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.
Robert Brown says:
January 28, 2012 at 6:27 am
One thing the neophytes do not understand is the remarkable interconnectedness of it all. Physics is not merely consistent, it exhibits an amazing self-similarity in the structure of the equations that describe quite dissimilar systems; dissimilar to human minds (springs versus capacitors for example), but not dissimilar to (for lack of a better term) the World. Change one of those Laws and the knock-on effect is to call into question all the other Laws that have the same mathematical structure. The Laws are like the pieces of a jigsaw puzzle. If you take a piece away, you can only replace it with one of the exact same shape, not one of a totally dissimilar shape. You can’t put a round peg in a square hole. That is why the Laws remain in place.
We say in principle the Laws may need revision, but the only revisions I can recall are minor tweaks. For example the smallchanges to f=ma at extremes of mass and acceleration and the increasing precision of empirical constants such as Avogadro’s Number. The conservation laws can be summarised as “you can’t get a quart out of a pint pot”, something any farmer can tell you.
There is considerable confusion about what is Law and what is Theory. Laws are universal, simple, true on every occasion they have been tested and are generally expressible with a simple mathematical equation. Theories are explanations of the world that usually, though not always, invoke physical law. Newton gave us his Law of Gravity and pointedly refused to provide a theory. Currently, there are two (incompatible) physical theories of gravity (that I know of): Einstein’s Relativity theory (space is curved) and a Quantum theory of gravity (gravity consists of particles called gravitons).
Thus theories tend to change rather more often than the Law. Trofim Denisovich Lysenko tried to replace a Natural Law with one based on human invention in his theory of plant inheritance and we all know, or should, where that got him.
Some here have claimed that physicists and engineers are engaged in a kind of conspiracy. I agree; there is indeed a conspiracy. The word conspire comes from Latin and literally means to breathe together. A conspiracy then is figuratively “a union or combination (of persons or things) for one end or purpose; harmonious action or effort”. As Emerson put it in Ode to Beauty “All that’s good and great with thee Works in close conspiracy”.
thepompousgit says
“Trofim Denisovich Lysenko tried to replace a Natural Law with one based on human invention in his theory of plant inheritance and we all know, or should, where that got him. ”
Lysenkos theory was known as “The inheritance of acquired characteristics”
It was an idea first proposed by Aristotle and later explored further by a scientist named John Baptist Lemark.
Recent evidence shows that for people there might be a grain of truth there.
Grandchildren have their genetic inheritance switched altered by events in their grandparents environment.
It just goes to show you that when an idea is dismissed as dead it gets up to bite your bum.
Robert Brown says:
January 28, 2012 at 6:27 am
You’re very kind, but there is an old saying in academia — you can lead a horse to water but you can’t make it think….
I am happy to have discussions and even debates with students
————————————————————————————————–
[SNIP: This kind of derogatory snark is inappropriate. Don’t do it. Dave. -REP]
Tim Folkerts says:
January 27, 2012 at 3:08 pm
I stand corrected. But make that turbulence rather than simply convection. Turbulent mixing is why you can mix cream evenly in coffee with just a few stirs with a spoon. Turbulent mixing extends through the stratosphere where there is little convection. The turbopause where the atmosphere starts to stratify by molecular or atomic weight is at a height of ~100 km. So 99.9999% of the atmosphere is well-mixed. But even turbulent mixing looks a lot like diffusion, and is often referred to as eddy diffusion.
In order for a tall column to be isothermal the density must identically follow pressure, there can be –no- deviation of the P/ρ ratio, and that gives me some intuitive heartburn. Have you ever thought from that direction? It seems to me if in the space between collisions if the exact tracks of a molecule is assumed to be a straight line, you would have an isothermal column. However, if tracks between collisions have an always –z curvature from gravity, it seems this would have to be some degree of a lapse rate. Can you see it from that direction?
Sigh. The model discussed in Jelbring and on this list is an ideal gas. So of course there isn’t any deviation. A non-ideal gas won’t affect the fact that equilibrium is isothermal, of course, but don’t change models in the middle of a stream.
In the original post I included the correct thermodynamic equilibrium state. I’ve posted a link to this question as it appeared on a thermo-stat mech final exam, with the full solution. Do you find any errors?
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thepompousgit says:
January 28, 2012 at 10:10 am
nitpick:
Quantum Gravity would be a gauge field theory, presumably abelian, with the gauge boson being the graviton, similar to Quantum Electrodynamics with the electromagnetic field and the photon. Not that I really understand what that means.
Yes, if thermal radiation is the equilibrium mechanism, I see that you are correct. I apologize for my obtustness, your derivation at the top is a mechanical one.
So radiative transport is the reason the evolved isothermal atmosphere departs from a equipartition of energy distribution? I’m sorry if i missed that earlier.
You still don’t see — if ANY mechanism (other than external work) can transport heat from bottom to top, a non-isothermal distribution violates the second law. Consider the gas in the sealed container. Even internal radiation is a means of thermal relaxation.
The problem is that your imagination has misled you — you have a heuristic in your mind — “equipartition of energy distribution” — that you won’t compare to the way the equilibrium computation is correctly done. If you use your heuristic in general stat mech computations, they will fail, because thermal equilibrium is not what you imagine. You also are completely, totally, confusing how gravitational potential energy is correctly included in the equilibrium computation. You can see at a glance that stable isothermal force balance is possible. Force balance must be energy balance.
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DeWitt Payne said @ur momisugly January 28, 2012 at 11:01 am
Me either; I included QG for completeness. Curvature of space seems entirely reasonable and sufficient to me.
“Many of the same sorts of arguments have come up a year ago, and they will come up again in another year, I am sure”
Not keen on that type of complaint. It is easy to imagine the same exasperation being vented about the merits of throwing virgins into the volcano. Isn’t that why science is hard? It’s not just hard mathematics and abstract concepts – it’s also because people refuse to back off when they are not persuaded.
I’ve heard all sorts of arguments about global warming catastrophe theory. But stubborn old me just keeps asking awkward questions because I find myself unpersuaded. I suppose I could just accept it because other people know more about it than me.
Back to the above discussuion, I’m genuinely unpersuaded, even though a very insightful model has been presented and defended. On a very recent post, I do appreciate more now that it is being put forward as a reply to Jelbring, and needs to be comparable in many respects.
However, I’d be interested in views on the following:
Is the Fourrirer Law invariant to a uniform force field? Or did Joules have a good point way back when he suggested mechanical conduction against the force field has more work to do?
What happens if collisions are not perfectly elastic? How does this change expectations of the physical state of the gas at higher pressure compared to lower pressure? Do imperfect collisions represent a mechanism for a temperature effect?
DeWitt Payne says:
January 28, 2012 at 9:55 am
And to bring things back full circle: If you can measure a temperature difference from the bottom to the top, you must also be able to extract work or transfer energy from the system because the measurement itself must transfer energy. If you extract energy and the temperature difference (lapse rate) remains constant you have a perpetual motion machine of the second kind, which is so unlikely as to be effectively impossible.
DeWitt says at 1/28 9:55am:
“…for those folks who still don’t accept that the equilibrium state is isothermal…”
Verkley paper authors don’t accept the Fig. 1 equilibrium state is isothermal. This is mathematically proven and shown in their part b.
DeWitt (and Robert Brown) – To help you come to grips (grok) with the 2004 Verkley proof that top post Fig. 1 achieves thermal equilibrium non-isothermally (meaning there exists their proven temperature gradient eqn. 18 in equilibrium), consider their explanation, this is somewhat more satisfying to me each time I re-read it.
For Fig. 1 in top post at non-isothermal equilibrium, meaning a thermometer will indeed read T1b and > T1t again at equilibrium consider Verkley discussion in b where the authors don’t accept that the equilibrium state is isothermal by proving Fig. 1 has an isentropic temperature gradient:
“This (non-isothermal isentropic profile) indeed brings us to the broader framework discussed by Maxwell, in the sense that convective turbulent motions are now taken into account, albeit implicitly….We should now interpret the state variables as averages over volumes that are large compared to the size of the turbulent motions….We see that the temperature gradient (Verkley et. al. derived eqn. 18) is considerably larger than in the empirical profile.”
Paul Birch: “What they explicitly say is that the assumption that “temperature is proportional to average molecular kinetic energy” is FALSE (for the finite microcanonical ensemble). They say that the statement “temperature decreases with height” is FALSE. The reason it’s false is different for small N and in the canonic limit, but it is false either way. This is what they say.”
Sorry for ignoring you, Paul. I had thought you were done, and it was by the merest chance that I saw your name on the WUWT home page as someone who had posted recently about this.
If I indeed said Velasco et al. agree with me on the use of the term “temperature”–and I didn’t intend to–I take it back. I know they aren’t using that term in the same way I am; if I recall, they instead say it’s something like a quantity inversely proportional to the first partial of the log of phase volume with respect to maximum energy: as I told DeWitt Payne, “temperature” for Velasco et al. seems to be a global quantity, a characteristic of the ensemble as a whole. I never intended to say that this definition was the same as mine. What I intended to say is that Velasco et al. say there’s a drop–minuscule, as I’ve said from the beginning–in mean molecular translational kinetic energy, and to this layman’s eyes that looks like a temperature drop.
So why do I disagree with their definition of temperature? Actually, I don’t; or, rather, I’m agnostic about it because I wasn’t immediately able to find out how their definition was derived. It’s just that I felt it was irrelevant to the discussion.
And why did I feel it was irrelevant in this context? Recall how all of this started, namely, with Dr. Brown’s (to me, completely unsatisfying) argument for isothermality here: http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-867311. You’ll see his argument is based on local quantities. In fact, you’ll see he says that the velocity distribution–and therefore kinetic-energy distribution–at any altitude is the same as at any other. This is why the definition of temperature I prefer in this context is the one we all learned in high-school (as we say here in the colonies) chemistry, i.e., mean molecular translational kinetic energy: it can be used as a local quantity.
Just in case anyone else is paying attention, I’ll add that what we’re arguing is an extremely academic point. Velasco et al. and Dr. Brown both say there won’t be any measurable lapse rate at equilibrium in an isolated gas column subjected to gravity. Dr. Brown began by saying–although he may have tuned his position since–that velocity distributions at all altitudes in such a system are identical. My interpretation of Velasco et al. is that they this isn’t true, because the mean molecular kinetic energy decreases with altitude, but, again, that it makes no difference in practice, because the difference is so small you’d never be able to measure it. I don’t understand Paul Birch to disagree with the interpretation as I stated it in the last sentence, but he objects to my calling such a small kinetic-energy difference a temperature difference.
So why did I bring Velasco et al. up if the issue is so minor? Because in the back of my mind I had for some time wanted a satisfactory basis for deciding between the isothermal and dry-adiabatic-lapse-rate schools of thought. Unfortunately, all the discussions I had previously seen were at the level of rigor exhibited by Dr. Brown’s discussion, which I did not find at all satisfactory. When I hit upon Velasco et al., on the other hand, I felt I had finally hit pay dirt, but some of the jumps between their equations were broader than I could easily make, so I wanted some vetting. Since, unlike Dr. Brown, Velasco et al. said there is indeed a velocity-distribution difference between altitudes, I thought I might provoke an attack on their paper and thereby get some light shed on its more-obscure passages.
I was wrong.
Trick says:
January 28, 2012 at 11:28 am
Turbulence is by its nature dissipative. From Wikipedia;
[my emphasis]
But the system is defined as closed. Any turbulence must dissipate. Verkley’s solution no longer applies. Then we’re back to conduction and an isothermal system at equilibrium.
Robert Brown says at 1/28 10:55am:
“In the original post I included the correct thermodynamic equilibrium state…. Do you find any errors?”
Comparing the work in Verkley to the top post, I see your equation 5 for dz up there, when integrated, takes T outside the integral apparently just making the assumption T is constant leading to isothermal conclusion.
T is function of P by ideal gas law (thus function dz meaning T cannot go outside integral) as Verkley paper correctly shows in eqn. 16 leading them to show top post Fig. 1 being non-isothermal isentropic equilibrium via Verkley et. al. eqn. 18.
Tim Folkerts says:
January 28, 2012 at 8:53 am
I also love the challenge that “It has never been resolved by experiment.” First of all, there is a good chance that the person making the claim simply does not know the relevant experiments.
Beyond that, often there are related experiment that do indeed show the expected results, just not in exactly the form the person want. For example, the satellite IR spectra looking down at the earth DOES show conclusively that the CO2 warms the earth, but only if you understand enough of the other science involved. It doesn’t show what ELSE might affect the surface temperature. It doesn’t show exactly how changes in CO2 would change the surface temperature. But is does clearly show a warming effect from the CO2 that is present. In this present case, there are centuries of experiments involving gases which are consistent with the laws of thermodynamics as presented in standard textbooks.
Gosh Tim, real experiments from satellite data looking down on the Earth proving carbon dioxide warms the Earth? We’ve been asking for this information for a, well, always. Where have you been hiding it? Do show it to us, and talk us through it, I’m sure others would like to see such proof that Carbon Dioxide warms the Earth.
I had a look, but couldn’t find it. I did find the silliest of graphs here, http://www.ncdc.noaa.gov/indicators/, showing the poster child CO2 levels from Hawaii against levels for the last 800,000 years from the Antarctic- what do you notice?
That carbon dioxide obviously was utterly irrelevant in the massive global warming every 100,000 years at the beginning of interglacials when sea levels rose 300ft plus as gazillion tons of ice melted? That the Hawaiian spike looks, well, rather odd? But isn’t that why Keeling chose to measure his mythical ‘background’ carbon dioxide there – on top of the world’s most active volcano? Tons and tons of carbon dioxide to measure and choose from, from the erupting volcanoes, from the venting, from the thousands of earthquakes above and below sea level, from the warm sea itself around the islands, and of course all on that super hot spot creating the islands. And, such a brilliant scientist, he could tell with less than two years data that man-made global emissions were rising annually…
Someone did an analysis of Gates’s technique, you too spend much of your posts agreeing with the prevailing mood and then throw in bits of nonsense as here, I’m calling you on it, I’ve highlighted it in bold. Provide the following experiment you say “DOES show conclusively that the CO2 warms the earth” and talk us through the science since you “also love the challenge that it hasn’t been resolved by experiment”:
Beyond that, often there are related experiment that do indeed show the expected results, just not in exactly the form the person want. For example, the satellite IR spectra looking down at the earth DOES show conclusively that the CO2 warms the earth, but only if you understand enough of the other science involved.
DeWitt Payne says at 1/28 11:45am:
“Any turbulence must dissipate. Verkley’s solution no longer applies. Then we’re back to conduction and an isothermal system at equilibrium.”
Notice that the wiki clip you posted mentions turbulent “flow”. There is no “flow” in top post Fig. 1 just molecules randomly mixing. Verkley et. al. b solution does apply as they further explain their concept of convective turbulent mixing. See their 1st Law eqn. 14 and explanation starting: “Even when on the scale of the turbulence the heating rate J would be zero…” and continues on to support their case for Fig. 1 being non-isothermal isentropic.
Very interesting discussion, thanks DeWitt.
Trick,
You don’t get turbulence without flow. Period. Any turbulence dissipates. Verkley, therefore, is not relevant to the subject of this post.
“if ANY mechanism (other than external work) can transport heat from bottom to top, a non-isothermal distribution violates the second law.”
But there is none that I have seen in these discussions.
There was an appealing idea to transfer energy up to altitude using black body radiation in a vacuum. Sorry to be so practical, but it is a highly idealised mechanism and depends on assumptions of loss-free transfers plus a good deal of organisation of the active transfer process (which implies work).
Even then, there is my question about Fourrier’s Law in a force field. If we could get a free transfer of energy to altitude, it doesn’t mean an isothermal outcome if conduction of temperature is influenced by the gravitational force field. It might alter a temperature gradient, but that doesn’t necessarily mean the gradient must disappear completely.
Ofcourse this could mean an indefinite circulation of energy around the system and some might object. But if we place a highlyidealised concept of a perfect conductor into a force field, we’re not placing ourselves into a convincing position to object to the consequences on real-world reasoning.
DeWitt – Verkley et. al is using the common definition of turbulence applied to ideal gas molecules which defines turbulence to mean their irregular motion. Surely the ideal gas molecule random movements are consistent with irregular motion.
Brownian motion is considered irregular motion of macro particles deduced from the molecules. (Robert Brown said that in 1827, he’s been around awhile!). Brownian motion thus is a form of turbulence.
Amazing where this thread, like many, evolves.
Bryan said @ur momisugly January 28, 2012 at 11:33 am
Lysenko replaced Mendelian genetic inheritance with a version of Lamarckism just because he was a Marxist and Lamarckism supported the Marxist idea of Progress. I am fully familiar with Lamarckism. Darwin was a Lamarckist. Lamarckism was fully compatible with Darwinism.
The
dismissed Lamarckism, and yes, it has come back to bite them on the bum which is why it has been renamed. But that’s a bit OT.
Trick says:
January 28, 2012 at 12:56 pm
Humpty Dumpty (Through the Looking Glass) much! Turbulence has a very specific meaning and it has nothing to do with the random motion of individual gas molecules whether ideal or not. Brownian motion isn’t turbulent movement either.
Myrrh askes: “Gosh Tim, real experiments from satellite data looking down on the Earth proving carbon dioxide warms the Earth?”
http://wattsupwiththat.files.wordpress.com/2011/03/gw-petty-6-6.jpg
… but only if you understand enough of the other science involved.
And I think I am now going to go back to other things …
DeWitt 1:26pm – Yeah, in aero work it is useful to think of turbulent flow vs. laminar flow. Here it is useful to think of turbulence to mean irregular motion (it IS the dictionary definition). We aren’t worried about stream lines in top post Fig. 1.
If you want, the Verkley paper may then mean more for you if just substitute the dictionary definition of “turbulence” with ”irregular” every time they write “turbulence” term.
My 11:28am post above then becomes this, a direct meaning but not direct quote from the paper:
“This (non-isothermal isentropic profile) indeed brings us to the broader framework discussed by Maxwell, in the sense that convective irregular motions are now taken into account, albeit implicitly….We should now interpret the state variables as averages over volumes that are large compared to the size of the irregular motions….We see that the temperature gradient (Verkley et. al. derived eqn. 18) is considerably larger than in the empirical profile.”
This does not change any Varkley et. al. logic, derivations or equations. Now others may post with the non-direct quote issue down thread…sigh. If they do, show the work that changes Verkley when substitute irregular motion for turbulent motion. No laminar flow here.
I don’t hold out much hope for Dr Browns latest suggestion of a lossless light tube.
I will restate my claim yet again, since people appear to be incapable of keeping it in mind long enough to reach the “Leave a Reply” box.
This post addresses precisely one thing. Hans Jelbring published a paper in 2003 in Energy and Environment. Tallbloke has posted the entire paper on his blog here:
http://tallbloke.wordpress.com/2012/01/01/hans-jelbring-the-greenhouse-effect-as-a-function-of-atmospheric-mass/
with a contemporary preface by Jelbring. I quote from this preface:
My 2003 E&E article (peer reviewed) was strictly applying 1st principle physics relating to a model atmosphere. Very strong conclusions can be made about such a model atmosphere and less strong ones about our real atmosphere. This was not discussed for reaching a maximum of simplicity and clarity approaching an educated but laymen audience. However, an investigating professional climate scientists should just reach one of three results; a) my logic is wrong, b) the major part of the Greenhouse Effect is always at hand in any (dense) atmosphere and c) any of the first law of thermodynamics, the second law of thermodynamics or the ideal gas law is invalid.
I accept the challenge. His logic is wrong. His article is utterly irrelevant to the actual GHE that can be verified by the merest glance at satellite IR spectra. Finally — and this is the point of my demonstration above — it is the model he proposes that is in violation of the second law of thermodynamics, not only in violation, but a textbook example of a violation.
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.
Here is an ordinary undergraduate exam question in a course in statistical physics and thermodynamics offered and the University of South Carolina and posted on their website. Note well that the question asks students to solve the exact same problem that Jelbring proposes — that of a vertical, isolated, column of ideal gas that must be in static and thermal equilibrium in a gravitational field:
http://www.physics.sc.edu/~yar/phys706_2011/Homework/final_solutions.pdf
If I, at least, were grading Jelbring’s supposedly professionally written paper against this textbook question, he would get a zero for the problem.
He would get a zero for two reasons. One is that no work is done in Jelbring’s paper. A physics problem is not solved in words! Especially not a difficult one. Of course this one isn’t all that difficult — it is a standard feature of any introductory physics textbook — but still, not one equation!
After a long and tedious description of the problem — a simple container of fluid like the one I drew up above would work as well as his complicated “adiabatically insulated planet”, he asserts that the “Greenhouse Effect” is entirely due to some sort of static gravitational effect that results in a “surface atmospheric mass density”. In particular, his assertion is that:
The GE is hypothesised to be independent of the amount of “greenhouse gases” in a dry atmosphere.
This makes it perfectly clear why this assertion is so zealously defended in this thread. It is literally what anyone who wants to deny the reality of the Greenhouse Effect being connected in any way to GHGs wants to hear.
He follows this by offering as logical proof — remember, we are asked to challenge his logic and he’s stated his axioms as being “physics is correct plus an ideal gas” — the experimental observation that the dry adiabatic lapse rate that is approximately observed in the Earth’s highly dynamic, externally driven atmosphere will be the thermostatic equilibrium state in his sealed container.
He does not prove that this is, in fact, true — he simply states that it is true, quoting a textbook derivation of the DALR as his “proof”. This is a double swindle. For one thing, where, exactly, is his contribution? Citing a textbook? Excuse me? That’s not even up to the standards of somebody who copies an answer on an exam — at least in that case one would be likely to recapitulate the algebra and see why or why not the gas in question was in thermal equilibrium and how, exactly, the DALR was arrived at.
Jelbring does indicate some of it — bits such as: “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.” Of course, in an isolated ideal gas left long enough to come to thermodynamic equilibrium, there are no moving parcels of air and there is no work being down against the gravity field. So even his English words describing a conclusion with many assumptions underlying a not completely trivial algebraic derivation leave considerable doubt that that conclusion should necessarily apply to a gas in static force equilibrium and thermal equilibrium.
Second, we have already heard, in the thread above, from the actual author of a freely available textbook that does derive and discuss the DALR, that the DALR is not, in fact, thermal equilibrium. This puts those who are reluctant to give up their irrational attachment to Jelbring’s conclusion simply because it mirrors their prior belief that the GHE is not due to GHGs in a difficult position. Jelbring implies that we can be certain that it is thermal equilibium because James R. Holton, in an introductory textbook written in 1979 says it is. However, examining this book it seems to me that he derives it by assuming a “perfect gas in adiabatic motion” — right next to a picture of (and in the context of) Richardson’s criterion for the stability of flow.
The last time I looked, a gas in convective flow is not in static equilibrium, and flow itself cannot be a long-time stable state of any isolated system with internal dissipation. Superfluid Helium, perhaps. An ideal gas, no. Is this a deliberate swindle? How can I tell? Probably not. Never attribute to malice something that can be attributed to simple incompetence. In any event, actually examining the only reference he cites to defend his assertion that the DALR is characteristic of actual thermal equilibrium in the absence of bulk fluid transport driven by thermal gradients readily demonstrates that it does not. In fact, the paper only has four references — Arrhenius to be poo-pooed, another textbook on dynamical climatology, not used in any relevant way, one of Jelbring’s own former papers, and Holton. Since Holton does not in any way suggest that the DALR is a static, thermal equilibrium process, we’re down to one reference that says that it is. Who is it? Himself.
This suffices to show his errors in logic. Stating a hypothesis and the stating that somebody else derived this equation with a thermal lapse (in an entirely different context) and so the hypothesis is proven, citing your own work several times in between, without so much as a single equation defining the criterion for static force equilibrium, adiabatic curves for an ideal gas, the actual definition of thermal equilibrium is not a logically valid proof, and it is certainly not a mathematically or physically valid proof. It is heuristic handwaving, nothing more.
Next, let us examine his really fundamental errors — the errors in simple thermodynamics. Oh, wait, that has already been done. But let’s bash some more. To quote Wikipedia’s article on Thermodynamic Equilibrium, where they discuss the difference between local thermodynamic equilibrium and global thermodynamic equilibrium:
Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell-Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally stably stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it in order to compensate for the melting, and continuously draining off the meltwater. Transport phenomena are processes that lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous.
Could it be that atmospheres with a DALR are only in local thermodynamic equilibrium (required so that one can discuss the temperature of a local parcel of air as it moves around) but are not in global equilibrium? Caballero, author of an actual textbook on physical climatology, says that is precisely the case. Every physics textbook on the planet states clearly that global thermodynamic equilibrium is isothermal. The zeroth law of thermodynamics is precisely that statement; without it there is no such thing as thermometry and we can’t even measure a temperature in the first place.
This merely leads us to the big violation, the elephant in the room: the violation of the second law in Jelbring’s paper. He clearly states that he assumes:
The energy content in the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule, in an average sense, will have the same total energy. In this situation the atmosphere has reached energetic equilibrium.
Here it is. If we leave his isolated ideal gas alone for a long time, energy will redistribute until the gas reaches “energy equilibrium”. This term is meaningless, of course — Jelbring just made it up. The correct term is thermal equilibrium because thermal equilibrium is the most probable way energy will be split up among the various degrees of freedom (including gravitational ones when present) in any isolated system after thermal relaxation of the sort he describes has occurred.
Clearly Jelbring thinks that his asserted “energy equilibrium” (thermal equilibrium) state is not isothermal. It is the entire point of his paper. But is this non-isothermal state equilibrium?
I have shown above, and can show over and over again that it is not! It is a textbook example from any textbook on thermodynamics to show that equilibrium is isothermal. If it were not, one could build perfect refrigerators and perfect heat engines. In fact, if Jelbring’s hypothesized atmosphere with a thermal lapse rate were a true thermodynamic energy equilibrium, one could take its heat content and use it to do reversible work that directly reduces the entropy of the Universe. It violates three out of three statements of the second law. The demonstration of the violations isn’t even specific to Jelbring’s system — it is generic. A reasonably bright premed who has taken a thermo course should be able to see the error, let alone a first year undergrad physics major or engineering student.
This is the reason that this terrible paper should never have been accepted and should be openly shunned by any real climate skeptic. Although it is a logical fallacy in a sense, when climate skeptics state “There is no such thing as the GHG GHE because Jelbring has shown that even a stable, isolated, non-GHG containing ideal gas atmosphere will have a permanent thermal lapse” what they are really saying is “We don’t believe in GHG GHE because thermal separation is really magic.” Even if they follow up their remarks with something that might be true — “… and besides, the GHG-based GHE is saturated, the feedbacks are actually negative, solar-induced variations in albedo are just as important, and if you would stop adjusting the bloody temperature record to show ever more warming and look at the actual data, you’d find that it doesn’t support your conclusions or prior predictions” you’ve already lost most listeners way back there with “magic”.
Don’t think that most climate scientists are stupid, or that they are all necessarily morally corrupt. Both of these are ridiculous assertions, even if you can find specific examples of both among their ranks. It doesn’t take a lot of knowledge of physics to understand the second law of thermodynamics and how a system with a thermal gradient can never be in a state of global, stable, “energy equilibrium” (whatever the hell that means) unless it violates it. If you are betting your credibility on it, you will lose, and unfortunately, you will probably lose in a way that makes it all too easy to marginalize and ignore any much more reasonable objections you might make.
On these pages, we regularly (and, I think, correctly) accuse at least some of the climate scientists out there of cherrypicking data, engaging in confirmation bias, misusing statistics. We frequently use the (fallacious) argument that simply because they do these things, their conclusion is necessarily wrong. Why give the climate sciences an open and straightforward way to do the same to us, a way that I agree with, a way that is totally justified?
My argument, and conclusion, is very narrow. I am not saying, for example, that atmospheric dynamics may not play an important role in determining the Earth’s heat transport system and hence its relative “warming” or “cooling” rates. I am saying that it is utterly false to claim that a static, stable, isolated atmosphere will have a thermal lapse rate and argue from this that the GHE is due to static compression in an equilibrium ideal gas. No, it’s not. That would be magic.
I have, along the way, commended the staunch if misled defenders of Jelbring’s work to entertain the idea that perhaps there really is a GHG GHE that really does help to warm the Earth’s atmosphere. I have suggested repeatedly that they examine, and try to understand, the satellite-based IR spectral data than in my opinion is direct experimental observation of and confirmation of the basic mechanism. I have suggested that the differential cooling established by GHGs is responsible for the DALR, not the other way around. I do not insist on the latter — it is just what makes the greatest sense to me at this time and seems to be in general agreement with the arguments in physical climatology where it is recognized that the moving parcels of air referred to in deriving the DALR are moving because of thermally driven vertical shear. But it is all, in the end, a lot more complicated than the simple flow diagrams that they often present in the atmosphere, however simple and revealing the outgoing radiative spectrum is.
I will finish — again — by suggesting that the remaining supporters of Jelbring’s paper not take my — or his — word for anything. Look inside any physics textbook that you like, and you will find the laws of thermodynamics laid out. Look inside any of the thermo or stat mech textbooks beyond the introductory level — which are hard going! — and you will find them laid out and derived and illustrated with many examples. Look in any textbook in physical climatology and you will never see the DALR derived or discussed without reference to uplifting parcels of air — air in motion, not static air. In the end, you will see why, and how, thermal equilibrium must be isothermal and how all of your efforts to argue that it is not each leads to a straightforward violation of the second law of thermodynamics (as well as not being the actual solution to the problem in thermodynamics or statistical mechanics, correctly done, as has been known for well over 100 years).
rgb
Looking for a second law violation:
Dr brown and others, I hope you will indulge one more question. It is a closed box (closed system) in the earth’s gravity.
In the first condition, the box is empty. So it is in thermodynamic equilibrium.
In the second condition, the box has gas in it that is opaque to thermal radiation. So it is a isothermic gas in thermodynamic equilibrium.
In the third condition the box has gas in it that is transparent to thermal radiation. Say there is a steady state condition where the gas molecules in the box, as they move, increase the kinetic energy of a molecule slightly when the movement has a component in the direction of gravity and looses slight kinetic energy when there is a component opposite gravity. The top of the box and the bottom of the box exchange thermal photons. The average temperature of the top of the box and the gas at the top of the box are the same. The average temperature of the bottom of the box and the gas at the bottom are the same. The thermal radiation exchange has a slight imbalance towards the top of the box and the kinetic energy exchange, from the top of the box, thru the gas and to the bottom of the box, has an equally small imbalance towards the bottom of the box. There is isohtermal gas and no equilibrium. I”m looking for the violation. I can’t think of any mechanism, within the box, that can use the temperature gradiant to increase the heat content of the box, or to increase the temperature differential within the box. (serious for real question)
Dr Brown, one small thing, and I mean it kindly; I just saw your example of carrying a sealed jar of air up some stairs, to exploit a pressure differential. I don’t know if this is what you meant, But i think that process only uses work against gravity. Air has buoyancy, and moving the sealed jar of air up or down is work against gravity.A mass less jar makes it obvious, carry the jar down stairs and let it go and it floats up to where you started, carry it up stairs and let it go and it sinks back, Use the pressure difference to do work, and that is just the same work it took to move the jar up or down.
PS Dr Brown, I’m not defending Jelbrings paper; it’s nothing to me, i’m not a climate skeptic.
I only saw things that didn’t make sense to me. Thanks!