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.
@mkelly >>>>Air is seen under natural circumstances to flow up hill water has not.
Reversing Falls: water flowing up hill. http://new-brunswick.net/Saint_John/reversingfalls/reversing.html
Tsunami: water flowing up hill: http://www.youtube.com/watch?v=w3AdFjklR50
The water in a 20-ft tsunami doesn’t stop when it reaches a barrier that is 20-ft. high, Momentum redirects the water upwards.
Robert Brown says: “At least some people — primarily the ones that aren’t heavily psychologically invested in there being intrinsic “non-Greenhouse heating” of an isolated atmosphere so they could continue to disbelieve in the GHE altogether — seem to get it. ”
Shrug, industry figures give 67°C for our atmosphere without greenhouse gases. The mass/weight/gravity/pressure/ play of the fluid gaseous ocean of nitrogen and oxygen above us is the greenhouse/thermal blanket around the Earth. Adding some fibres of water vapour in the Water Cycle cools that by 52°C to bring it down to the 15°C we have. Carbon dioxide fully part of the water cycle, all pure clean rain is carbonic acid, can only aid the main greenhouse gas water vapour in its role of cooling.
For goodness sake, just step out into a desert to get some grasp on this.
I’m well aware that air is more compressible than water (though not incompressible), which is why I mentioned it when I introduced the example, to anticipate an obvious objection. But is that a relevant difference in the context of Jelbring’s theory? I thought that depended on a pressure gradient, which does exist in the case of water.
But at least we have made progress if it is accepted that the Jelbring theory depends on compression. Of course, it is true that a gas can be heated by compression, as I mentioned in an earlier comment on this thread. If you take a long horizontal cylinder of air and then raise it to vertical, the gas at the (new) bottom of the cylinder will be compressed and heated, while the gas at the top will be rarified and cooled. A temperature gradient will thus arise. But that is a one-time effect which fades as heat flows from hotter to colder areas, in accordance with the Second Law. It does not explain how a permanent gradient is maintained in a planetary atmosphere.
@joules >>>>It’s a given that no one here is willing to cast aside the ideal gas law we should all agree that spinning up and spinning down the centrifuge will create at least a temporary temperature/pressure gradient predicted by the ideal gas law.
I would hazard a guess that by now, millions of hours of gases being spun in gas centrifuges have been completed over the past decades, all around the world. Uranium hexafluoride used U-235 / U-238 separation processing. There is probably data on gas temperature profiles available somewhere.
Just to reiterate, this experiment is being conducted, tens of thousands of times every day, in the gas centrifuges used for uranium isotope separation, which generate g-forces sufficiently large that the on-axis pressure is a near-vacuum, which the outer-rim pressure is many atomospheres — precisely the conditions of interest.
These gas centrifuge “experiments” concretely affirm Brown’s theoretical arguments: the observed equilibrium temperature distribution is isothermal. Indeed, the multibillion-$ isotope separation industry would fail otherwise.
For more theoretical and experimental details than most folks want to know, see @article{Kemp:2009lr, Author = {R. Scott Kemp}, Journal = {Science and Global Security}, Number = {1}, Pages = {1–19}, Title = {Gas Centrifuge Theory and Development: a Review of US Programs}, Volume = {17}, Year = {2009}} and references therein (a Google search will find it).
Elevator Summary: “Gravito-thermal” theories are just plain wrong.
Paul Birch:
Thank you for your recent posts. I apologize for not having acknowledged them in my most recent one; I somehow failed to see yours before I sent mine.
I believe I now understand your position, and, as you say, it is entirely possible that I am “trying to read far too much into a mathematical subtlety [I] don’t understand,” although I see no evidence so far from which to conclude that. However that may be, I’ll give some feedback in case any lurkers find the issue of interest.
First to your contention that we are not talking about the microcanonical ensemble. Here a little context is in order. Recall that both Robert Brown in this thread and Willis Eschenbach in the previous one were addressing themselves to refuting the Jelbring paper. That paper began with a hypothetical ideal gas G disposed between concentric spherical surfaces A and S. Jelbring said that “A and S are thermally insulated preventing heat from entering into G and infrared radiation to reach space.” It is no doubt to parallel this condition that Robert Brown says of his thought experiment that it involves an “adiabatically isolated column of an ideal gas.” In short, heat can flow neither into nor out of the gas, so by definition it is indeed a microcanonical ensemble.
Next I consider your statement that “for any reasonable number of particles, it makes no difference” whether we’re dealing with the microcanonical ensemble or not. I agree with you that as a practical matter any lapse rate as small as I’m saying Equation 8 implies would be too small to measure. But, again, the context needs to be considered. What Robert Brown and Willis Eschenbach are both saying is that any non-zero lapse rate at all would violate the First Law because there would be a perpetual heat flow through the external wire. Had they instead based their proofs on a lapse rate of the magnitude for which Jelbring contends, then I would agree with them that they had proved their case. But they insisted that they needed no such limitation. So any non-zero lapse rate is relevant, no matter what its magnitude is. So the microcanonical ensemble is indeed relevant to the issue under consideration.
You make two further points that at base are not technical arguments so much as statements of your point of view. You say, “However, even in this extreme case, the temperature at equilibrium will still be the same throughout the entire height, in the crucial sense that no net work could be extracted from the gas by connecting different levels, by any means whatsoever.” Essentially you’re saying that even if a difference in mean translational kinetic energy is non-zero, it doesn’t qualify as a lapse rate in your view if it’s exhibited by a maximum-entropy configuration and therefore results in no net heat flow. Okay, I understand your redefinition.
You additionally observe that I am “taking the extreme and irrelevant sub-thermodynamic case of a minuscule total number of isolated particles – in which regime the macroscopic temperature is increasingly ill-defined and no longer simply proportional to the kinetic energy per particle.” Let’s set aside what exactly you may mean by imprecise terms like “sub-thermodynamic,” “macroscopic,” and “increasingly ill-defined.” And let’s concede that the case I discussed was an extreme case. That case nonetheless remains relevant, because it illustrates by exaggeration something that remains true independently of how large the number of molecules gets: the mean molecular translational kinetic energy decreases with height, and it does so at a rate that is finite and non-zero, albeit negligible for most purposes.
In any event, I think these on-line interchanges have the potential to be enlightening, and, although I can’t profess to have made any great strides in this case, I do appreciate your making the effort.
@Robert
“In figure 1 above, an adiabatically isolated column of an ideal gas is illustrated.”
It has been a great week to review the basics of physical phemonena. I have been serially convinced by many contributions in opposite directions. I agree that there is a conduction issue as you have pointed out, Robert, but a guy named Kevin and I agree that it is not going to create an isothermal condition.
If the atmosphere does not conduct heat (which seems to be Jelbring’s assumption) it is an unreasonable experiment. But you can’t have lots of conduction just because it is convenient. It has to be realistic.
If the atmosphere was warmer at the top than the bottom, it would have stable and unequal temperature distribution. The reason is that gases are really lousy conductors of heat, especially downwards, meaning downwards in a gravity field. Bouyancy can override conduction in this theoretical atmosphere in some cases.
In your example above, the gas is treated as if it was a solid at certain times, which it clearly is not. It has to be discussed as a gas at all times. You have mentioned several times that if the gas moves it has to have a driver (some work going on). But gas is always in motion – perpetual motion as far as we know – and also we know that individual molecules contain more energy than their neighbours. Many energetic molecules of gas are literally hotter than the others. There are gazillions of molecules in continuous motion with no energy input from outside the column. At any time that on average a group of molecules is slight hotter and lighter than a neighbouring group, they separate with the hotter ones rising slightly because of bouyancy. This is gravitational separation that is not caused by the density of the molecule, but by the well known convection principle applied at the molecular level. Will conduction overwhelm this? I am raising that question.
Left alone, there are two forces opposing each other: the tendency of hot gases to rise and cool gases to fall, opposed by conduction that tends to average the temperature in the system.
If on average the temperature of a gas is some fixed value, we know that is an average. If molecules of gases and even water behaved like the average, water would not evaporate from a pot at 80 Deg C.
The isolated, undisturbed column would tend to separate the more from the less energetic.
Also, it is known that as the gas pressure tends to zero, conduction reduces faster than the tendency of hotter molecules to rise. This creates a bias in favour of thermal segregation, assisted by gravity.
At some point either in the entire column, or near the top, it will be hotter above and cooler below and this condition will be permanent on condition that the bouyancy exceeds the thermal conduction at that pressure (and gas characteristics).
A silver wire conducting heat from the top to a point where it is cooler will indeed see heat flowing continuously (and slowly). That is not perpetual motion any more than the vibrating and moving gas molecule is perpetual motion (as we normally mean it).
For heavens sake, people, do not interpret this heat flow as being able to ‘do work’ unless the system is cooled as a whole. There is no free lunch!
The movement of heat through the silver wire is not perpetual motion and thus ‘ruled impossible’. Yes the heat will flow continuously, as fast as the hotter molecules can rise in the gravitational field.
Heat transfers from one molecule to another continuously and we do not call that transfer of heat ‘perpetual motion’ capable of being tapped for ‘doing work without an input of energy’. It is just a characteristic of gases. Energy flows all the time in stable conditions we view (on average) as unchanging.
As far as I understand adibatic cooling, it will not prevent the more energetic molecules from rising. If it does for some reason I can’t see, then a different temperature profile will prevail (possibly a different one foreach unique gas). Save in special cases, not all of the column can be isothermal.
The whole point is that if you could achieve the totally impossible conditions that Dr Brown proposes for his thought experiment, you probably would have a perpetual motion machine. After all to get the conditions proposed would take magic in the first place.
It is an imaginary concept, so is Alice in Wonderland.
The totally impossible conditions like the adiabatic planet discussed in EEJ. Have you even read the paper that this whole discussion refers to?
Besides, these aren’t “totally impossible conditions” at all, not for discussing whether or not an adiabatic lapse rate is a stable equilibrium. The point isn’t that I’ve designed a perpetual motion machine — the point is that a stable thermal equilibrium of an isolated ideal gas with a lapse rate violates the second law of thermodynamics. The proof, my friend, is by contradiction — if one postulates that an isolated ideal gas is in a stable equilibrium with a lapse rate, I’ve shown that it enables a perpetual motion machine to be built. That is a sufficient thermodynamic proof that the postulate is untrue, as it leads to an impossible conclusion.
I did it this way because it avoids arguing about the details of straightforward (but far more difficult) textbook calculations that directly show that the equilibrium is the isothermal state I describe above, or the much more difficult calculation in stat mech that directly shows that the equilibrium is the isothermal state that I describe above. I’ll probably eventually put the detailed balance demonstration up that the equilibrium is the isothermal state that I describe above.
This is entirely relevant to the laboratory. After all, if you take an empty thermos bottle and set it on a desk, it either has a stable adiabatic lapse rate (after a reasonably long time) or it is isothermal equilibrium precisely like I describe above. The difference would be difficult to measure, but the implications are profound. One of the first things almost any intro book on stat mech or thermodynamics does is demonstrate that thermal equilibrium is isothermal — the zeroth law of thermodynamics. If I stick a thermometer in at the top of static, isolated air column, and it reads some temperature, and I stick it in somewhere else and it reads another temperature, the zeroth law clearly states that the two locations (with different temperatures) are not in thermal equilibrium. It clearly states that connecting them with any sort of conducting pathway will cause heat to flow — it is really pretty trivial to look at the distribution of microstates and show that equilibrium will have the same temperature. The gas itself is always such a conducting pathway.
Asserting that a thermal equilibrium exists in some straightforward, isolated, thermally connected system that has sat around for many thermal relaxation times that has a macroscopic distribution of local temperatures isn’t trivial. It is a complete and utter disaster for all of thermodynamics. The second law is only the first consequence.
Which one is more likely: All basic thermodynamics and stat mech textbooks are wrong, including the ones that make showing that there is no lapse rate a homework problem or that do it in the actual text, or some people who have a really hard time understanding what a degree of freedom is or how to do an integral or mess with logarithmic expansions have made a mistake, the biggest of which is assuming that the DALR worked out in climate systems is stable in the absence of a driving thermal gradient and that air is locally truly “adiabatic”, instead of just having a thermal conductivity that is slower than convection?
Anyone who can’t understand this simple presentation is going to have enormous difficulties with the more complex ones. Sorry about that, but that’s the way it goes.
Sorry about the accidental italics inversion too. Truly wish for edit and preview, I do.
rgb
Robert Brown says 1/25 at 12:09am:
“Turn to page 36. Read section 2.17. Work through it carefully…”
Thank you Robert, now you are engaging in calm scientific discourse. This is interesting progress.
I have worked thru Caballero sec. 2.17 page 36 very s-l-o-w-l-y & carefully. I return.
I note that in section 2.17 to develop the temperature field eqn., Caballero refers us to Fig. 2.3 for the gas in a pipe where it is assumed to quote Caballero: “…consider a pipe of cross-sectional area A containing an ideal gas with an isotropic velocity distribution (Figure 2.3).”
Isotropic velocity! So there is NO gravity field used to develop the temperature field in Caballero 2.17. There is no g in temperature field equations 2.74 or 2.75 by inspection. They are pretty obviously not dependent on the g field in z direction.
Caballero in 2.17 writes for no gravity & I quote: “Thus, heat flows down the temperature gradient (from hot to cold) and ceases to flow when temperature is uniform, exactly as required by the Second Law. A more precise calculation using the full apparatus of kinetic theory gives the same qualitative result.”
This proof you have referred me to is for the isotropic velocity/temperature field ideal gas NOT in gravity field. Yes, I grok this previously & agree w/o gravity: the temperature field will be isothermic from 1st law b/c the velocity hence KE from top to bottom does not vary – no g temperature field is indeed uniform as this isothermal derivation shows.
Caballero here in 2.17 is NOT talking about hydrostatic equilibrium temperature with dp/dz non-zero in a gravity field where the velocity and KE of the molecules vary.
In fact, for gravity field acting, Caballero agrees the temperature field is non-isothermal as the mean velocities vary from top to bottom of the air column in sec. 2.3 where he does add the gravity field: “…this time we’ll add the effect of gravity….the effect is quite interesting:… Mean velocities will be greater near the bottom of the box than near, the top…”
Read that slowly again, the temperature field in the presence of gravity Caballero shows it is non-isothermal in the up/down direction. You cannot refute a non-isothermal science paper based on sending me to isothermal examples.
Robert continues:
“Then be sure to do exercise 2.17. I quote: Exercise 2.17: Extend the argument above to show that (2.75) also applies to a vertical column of air in hydrostatic equilibrium.”
Eqn. 2.75 just shows the “net rightward flux” where even in hydrostatic equilibrium, dp/dx =0 which is what it takes to derive 2.75 in the isothermal case. This is trivial for hydrostatic case, since we are really interested in temperature field z variance with non-zero dp/dz.
I could agree air column temperature is isothermal horizontally even in the presence of gravity.
Robert Brown has not yet shown how temperature could possibly be isothermal in the air column z direction in the presence of gravity to refute any science paper esp. when Caballero relying on “Bohren and Albrecht’s excellent Atmospheric Thermodynamics” tells us above in sec. 2.3 the z temperature field in the presence of gravity is non-isothermal.
Robert Brown continues:
“Goodness, could Caballero be saying that thermal equilibrium is isothermal, regardless of whether you move up or down in a static air column? Even in Climate Science? Do you think? Is he asking you to (gasp) actually prove it? Well heck, it ought to keep you out of trouble for a while. Give it a shot. In the meantime, meditate upon that “exactly as required by the Second Law” bit. It’s important!”
Yes, Caballero in velocity isotropic pressure sec. 2.17 is saying thermal equilibrium is isothermal regardless whether I move up or down in a static air column with no gravity field. Yes, I think that’s obvious even in climate science; I gave it my shot. It did indeed keep me out of trouble for awhile and I did meditate some more on the 2nd law, it is really pretty interesting.
However, Robert Brown still has to find a refuting ref. to cite in order to support Robert Brown’s refuting theory that temperature is isothermal in the gas column of interest in the presence of gravity where M-B cannot be invoked due to M-B applying only to the special case of no gravity.
Otherwise proper application of 0th, 1st,2nd & Caballero does refutes top post. Cabellero teaches: an adiabatically isolated column of gas in a gravitational field CAN have a thermal gradient maintained by gravity.
Robert Brown’s thermal law inconsistent conclusion in top post is hereby still refuted (my cap.s): “an adiabatically isolated column of gas in a gravitational field CANNOT have a thermal gradient maintained by gravity.”
Joules Verne says:
January 25, 2012 at 9:49 am
Why do you not just think about this in as simple terms as possible.
Forget about any mechanisms that causes it, what are you saying is the outcome?
You are saying that Gravity can cause an everlasting temperature gradient in a column of gas in a closed system with no possible energy input.
Right now think about just one inevitable consequence. Convection.
Convection must occur because we have hotter gases at the bottom and there will be constant particle movement up and down the gravity well as particles heat up and cool down and are affected by the gravity well.
Ok what is needed to move a particle up a gravity well………work! Or explain how you move a particle up a gravity well without performing work.
What happens when work takes place?
Well the 2nd Law of Thermodynamics says that entropy must increase and that entropy can never decrease in a closed system without the creation of energy.
So how do you maintain an everlasting temperature gradiant in this column of gas?
Well the 2nd Law says you can’t. Entropy increase will eventually lead to the ‘heat death’ of the system as temperatures equalise accoss it.
To do it, you have to create energy and the Laws of Thermodynamics says you can’t do this either.
So tell me how you maintain an everlasting temperature gradient without breaching the Laws?
Alan
Myrrh said @ur momisugly January 25, 2012 at 4:19 am
Brownian motion has nothing whatsoever to do with electrons; it’s the motion of small particles of matter (originally pollen grains) being jostled by the random movement of molecules in a fluid. Heat is one form of energy among many: chemical, kinetic etc. Photons are packets of energy being exchanged between atoms. They are not heat so they don’t care about the temperature of those atoms. Heat flows from hot to cold only. Physics is divided into Classical and Quantum descriptions of the world. They describe the same world in different ways. From your questions, and there’s nothing wrong with your questions, it’s clear that these two views are conflated in your mind. You definitely need to learn some basic physics. Mine came from Resnick, Halliday & Walker in 1969. While the papers being discussed are recent, the physics isn’t.
An ad hominem BTW is when you claim that what someone claims is false by virtue of who they are. Insulting someone is not an ad hominem. The first is a logical fallacy, the second is being rude and not a logical fallacy.
A good insulator is one that conducts heat slowly. A bad insulator is one that conducts heat quickly. All matter conducts heat, but the rate at which it conducts depends on the state (solid/liquid/gas) and chemical composition. Air conducts heat very slowly, but perforce will reach an equilibrium temperature very slowly in the absence of convection. In any real atmosphere, convection will predominate over conduction.
Unfortunately Myrrh you have chosen the wrong classroom in which to learn the basics. There’s not just basic thermodynamics and quantum physics, there’s basic boundary layer climatology being discussed here. A lot of the discussion is frankly a display of ignorance. There’s nothing at all wrong about ignorance per se, but wilful ignorance is a different matter. This muddies the water and makes learning extraordinarily difficult for those who have yet to grasp the fundamentals. This saddens me; I experienced this in a cosmology class I took; our lecturer/tutor had a very difficult time keeping to the arguments he wanted us to focus on because of students who lacked the underpinning knowledge required to understand those arguments. It was very frustrating.
Bottom line is: get that basic physics under your belt. If you can find a friend who wants to do the same, you will make much more rapid progress. To teach is to learn twice.
And please forgive Willis. Unfortunately, his mother neglected to put a warning notice on him: Handle with Care. He’s been a reforming cowboy ever since I first came across him nearly a decade ago and I have learnt heaps from him.
Live long and prosper Myrrh. Your questions are not stupid. The answers you have received are not stupid, either. Confusing you, yes, but not stupid.
thepompousgit says
” Live long and prosper Myrrh. Your questions are not stupid. The answers you have received are not stupid, either. Confusing you, yes, but not stupid.”
Myrrh states up front that he has no formal science training.
Sometimes this shows through in his questions.
However this sometimes has its advantages as he is not soaked in a particular paradigm.
Quite often he is the boy who spots the ‘Emperor has no clothes’.
I think he made a valuable contribution when he noticed that the NASA educational pages were being reinterpreted to blur the differences between light and infra red radiation.
Some would think that this was done to make IPCC science more believable.
Ken Finney says:
January 25, 2012 at 10:03 am
Thanks for the links.
I think you know what I was getting at.
kdk33 said
Sound is the alternating compression & decompression of a fluid. A practical experiment for you:
Partially fill a bathtub with water. Take a portable radio, or CD player into the bathroom and turn on. Your choice of music. Lie in the bath and submerge your head in the water. If you still believe in the incompressibility of water, please keep your head there.
gbaikie says:
January 25, 2012 at 3:15 am
That is not correct. The lapse rate is almost always 6.5 K/km. High humidity makes the tropopause higher, but does not change the lapse rate. The one exception is when clouds form and the lapse rate is variable between 4 and 6.5 K/km.
Actually, it is not – it is about cooling the atmosphere. A fraction of that heat returns to the surface (back radiation) and makes it a bit warmer. To be perfectly clear, because some of the heat comes from conduction/convection, greenhouse gases emit more energy than they trap.
thepompousgit says:
January 25, 2012 at 10:55 am
Sir your responce to Myrrh was a very nice display of kindness oft lacking by some. You are to be commended. As we used to day in the Navy, BZ (bravo zulu).
wayne says:
January 25, 2012 at 4:05 am
The atmosphere becomes isothermal when the cooling is removed from the top. The amount of energy arriving at the bottom really does not matter. It merely sets the final temperature, not the lapse rate.
A physicist says:
January 25, 2012 at 10:23 am “For more theoretical and experimental details than most folks want to know, see @article{Kemp:2009lr, Author = {R. Scott Kemp}, Journal = {Science and Global Security}, Number = {1}, Pages = {1–19}, Title = {Gas Centrifuge Theory and Development: a Review of US Programs}, Volume = {17}, Year = {2009}} and references therein (a Google search will find it).”
I think you need to re-read the Article.
It talks about “assuming a linear-thermal-gradient profiles” and “reate a dynamic equilibrium”, not thermal equilibrium.
The word “Isothermal” does not appear anywhere in the available text whatsoever.
My admiration to Professor Brown. It was an elegant demonstration and a tenacious defence.
You asked about convection on a world with no GHGs
I think it would work a bit like the convection pattern of the thermohaline circulation, inverted. The oceans are warmed at the equator and cooled at the poles. The cold water at the poles sinks, flows equatorwards across the ocean deeps. Water at the equator is warmed, rises and spreads out polewards. Because the deep oceans receive no heat input, at least not on the scale of the circulation time, they are fairly uniformly at the temperature of the descending polar waters, even below the equator. There is in fact a lapse rate in the deep oceans of about 0.1 C/km.
With GHG-free atmosphere, you have to swap warm for cold and up for down, and equator for pole. Thus, air is warmed at the equator, rises, and spreads polewards. Its potential temperature (adjusted for lapse rate) remains constant then, and most of the atmosphere is equatorially hot, even at the poles. The thin layer in contact with the ground there cools, and flows back to the equator over the surface. There would be a lapse rate, as there is in the oceans, and I think it could extend high up, as the ocean circulation goes deep. While you might think that polar waters need only sink below the thermocline and could then flow back equatorwards only a few hundred metres down, analogous to the low tropopause, it doesn’t work that way.
Pressure is exerted omnidirectionally, and unless channelled/diverted by some external force, an upward force on air at the equator will push all the air above upwards until forced sideways by the top of the atmosphere. The upwards push can’t be changed entirely to a sideways push 100 m up unless there is somethere there to actively resist it. And since all the atmosphere far above the surface is at the same potential temperature, and neutrally buoyant, I don’t see how or why this could happen.
The idea that you can get convection cycles driven by temperature differences from the top sounds odd, but I find it helps to think of it as cooling of the fluid over one area giving the fluid negative buoyancy, and driving the fluid down – this being analogous to heating from the bottom causing positive buoyancy and a drive up. It helps as well to remember convection is about the whole cycle – what goes up must come down – not just hot air rising.
(There are complications, of course. On a rotating planet, air converging on the poles would spiral into a cyclostrophic vortex. You’d get multiple Hadley cells and jet streams and so on. I’m not claiming it would really be that simple.)
It’s a controversial idea – I know several people have objected vociferously when I’ve mentioned it – but that doesn’t mean it’s therefore incorrect. If you can see anything obviously wrong with it I’d be grateful.
Bryan said @ur momisugly January 25, 2012 at 11:15 am
Yes, I noticed. That’s why I went to the trouble of answering his questions at length. Robert’s been doing most of the heavy lifting around these parts and I thought I’d lend a hand.
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Just a thought, for you all.
There are (I think) two main ways of reducing heat-loss from a planet (resulting in warmer surface temperatures):
a. LW absorption and emission (greenhouse gasses and effect).
b. Conduction-convection (atmospheric effects).
Let me explain what I mean. We have three types of planet:
a. Airless planet.
Cooling via LW, and no ‘insulator’ to reduce LW cooling. (An insulator being any method of preventing cooling.)
b. Atmospheric planet, with no greenhouse gasses.
Cooling via LW.
Reduced cooling via conduction-convection to the atmosphere. Initially, this process simply warms the atmosphere, until the atmosphere is so warm it absorbs little more surface temperature. Now this warm atmosphere cannot cool itself via LW emission, but it can cool itself via conduction to areas of the planet in shadow. Thus the atmosphere is ‘warming’ (or reducing cooling) areas of the planet in shadow. This will surely make the average surface temperature of the planet higher, than if there was no atmosphere (because the cold shadow areas are now warmer, resulting in a higher average temperatures.)
As an aside, this means that the effective surface LW cooling area of a hilly planet like the Earth is much greater than a simple sphere would lead us to believe. Up to 20% greater surface area. I presume this greatly effects the w/m2 calculations that have been tossed around. (The incomming SW radiation only sees the area of a smooth sphere, but the outgoing LW radiation sees a much higher surface area than a normal sphere.)
c. Planet with greenhouse gasses.
Cooling via LW
Reduced cooling via conduction-convection (as explained above).
Reduced cooling via gasseous absorption and reemission (greenhouse gasses). In a similar fashion to conduction (above), the re-radiation of LW from H2O and CO2 towards the surface delays and reduces the coolling of the surface, resulting in higher average temperatures than if there were no such gasses in the atmosphere.
Thus (in my opinion) both the greenhouse gasses and the atmosphere itself act in partnership to reduce the cooling of the surface (erroniously called warming, but you know what I mean).
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OK,
For all the smarties that want to point out that water is actually compresible. Yes you are right.
But relative to a gas? Not so much. A lapse rate in the ocean? Sure maybe a tad. But relative to the atmosphere? Not so much.
Happy now?
Robert Brown,
I can’t help with edit, but you can get preview. CA Assistant works just fine here. Go to: http://climateaudit.org/ca-assistant/ and follow the instructions. It does require that you use Firefox as your browser. I’ve never found a place where the subscript/superscript HTML quicktags work, though.
Robert Brown says:
January 25, 2012 at 5:33 am
Actually, it is water vapor (not CO2) that becomes optically thin at the tropopause. It is about 200 ppm below the tropopause and 5 ppm above. In the tropics, where there is more water vapor, the tropopause is higher.
In the stratosphere, CO2 is the main greenhouse gas, more than 100 times more abundant than water and more than 1,000 times more abundant than ozone. I have seen the TOA spectra you have referred to, I still can’t explain the CO2 emission that appears to come from the tropopause, but I am certain that that is not the correct explanation. It is possible that the feature originates from (and perhaps causes) the thermal anomaly at 32 km, in the mid-stratosphere. One problem is that the resolution of space borne instruments is not quite good enough to know how to interpret that feature.
To be very clear, at the tropopause, water vapor and CO2 emit the same amount of energy. However, CO2 is emitting energy from the stratosphere toward the tropopause and water vapor is emitting the same amount of energy toward space. At that level of the atmosphere, the CO2 and water spectra no longer overlap by much.