics as it causes and maintains such a separation without the input of external work.”
No, Robert. The second law requires that no energy gradient can be maintained without input of work. It requires the reservoir of gas to be isoenergetic not isothermal. A horizontal layer may be a different temperature than another if the cooler layer has its lesser kinetic energy balanced by greater gravitational energy. This is obviously the case since it goes without a shadow of a doubt that a molecule of air in a higher layer has more gravitational energy than a molecule in a lower layer. Thus the second law actually demands a temperature difference of equal and opposite polarity to compensate for the difference in gravitational energy. An isothermal atmosphere in a gravity field is the one that violates the second law.
Joules is correct, and to push the point home a bit further I will be posting a new paper by Hans Jelbring on my website later this evening which demonstrates the dynamic situation. This will complement and supplement the earlier 2003 paper setting out the static situation which Robert refers to in this article.
Hans has been working steadily on the new paper over the last few weeks and now seems to be the apposite time to publish it.
Basically, the Second Law is used to prove the second law isn’t violated. That’s circular logic. It’s like using the Carnot Cycle to prove the Second Law.
As I said at Tallbloke’s, I think the silver wire is a terrible design. You’d be lucky to extract kbT from it. IIRC, Feynmann showed it was possible to extract nearly that much from a Brownian Ratchet, without anyone getting excited.
A better design would be to use a single column containing two gases, one of which is heavy with a low boiling point, and the other is light with a high boiling point. A reservoir of the light gas in condensed form at the bottom of the column also serves as a thermal reservoir. At the bottom, the light gas will be in equilibrium with its condensate.
Fill the column with a significant majority of the heavier gas, such that its gravitational lapse rate dominates. The temperature/pressure profile of the lighter gas (being a lifting gas in context) will be saturated at all elevations above the reservoir.
A series of basins and catchments can be arranged to collect the condensing lighter gas.
By George (Westinghouse), it might work!
People being invited to consider an argument should have the opposing argument easily available to them. This enables people to form their own judgment as to whether the opposing argument has been correctly and fairly represented. Especially considering the paper in question was written by a Phd Meteorologist.
Since Robert Brown is setting a refutation of Hans Jelbring’s 2003 paper, it would be a common courtesy to provide a link to that paper in the headline post.
It is available with a new preface written at the time of publication on my website here:
http://tallbloke.wordpress.com/2012/01/01/hans-jelbring-the-greenhouse-effect-as-a-function-of-atmospheric-mass/
If WUWT has some problem with providing a link to my site, the paper without the 2012 preface is available here:
ruby.fgcu.edu/courses/twimberley/EnviroPhilo/FunctionOfMass.pdf
[Thanks, tallbloke. I’ve added the link up in the head post. -w.]
For those seeking detailed quantitative thermodynamic analyses of the atmospheric lapse rate see:
Robert Essenhigh Prediction of the Standard Atmosphere Profiles of Temperature, Pressure, and Density with Height for the Lower Atmosphere by Solution of the (S−S) Integral Equations of Transfer and Evaluation of the Potential for Profile Perturbation by Combustion Emissions Energy Fuels, 2006, 20 (3), pp 1057–1067 DOI: 10.1021/ef050276y
Sreekanth Kolan Study of energy balance between lower and upper atmosphere MS Thesis