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.
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I made a mistake above; I meant there is no isothermal gas in the box in te third condition
Again, Thank you Dr Brown!
sorry, one more mistake;
I mean in the third condition of the box in the question above, that there is a slight temperature gradiant between the top of the box and the bottom of the box. And that the slight net radiative flux and the slight net kinetic energy flux exactly balance in opposite directions. sorry again for the mistake.
JimZ: “i’m not a climate skeptic.”
So does that mean you do or don’t believe there is a climate?
Jim Z said @ur momisugly January 28, 2012 at 3:35 pm
In the first box you state there is nothing: “The box is empty”. If there is nothing it cannot have a temperature and therefore cannot be in thermal equilibrium.
One more mistake. Having fun yet?
Dr Brown,
Yes, I now see how it is and you are correct. The atmosphere relaxes to an isothermic state.
Thanks for your patience, you taught taught me something important, humility, along iwth some physics.
Thank you again!
Well In addition to sharing Prof Brown’s incredulity, that so many people can’t even grasp the simplest of simple thermodynamic problem examples, this thread, has been an additional shock to me.
If you read through the various posts, and also the responses from others (some) to those posts, it will become apparent that many (too many) of the posters here, are either trolls deliberately trying to muddy the water, or their understanding of the English language is as dismal as their understanding of some simple physics. Now lack of understanding of the physics is forgiveable.
I have said on many occasions :- ” Ignorance is NOT a disease; we are all born with it; but stupidity has to be taught, and there are plenty of people who are eminently able, and willing to teach it.”
Ignorance can be dispelled by teaching and learning; stupidity can’t.
I have a son who is taking some classes at San Francisco State University (of necessity), and that institution seems to be most famous for its “School of Racism.”
Well they call it euphemistically “Ethnic Studies.” Trust me it’s a school of racism.
But I digress; when I went with my son for his first orientation seminar, when he started at SFSU, they told us all, that every single student who goes to SFSU must pass a test following a compulsory course in Remedial English. They can take the course and the test almost any time, but they can’t graduate without doing so.
Now let me state most emphatically, that I am not talking about people for whom English is a second language; we have many here at WUWT, and I just wish I had any skills at all, in any other language, even a fraction of the English skills, some of our ESLs here have. Hell I even get my umlaut’s in the rong places.
But it’s a sad commentary, that people who are native English speakers, have to take a remedial course in order to attend a major city university. My wife is a school teacher, so I know pretty much how that sorry state comes about; she gets extra pay, because she is a bi-lingual teacher; who actually teaches monolingually, just not in English. And that has been illegal in California for quite a few years now, but some parents are bound and determined to keep their kids behind the eight ball, and out of the main stream of US life.
So a lot of the fuss and bother in posts above seems to be some posters can’t even read what is written by others and understand the simple English meaning of what they are reading.
I’m happy to attempt to pass on, what limited Physics, I know; but I’m not about to start trying to explain English to folks who ought to know it; I’m English handicapped myself and tend to speak the British variant of it, which doesn’t really go down well in America.
I didn’t even bother to go and figure out what Jellbring’ hypothesis was or is; I was sufficiently mesmerised by the lack of understanding of Robert Brown’s elegant demonstration, that whatever Jellbring was talking about seems irrelevent.
You can turn loose your terracomputers on a lot of this climate stuff; but most of the crucial points don’t require more than a sandy beach, and a stick to scratch on it with
“Quite aside from this the article is a terrible example of science — I cannot imagine how it was ever accepted by either editor or referees. The article does not include a single line of algebra. I have literally never read a supposedly serious, non-bullshit work on the physical thermodynamics of a model system that did not even define the forces, energies, conditions, assumptions made in algebraic terms. This paper shows nothing in the actual language of physical science; it presents a purely heuristic, question-begging argument with numerous errors and internal inconsistencies.” – Brown
“…for reaching a maximum of simplicity and clarity approaching an educated but laymen audience.”
“This paper has purposely been kept more qualitative than quantitative to avoid
elaborate formula and explanations – and to make it easy for all to digest. The more
theoretically competent readers should have few problems if they wish to perform
quantitative calculations for themselves, following the guidelines presented here. – Jelbring
“If you can’t explain it simply, you don’t understand it well enough.” – Albert Einstein
The only issue I have with this, is that it obviously had to be well known once upon a time since, as I’ve given above, minus the main greenhouse gas water vapour, our atmosphere of practically 100% nitrogen and oxygen, dry air, would be 67°C, standard industry figures. It’s the greenhouse gas water vapour which brings that down 52°C to the 15°C.
Now, there’s around four times as much nitrogen in the atmosphere as oxygen and since nitrogen in its diatomic form is difficult to break to form compounds, then it could be said to approximate to an ideal gas (elastic collisions not inelastic), and, oxygen and nitrogen don’t combine in the atmosphere but mix, and, oxygen is practically the same weight as nitrogen, and, oxygen has practically the same heat capacity, then, not a bad approximation to the ideal gas of Jelbring’s thought experiment.
And, since our atmosphere is more than the tropopause and there is a rather large and very hot layer someway above the tropopause, his closed scenario not a million miles off from what we have, which is that temps decrease as gravity’s grip lightens.
So, we know that his approximation is fine for our atmosphere as we have it, with greenhouse gases included, because temps decrease as we move away from the surface and that has been measured and shows regularity of decrease in the play between gravity, density and distance. Taking out the greenhouse gases, which in all logic seeing the effect just a small percentage of water vapour has on temps need not include any other, then we have Jelbring’s experiment, a very good approximation, just by stepping into a desert.
Since this Jelbring’s scenario has actually got back to what we know we have, I can’t see anything wrong with it.
The only problem is, as I’ve mentioned before…, the energy budget that both pro and anti AGW use is fictional because it has excluded the Water Cycle, and you don’t know this.
Y’all (generic) think it’s real because you’ve all forgotten the Water Cycle because you no longer have it in your calculations because distracted by a sleight of hand by AGW (for it is AGW’s energy budget you’re using), and so all this appears new to you.
This sleight of hand has taken the difference between -18°C of the Earth without any atmosphere at all and the 15°C of our atmosphere as we have it, and attributed the difference to the imaginary supermolecule properties of our beloved carbon dioxide, without ever giving any details of how this wonderfood for plants and oxygen transporter for our blood can raise the temp of the Earth 33°C from -18 to +15..? Tim?
So, our approximate to the J model Earth is 85°C with an atmosphere of practically 100%nitrogen and oxygen as we have it but without the Water Cycle.
“A simplified model of Earth, along with a formal
proof concerning the model atmosphere and evidence from real planetary
atmospheres will help in reaching conclusions. The distinguishing premise is that
the bulk part of a planetary GE depends on its atmospheric surface mass density.
Thus the GE can be exactly calculated for an ideal planetary model atmosphere.” – Jelbring
“A simplified model of Earth will be considered. The model planet does not rotate. It
neither receives solar radiation nor emits infrared radiation into space.” – Jelbring
So, please work it out you maths boffs, how much heating would there be if we switched the Sun off?
And, do stick to the scenario he presents, so we can all follow the picture..
“Quite aside from this the article is a terrible example of science — I cannot imagine how it was ever accepted by either editor or referees. The article does not include a single line of algebra. I have literally never read a supposedly serious, non-bullshit work on the physical thermodynamics of a model system that did not even define the forces, energies, conditions, assumptions made in algebraic terms. This paper shows nothing in the actual language of physical science; it presents a purely heuristic, question-begging argument with numerous errors and internal inconsistencies.” – Brown “.
Sounds like a very good description of the greenhouse effect.
Robert Brown, in your example physics paper (posted 2:33pm above) I found an error in the solution in 1(b) … the word calculate is misspelled as ‘calcfulate’ … does this qualify me for any credit towards a physics degree, or does that just make me a run-of-the-mill pedant? 😉
kuhnkat says:
January 28, 2012 at 7:48 pm
Radiation? Where is there radiation in Dr. Brown’s thought experiment? Here’s the question:
Do you think that the gas will stratify thermally?
If so, will heat flow in the silver wire?
Thanks,
w.
Willis,
You mean I missed where he said the silver and nothing else in the “experiment” will radiate? Gee, what other basic physics is missing that I missed? I mean, Nobel Gases have extremely low absorption/radiation, but it isn’t nonexistent. With collisional energy being transferred we will get emission occasionally. May not be enough to alter any balance, but, the silver dang well will emit if it can conduct. So, like many other of these things, how much real physics is being excised to get the desired result?
I am stuck in ancient times when heat was called kinetic heat. If two things collided you had conductance. I just don’t GROCK this idea of no energy flow, with gases will be conducting continually until they are approximately equilibrated. Of course, as soon as one bounces in the vertical axis the distribution of its energy state changes with time due to the gravity gradient. So it is all going to be moving around a mean and this satisfies the requirement?
After reading the Verkley Gerkema paper, it seems to me that the idea of a planetary atmosphere relaxing to an isothermal profile in the absence of greenhouse gases is absolute foolishness.
Unfortunately many proponents of AGW are so willing to misuse Dr. Brown’s elegant refutation of Hans Jelbring’s E&E paper to conclude that GHG’s must therefore be responsible for the temperature lapse rate observed in planetary atmospheres. This is foolishness since neither the original E&E paper, nor Dr. Brown’s refutation address planetary atmospheres – they look at a very theoretical tube of gas in a gravitational field.
A planetary atmosphere has several critical features. First, it exists on (or consists of) a rotating imperfect sphere (barring of course the trivial case of a non-rotating perfectly spherical planet). Second, the planet is revolving about one or more stars. Third, the planet (including the atmosphere) is subject to some tidal forces (again, there is a trivial case of a perfectly tidally locked planet…). All three of these features are indisputable features of a real planet since they essentially derive from the definition of ‘planetary.’
So what to conclude about planetary atmospheres? First, the atmosphere is not in thermal equilibrium – there are day/night cycles, Coriolis effect, tidal effects, variations in heat transfer from the surface – it goes on and on with one conclusion: atmospheric mixing. With mixing comes an overall tendency toward an intermediate profile between isentropic and isothermal – no GHG’s involved…
“DeWitt Payne says:
January 28, 2012 at 9:30 am
gbaikie says:
January 28, 2012 at 1:46 am
But air does not conduct the heat. You can’t compare air to silver or stone. It’s not just that air is poor conductor. Air molecule is excellent conductor to itself- the molecule velocities are “transferred” at 100% effectively in less than nanosecond, but the only way energy through air is “conducted” is via air packets- or air doesn’t conduct to itself, it transfers heat from one location to another via movement of air molecules- convection. Other than redistribution or averaging velocity of molecules, air only transfers energy thru air via convection. So if you have a condition of not having some buoyancy difference of air packets, is no conduction of heat via air.
Wrong, wrong, wrong. Air conducts as well as convects. Otherwise stagnant air would be a perfect insulator. ”
Air does conduct heat to solids and liquids. Heat for gases is velocity of gas molecules- unlike liquids and solids.
Air molecules exchange velocities with each other, and suppose you could choose to say gas molecules conducts heat to other gas molecules. But stagnant air suggest you mean gas molecules which have the same average molecule velocity, and exchanges of velocities of gas which have the same average molecule velocities is not conducted heat anywhere.
Air is good insulator. Having or causing air not transfer heat via buoyancy of air packet would be would be one of best insulators, and this basically descriptive of what fiberglass insulation does- the fiberglass inhibits the convection of air.
A vacuum would be only better insulation vs conduction and convection- a vacuum could said to be perfect or best as far preventing conduction and convection of heat.
“But, of course, it’s not. It’s just that convection is orders of magnitude faster than conduction because the viscosity of air is low.”
It’s more a matter of density rather than viscosity.
” What you fail to consider is what happens after an air packet moves somewhere, in particular, to a surface boundary. It can only transfer energy to or from a surface by conduction. Period.”
Essentially I agree. I tend to think that if there is anywhere where individual gas molecules *tend* not to move much it’s at the surface. It’s vector is limited- terrain at the microscopic level has be very rough, and other factors could tend to bind individual molecules.
” Conduction works something like a Newton’s Cradle. The balls in the middle don’t move, only the balls on the end.”
But all air molecules do move, where they move and at what velocity vector is not knowable, an air molecule might stay in one place, but it’s not likely. And if one instance it’s going up, it could nanosecond later be heading down, or sideways. One might choose to mathematically describe them as going nowhere, but they can also go anywhere- limited by time and highest probable velocity.
[Considering that it’s possible {very, very low chance} they could hit by a atom traveling near the speed of light, the individuals aren’t constrained]. The Sun bombards earth with high energy particles, and the universe can hit earth with much faster particles- which can reach the surface.
But all the above is not related to the point, gas molecules, unlike solids and liquids, can have density affected earth’s gravity, and though gas molecules can be traveling at same velocity, the total amount gas molecules in higher elevation are a lower temperature- as measured by how much they warm up liquids or solids. And silver wire’s density not similarly lessen because at a higher elevation.
Robert
“Here, I’ll reduce it to a one line “elevator speech”. If a supposed equilibrium distribution of temperature in an isolated system is capable of doing work, it is neither an equilibrium distribution nor is the system at maximum entropy.”
I think you are repeating an error made earlier: even at the atomic scale, energy flows from one atom to another, gaining and losing energy. This is by definition a ‘flow of heat’ and no work is being done and it is at maximum entropy. Maybe that is not important to heat flow in the atmosphere.
You rule out a flow of heat (at all) in an isothermal system. Yet within that ‘isothermal’ column, there is all sorts of heat flowing around. I guess others have noted that. Man, these absolutes…
OK: picture an atmosphere with a lapse rate, a warmer bottom and cooler top. Introduce the silver wire. Heat will flow up the wire and because there is no lapse rate for silver, it will warm the gas at the top. You put a larger heat exchanger at the top to overcome the collision rate difference due to the pressure differential. Objection overcome.
Eventually it will reach thermal equilibrium, correct? At that time, in a gravitational field, the total energy of any upper molecule will be much greater than at the bottom (K+P), correct? Is that a state of maximum entropy?
Some say that unless the total energy (P+K) is equally distributed, it is not at maximum entropy. Well it cannot satisfy both demands simultaneously: equally distributed total energy and equal temperature. Perhaps I should rephrase that: Those who think they can both be simultaneously true please explain how.
Willis says, “Instead, the maximum entropy is when each volume of air has the same average energy.” If they have the same energy, they cannot be at different elevations and the same temperature, correct? (K1+P1)@T1 = (K2+P2)@T2 where T1 = T2??
There seem to be two schools of thought tugging in opposite directions. In the presence of a gravitational field, both conditions cannot be satisfied at the same time unless there is no energy in the system. (Yet even in a frozen state the top of the ice would have higher total energy with respect to the surface than the bottom.)
It seems to me Potential Energy is a red herring for this discussion.
And Wayne, I agree, the pressure/density curves diverge. Plus consider the planet may be spinning. Z+dZ and all. Very interesting. Will think about it. It seems to fall on the ‘equal distribution of total energy’ side of the fence.
Kuhnkat: When they finally equilibrate they do not stop radiating (transferring energy). Energy flow continues ad infinitum.
Robert said, ““Yes thermally induced vibrations of molecules can and do transmit to their neighbors in EVERY direction, even from cold end to hot end; but since the vibrational energy of the molecules is higher at the hot end, than at the cold end, the process of INCREASING the vibrational energy of the neighbors only happens from hot to cold.”
++++
This week I was talking to Steve Garrett, he of thermoacoustic fame. He can show you a steel tube with a hot and cold section in the middle, but a FAR colder tube end. The heat entering the very cold end moves to the not so cold middle, as does the heat from the hot middle. And he accomplished this by shaking the daylights out of it – well, it shakes itself. That is an example of heat flowing from very cold to cold. It is counterintuitive. It creeps along the walls, if you must know. Work is involved.
kuhnkat says:
January 28, 2012 at 8:50 pm
kuhnkat, I think you misread DeWitt’s words. He said we indeed can measure the average kinetic energy. It’s called “taking the temperature”, and it’s the only way to measure the KE because there’s no “radar gun” to measure the KE.
w.
kuhnkat wrote:
QDaniels,
the Eddington quote is very interesting. I have been assured by well educated warmers that even conduction breaks the 2nd at very low levels at times. Whether they are claiming that this is measured or a result of solving statistical mechanics they did not explain. So, because it is a really small violation, do I apply the quote or not?? 8>)
It’s generally accepted that thermodynamic systems can be off by kbT. This is a very small amount of energy, roughly 25 milli electron volts at ambient, and not regarded as significant, or usefully extractable.
In case people misunderstood my comments, I agree with Robert Brown, that a gravitational lapse rate would contradict the Second Law of Thermodynamics.
Robert Brown wrote:
Yet a large number of unreasonable people take it upon themselves to completely reinvent all sorts of physics just to suit the conclusion that they wish to draw, that such a lapse is possible because then they don’t have to give credence to the GHE. They have lost any pretence of objectivity, and there is an appalling lack of respect. Physics, as it now stands, is largely consistent. A large number of very smart people have worked for centuries to make it so. It is not perfect, it is not beyond doubt, but it is beyond reasonable doubt and the onus of proof is very much on anyone who wishes to reject things like “thermodynamics” to do an ENORMOUS amount of work to show that their new “theory” is both consistent and confirmed by experiment.
None of this has been done. People assert absurdities, one after another, without even thinking about the consequences, and without ever doing any actual algebra to support it.
The experiment has been done, but the results have been ignored. I offered it in my first post on this thread. For those who have a problem with the silver wire, my example may be easier to understand.
Yes, the physics is consistent. That does not mean that it is the only possible or valid result. I assert (without evidence) that it would be equally valid and consistent, if not more so, if the Second Law were restricted to the regions where it actually holds.
A lot of very smart people have worked on physics, with great success. There are, however, certain mental and cultural roadblocks which have restricted our progress. The Eddington quote is an example of the cultural roadblock.
For that quote, I offer a one word translation: “Inconceivable!”
I think this article and the subsequent discussion is utterly fascinating – because the physics is so simple, but I am faced with two different conclusions that are utterly at odds with each other!
I very tentatively suggest that the answer is that heat conduction up the silver bar will be subject to an effect similar to what happens in the gas – i.e. as a silver atom moves a tiny distance upwards to hit the next silver atom (and transmit the heat), it will lose a tiny bit of energy due to gravity. Repeated all the way up, this would mean that the silver bar would be in equilibrium even though it maintained a temperature gradient!
David
Do you think that the gas will stratify thermally?
Of course, because it does on Earth…
Maybe, once there are pressure differences, because it does on Earth, but, I’m assuming his ideal gas has volume, since he’s included gravity which ‘real’ ideal gases aren’t subject to I’ve included volume which ‘real’ ideal gases don’t have, and it’s volume, isn’t it?, which enables there to be packets of air in convection which if hotter rise and so colder packets of air displace these (which as he says from meteorology are already knowns), and, as soon as pressure differences introduced ideal gas no longer applies. The only thing I’m keeping from ideal gas is elastic collisions (which as I’ve given re actual properties of nitrogen and oxygen make our atmosphere approximate to his model).
The only thing I’m having a problem with, so far.., is switching off the sun. He says to take examples from real world, (as he’s done with the example of packets of air rising which is already well known and which is what gives us our weather), but on a non-rotating Earth it’s the difference of temperature provided by the Sun between the equator and the poles which sets up the basic pattern of packets of air on the move (which is wind, wind is volumes of air on the move) from the equator to the poles where they cool and are drawn back to the equator where the heating cycle begins again. (The rotating Earth just adds more interesting patterns to this basic process.)
If there’s no radiation from the Sun, no heat capacity in the model planet, no mass big enough to effect pressure changes (‘real’ ideal gases which don’t have mass), nothing much is happening because there’s no movement, (movement from the play of hot and cold volumes as hot gases rise and cold sink, becoming less dense and gaining density), but,
even with masses big enough to create pressure differences, real gases, if there’s no input of irregular heat from the outside as we have it, the gases gaining kinetic energy near the surface would be doing it equally, ah, is that all he’s saying? It’s just a swap of kinetic for potential in the movement up and down and potential here on the way up becomes that from giving up kinetic which is heat?
So if there’s no external heating setting up temp differences and none from the planet (as we have from different heat capacities of surface stuff), does that really make it any different from what we have on Earth, because what we have on Earth is more interesting with all the temp variations coming into play, but they are, it seems to me, sort of superimposed on and weaving in and out of a basic which doesn’t change, with stratified temp differences by gravity already well mapped.
So it’s all gases at greatest density will be doing the same thing around the planet at the same time(*) and as these change with differences in density in the play between gravity and pressure and kinetic and potential from greatest near the surface to more rarified, less dense and absent any kinetic to write home about the higher one goes, then, energy conservation intact, the hotter will rise and cool because losing kinetic energy means losing temperature, thus cooling they which began with the closest in density and kinetic energy as a sort of band of brothers near the surface will rise and cool at the same time whereupon they’ll all come down together colder but wiser that great heights don’t make for more comfort and giving up their heat will sink displacing the hotter now in their place when they first went travelling. So, without any external heat source and none from the planet all that’s in play here is the heat this chilled out band of brothers gains on the way down, heavier and sinking gaining kinetic energy and therefore temperature the denser they get until finally at the surface becoming too hot they expand and rise slipping out of their restricting gravity and rude neighbours bumping into them they get themselves some space and cool off, then coming back off their high when they realise just how cold and lonely they are, getting nostalgic again for their noisy neighbours who won’t stick to their side of the road, forgetting, we do forget just how horrible horrible past experiences were, that they’ll just get all hot and bothered again.
(*)The differences at the ‘edges’ of the bands not an issue as these are smoothed out in the gradient as we see on Earth, and, then, maybe a bit like our electromagnetic spectrum, those with the highest likeness to each other actually do keep together and act similarly and have properties distinct from other bands of colours. So, we end up with a model world with distinct bands of pressure gradients?
If I’ve understood what he was saying in his thought experiment of model planet, and if my reading of ideal v real gases applicable in his thinking, then I’d say yes.
If so, will heat flow in the silver wire?
Sod the silver wire, if you’re going to argue agin him, quote his words… 🙂
..stick to his thought experiment, not strawman inventions.
p.s. Willis – thanks for the electricity direction, I’ve been doing a bit of looking and am rather taken with the knowledge that what all batteries do is stop the ambient energy supply…
I very tentatively suggest that the answer is that heat conduction up the silver bar will be subject to an effect similar to what happens in the gas – i.e. as a silver atom moves a tiny distance upwards to hit the next silver atom (and transmit the heat), it will lose a tiny bit of energy due to gravity. Repeated all the way up, this would mean that the silver bar would be in equilibrium even though it maintained a temperature gradient!
David, just as a matter of curiosity, why do you select this possibility instead of the far simpler one that silver is just silver and conducts heat uphill just fine and Jelbring’s paper is simply wrong because it proposes a final state that egregiously violates the second law of thermodynamics, one that is derived by ignoring heat conduction in the first place?
You’ve had a half dozen actual physicists and a physical climatologist explain to you that this is the case. The DALR isn’t even derived as a global thermal equilibrium state, and it is child’s play to see that the entropy of the system can be increased by equalizing the temperature difference. The paper is simply wrong. It isn’t even good work in the sense that it might have been right or under some circumstances could be right. Violating the second law is as wrong as you can get short of violating the first law, in this game.
So why do you persist in trying to imagine some way that it might turn out to be true, but only if all of our understanding of thermodynamics and heat transport and energy and so on are wrong?
I’m serious, this is an actual question. Why?
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For that quote, I offer a one word translation: “Inconceivable!”
Well played, sir. One of my favorite movies too.
However, would you agree that the default position on this, the one that should have been taken by the referee of this paper, is “Ha ha ha, no.”, phrased more politely, perhaps accompanied by a strict requirement that all of the physics from the microscopic level to the macroscopic level be fully explained to show how the system does or doesn’t violate the second law before accepting it for publication?
Which, in the specific case of this specific ideal model is impossible, of course, because it obeys the second law just fine, as full stat mech computations have been able to show for a long time now.
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Sounds like a very good description of the greenhouse effect.
This is a good subject for another top post. There is direct, in my opinion incontrovertible, evidence that the GHG-driven GHE is real: The satellite IR spectral data. We can “see” it with electronic eyes. We have taken its picture. You can, whenever you like, look at those pictures.
For Ifni’s sake, man! You sound exactly like a Creationist, who refuses to look up at the stars and examine the evidence of our own enhanced “eyes” and the connected chain of reasoning that shows that the Universe is older than 6000 years. Give it a try.
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Robert Brown says
“You sound exactly like a Creationist, who refuses to look up at the stars and examine the evidence of our own enhanced “eyes” and the connected chain of reasoning that shows that the Universe is older than 6000 years. Give it a try. rgb”
This is exactly the phraseology of Joel Shore!
Are you perhaps related?
Why drag Creationism, Young Earth-ism and similar pointless dead ends in, its a sign of desperation.
My posts here have been about the lack of experimental evidence for isothermal/adiabatic distribution.
You have come up with lossless silver wire and magic light tubes.
Moving on you show a picture of a satellite looking down spectra and say
‘that proves the green house effect’
First define the greenhouse effect that you think it proves.
Jelbring says his theory proves his version of the greenhouse effect.
David Bailey: “I very tentatively suggest that the answer is that heat conduction up the silver bar will be subject to an effect similar to what happens in the gas – i.e. as a silver atom moves a tiny distance upwards to hit the next silver atom (and transmit the heat), it will lose a tiny bit of energy due to gravity. Repeated all the way up, this would mean that the silver bar would be in equilibrium even though it maintained a temperature gradient!”
Exactly the conclusion I have come to, although, to appease other disputants, you may want to say that it is a gradient in mean molecular translational kinetic energy rather than temperature that is being maintained. The distinction in their minds arises from the fact that, despite that gradient, no heat (after that initial adjustment) would flow. Since heat always flows from hot to cold, they say that minuscule difference in mean translational kinetic energy is not a temperature difference.
I think you are repeating an error made earlier: even at the atomic scale, energy flows from one atom to another, gaining and losing energy. This is by definition a ‘flow of heat’ and no work is being done and it is at maximum entropy. Maybe that is not important to heat flow in the atmosphere.
You rule out a flow of heat (at all) in an isothermal system. Yet within that ‘isothermal’ column, there is all sorts of heat flowing around. I guess others have noted that. Man, these absolutes…
No, no, no. I am following the usual practices of thermodynamics and stat mech, coarse graining all of that. There is no net flow of heat in a system in thermal equilibrium, which is indeed an isothermal system. Do you have some other definition of equilibrium?
As for the gas being at maximum entropy with a lapse rate, pay close attention, as I’ve done this three times or so already. Take a dollop of heat at the bottom — let it be absorbed by a piece of metal, for example. Move it to the top. Let it cool. Move the metal back to the bottom, all reversibly (as far as the motion of the metal is concerned). What is the entropy change of the Universe? Would that be strictly positive? So I suppose the state with a thermal lapse wasn’t maximum entropy after all, because we can trivially increase its entropy by moving heat by any means you like from the bottom (at higher T) to the top (at lower T).
If we wish, we can exploit the temperature difference to run a simple heat engine in the gas. This engine will run as long as there is a temperature difference, and can store the work done reversibly. Voila! A system that does nothing but convert heat directly into work, cooling itself spontaneously, and decreasing its net entropy!
Perhaps you can stop trying to solve complicated statistical mechanics problems in your head, incorrectly, and concentrate on the egregious violations of the second law.
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Unfortunately many proponents of AGW are so willing to misuse Dr. Brown’s elegant refutation of Hans Jelbring’s E&E paper to conclude that GHG’s must therefore be responsible for the temperature lapse rate observed in planetary atmospheres. This is foolishness since neither the original E&E paper, nor Dr. Brown’s refutation address planetary atmospheres – they look at a very theoretical tube of gas in a gravitational field.
And note that I’ve very carefully restricted my argument to the specific case of Jelbring, because it is simple enough to trivially refute. It also establishes an important point. In no case — not just this overidealized case — can an atmosphere spontaneously generate a thermal profile. A thermal lapse in an isolated atmosphere violates the second law. This is a useful thing to recall in further discussion.
Thermal lapses in dynamic atmosphere go without saying — you can simply measure the temperatures in a sounding of the troposphere. But even here strict thermodynamic bounds exist. You will have to work pretty hard, for example, to come up with natural systems of circulation that increase the temperature of the hot reservoirs, because energetics pushes the gas the other way, heat flows in general from hot to cold under all the driven transport mechanisms. Yes, there are exceptions, yes, they may be relevant, but it isn’t enough to just say “they might be there”, one has to do a lot of algebraic work and difficult reasoning to establish that they really might be there, and then it is always good to observe them experimentally in action.
And none of this means that the GHG GHE isn’t real. IR spectroscopy is direct experimental evidence that it is real. These other proposed mechanisms or modulators must come in with an and operator, not an exclusive or operator, or they simply don’t agree with our observations of cold IR radiation from the CO_2 band in the upper troposphere.
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