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.
This is all stupid. You don’t need gravity or miles tall cylinders. Fill a cylinder with gas to a bzillion PSI. Put it on an atmospherically evacuated centrifuge. Spin it up to 100G. A thousand G – doesn’t matter. Measure the temperature along the length of the cylinder.
No matter how fast you spin the centrifuge, no matter how may G’s you impress, so long as the G force is constant the gas temperature will be the same along the length of the centrifuge. It is in equilibrium. It is happy gas. Is there more energy/CF at the outer extremity of the cylinder? Yes – the gas is more dense there. No surprise. This is not new energy.
The dry adiabatic lapse rate determines how high thermals will go – usually, only a few kilometers. The actual lapse rate is normally significantly different from the DALR.
As this article argues, the lapse rate without IR emitters would be zero. It is the greenhouse gases that move the actual lapse rate (ELR) from zero to -6.5 K/km. The DALR is -9.8 K/km. To claim that anything “maintains” the DALR simply means that you have not looked at the data.
Oops, sorry, answered the previous one before I read yours. As you can see, I agree. I was speaking sloppily about one factor of a trinity consisting of differential heating (greenhouse effect), convection and other mechanisms for heat transfer, and gravity that together make a self consistent troposphere that tops out roughly where the greenhouse gases become transparent and greenhouse cooling of the upper troposphere goes away.
But I’m sure you understand this better than I do. As I’ve pointed out myself, though, the DALR does go away as soon as you eliminate solar driving, e.g. the poles in the winter night. You can easily end up with the upper troposphere as warm as or warmer than the ground, easy proof that it isn’t just “gravity”.
rgb
I’m curious, what if the gravity isn’t constant, but is fluctuating?
Then it constantly does work on the system. Probably not a lot of work, but some. Think of a perfectly insulated jar full of air. If you shake it back and forth violently, you do a bit of work on the gas in the system every time, and some of that work gets transformed into heat. The gas in the container gradually warms, just as it would if it were stirred. Shaking it is absolutely indistinguishable (to the gas) to having a wildly variable gravitational acceleration (equivalence principle).
This actually happens. Tidal pseudoforces cause small fluctuations in “gravity” all over the Earth, every day. The Earth and the oceans actually expand and contract. Some of the energy associated with lifting and dropping turns into heat. At the same time, the Earth’s rotation slows just a bit. The moon picks up the angular momentum and moves into a higher orbit. The moon’s orbit is lifting around 3cm a year, IIRC, and has been for the last 3 or 4 billion years. That sounds like a lot, but 3 x 10^9 x 3 = 10^10 cm, where there are 10^5 cm in a km, so this is only around 10^5 km. The moon was nearly half of its current distance from the Earth around the time it was formed. Interestingly, it is only in a fairly narrow window of time (geologically speaking) that the moon will be just the right distance away for the kinds of eclipses that we have, close to perfect equality of the angle subtended by the sun and the moon as seen from Earth.
HTH.
rgb
Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?
Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?
I’m not the best person to answer either one, but my short answer is that without GH gases there would be no or a vastly reduced DALR, one maintained by a very different convective mechanism (such as equator-polar circulation). The atmosphere might even entirely invert. But this is only a slightly better educated guess than yours might be.
Similarly, I have little doubt that an atmosphere with no GH gases would have a very different overall equilibrium temperature, and probably a different distribution. It would certainly depend somewhat on pressure, because atmospheric density depends on pressure, and the actual heat capacity of the atmosphere where it picks up heat from the ground would therefore depend on pressure. I’m still thinking about how it might vary — I’d like to/need to run some actual models (necessarily based on assumptions) to get a feel for it. One really can’t answer every complex question off of the top of one’s head (although I certainly try, unafraid of and even embracing error as an essential step towards learning:-).
rgb
Mr. Brown:
Thank you for taking the time to post and answer questions.
While the assertion of Hans Jelbring is an interesting thought experiment, it does not pass the laws of physics.
Walter said @ur momisugly January 24, 2012 at 10:55 pm
Hope he doesn’t; he’s a helluva better physics teacher than I had back in 1969.
That’s almost certainly true.
Not so sure about that one; I know people who managed to kick heroin and alcohol addiction. Tough, but obviously not impossible.
I think you might mean golf rather than gold. Ayn Rand wrote books about the “doers” going AWOL. They made a big impression on the Git in 1969.
Nothing wrong with being a grumpy old fart. Gits actually enjoy it 🙂
Watch out for the giant invisible mutant space goat. You’re probably safe though; apparently it prefers eating documentary film-makers, hairdressers, telephone sanitisers etc etc.
Robert will be way better off moving to grokness equilibrium understanding the non-isothermal gas column upon reading Caballero section 2.3. Then return.
Or, you could explain why the heat flow in figure 2 isn’t established if the temperature at the bottom is higher than the temperature at the top. It saves so much time when you just use the laws of thermodynamics instead of attempting a stat mech computation in words.
In the meantime, lift a jar of air up and see how much it cools.
rgb
I thought that in the adiabatic case (in order to mirror the atmosphere) there is nil radiative or conductive heat flow.That is the standard atmosphere model where conduction is very small compared with other energy transfers. Also the column is deemed to be devoid of GH gases
Obviously we are talking about different thought experiments
If you want to have conductive gas why dont you suppose a perfectly conducting cylinder on the inside and perfectly insulating on the outside instead. This gets ride of hundred of words about about molecules interacting etc
Then we get the isothermal case
You did not comment on the fact that in the adiabatc case it needs a negligable amount of energy to raise a parcel of air from botton to top but if your silver wire delivers heat from the bottom layer to the top layer the outside work must be done to restore DALR. Of course the gas at the bottom does not know it is at the bottom of a tall column but it knows that there is warmer gas above and so it cant move upward
This is because the gas cant move upward against an inversion without an outside driver
The heat transfer cannot continue without this input.
I would like an answer to what happens to the initial small hotter layer at the top — dont quote conduction as we have none in the adiabatic case
Your transfer of heat between two horizontal jars is nothing to do with this case and requires a gas conduction which is assumed to be zero in the adiabatic column
PS What do you think insulates your house. I could bet 500:1 it is not a vacuum — even your double glazing is gas filled
The atoms of the wire will lose velocity as they rise in the gravitational field just as those in the gas, thus there is less energy available transferred in interactions this will produce an gradient in the kinetic energy of atoms that make up the wire resulting in a temerature gradient due to gravity. That the distance covered between interactions is much smaller in the solid than it would be in the gas and that there are other interactions in a solid does not change this fact.
Good try! I was waiting for somebody to try this one. However, imagine a vertical stack of pool balls. Hit the bottom one up. What happens to the top one? Does it depend on the size of the stack?
One of the many errors you and so many others make is that gravity does no net work in the upward conduction of heat. Really.
rgb
Here is where I was going wrong. I mentioned that gas near the bottom of the column has a smaller amount of potential energy than gas the top. While this is undoubtedly true, that potential energy only comes into play if the gas is being mixed or is otherwise dynamic, that is, if such energy is being released as a result of changing the height of some of the gas parcels. But of course the equilibrium state does not have any such mass motions, and so no work is being done on the fluid. As a result, the internal energy of the gas is the same everywhere, and thus the gas has the same temperature everywhere.
So absolutely perfectly correct, I award you the A+ for the day. In isothermal equilibrium, the system is in perfect force balance, there is no net dynamical transport of mass up or down, no net change whatsoever of gravitational potential energy — but heat conduction still functions to maintain equal temperature and restore equilibrium after a perturbation.
So simple.
Now at nearly 3 am and with a busy day tomorrow (which starts at 5 am) I think I’ll quit, at least for the day, er, night, er, whatever. I really tried to answer each and every comment, but after some 20 or 30K words of text, some people are having a really hard time grasping this simple idea, others are extending the error to the solid wire, still others are doubting the second law of thermodynamics instead of a static lapse (!), and a few are just crazy.
The only kinds of potentials that contribute in statistical mechanics are the ones associated with state changes. The oscillator mode for a diatomic gas, for example, doesn’t get two degrees of freedom, only one. The exact same thing is true for gravity, and for the forgotten forces between all of those ideal gas molecules, and for the walls. In equilibrium, the average potential energy of each and every molecule in the systems is constant. That’s all that matters. They are constantly borrowing and returning energy to gravity, but their average gravitational energy is constant, and it does not count as an additional degree of molecular freedom unless it can change to take up additional heat. Does anyone recall adding “gravity” to the number of degrees of molecular freedom in C_v or C_p? I don’t think so…
rgb
Robert Brown needs to read Caballero sec. 2.3 that proves the zeroth is not violated & the 2nd is not violated for “adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field” which Caballero proves is non-isothermal & there will be a thermal lapse rate.
OK, Trick, I’ll try one last time. You like Caballero? Well, so do I. Turn to page 36. Read section 2.17. Work through it carefully — this principle is called “detailed balance”. 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.
Don’t forget that last little quote at the bottom of 2.17 right before the bloody textbook exercise:
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. (Emphasis my own.)
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!
rgb
Correct.
All real heat engines increase entropy. Engines do work. Figure 2 doesn’t.
It is left as a not-terribly difficult exercise to the reader to work out how, if the heat flow in figure 2 is stable, it can be transformed into a perpetual motion machine that amazingly, does not increase entropy as it blithely converts heat into work.
The violation of the second law is in the assertion that a non-isothermal state is at stable thermal equilibrium. That means that any heat engine that runs between the reservoirs can turn some of the temperature difference into work, increasing the entropy of those reservoirs, but gravity sorts it all out again and makes the energy available for re-use. EEJ is particularly pernicious in this regard, as it proposes a static DALR, one that is independent of the actual temperature of the gas. So if one uses the heat engine to do external work, the gas in the cylinder will indeed drop to zero in temperature as all of its internal energy drops to the bottom to maintain a constant temperature difference right up to where the temperature of the ideal gas at the top reaches zero.
If that doesn’t fail both the heat engine and refrigerator statements, nothing does.
Besides, we know that heat flow only happens until the system becomes isothermal. As this one would, with or without a silver wire or heat engine, because a gas with a DALR is not in equilibrium and ideal gas is still a thermal conductor of heat.
rgb
I’m getting sorely dismayed by these threads so let’s try a different tack. For those who understand plain English rather better than accepted basic physics, why do you think Rankine coined the phrase Potential Energy in the first place? Do you imagine he just used fancy words for the sake of it? Here, read about the guy and let’s have no more nonsense about engineers versus physicists for starters.
http://en.wikipedia.org/wiki/William_Rankine
Forget decent basic physics text books; they’re obviously never going to help you. Look the word up in a dictionary instead.
Potential:
(noun): Capacity for development
(adjective): Possible but as yet not actual
(synonyms): Impending, Would-be.
Why do you think he used that word when he could have used any of the dozen or so more common ones that writers of dumbed-down textbooks often substitute? It’s because he was being precise – like any good engineer or physicist.
It means “not manifest until realized by some phenomenon doing something”. And it’s always realized in some actual form – kinetic, in the case of gravity. It does not, for example, mean ‘stored’ energy. Any text book that says that should be incinerated on the spot IMHO, it leads to exactly the sort of immovable confusion displayed in these threads.
Aside from kinetic energy there can be no other joules present at equilibrium, only the potential with altitude to have more when gravity does its stuff by causing something to move and acquire actual energy (thereby becoming capable of ‘doing work’).
As for conservation of energy, look at it this way: PE is a measure of the energy that will appear in future when gravity does its stuff and actually moves something. It isn’t actual energy present at rest. If that sounds like magic to you, it’s why we can’t explain gravity. PE is just bean counters’ double-entry book-keeping, necessary only because we can’t.
You cannot therefore count joules of PE and trade them off against KE at equilibrium. It makes no logical sense. No auditor will sign off accounts done on that basis, not even in Brussels!
If you’re going to maintain this concept is wrong you’re flying in the face of not only Rankine but Maxwell, Carnot, Clausius, Thompson, Hugoniot and all the rest even with the benefit of all subsequent experience they did not have (space, etc.).
You’re saying that potential energy is somehow actual energy in gaseous matter and you’ve therefore effectively explained gravity. In that case, how does gravity act on solids and liquids in a vacuum? Why do they still behave the same way? What then does compressibility have to do with PE being actual energy?
Next up you’ll be somehow extending your new found principle to plasmas to explain the coronal heating problem on the Sun or claiming gravity must be ever so gradually being used up so you’ve re-written the expansion of the universe turning the whole of contemporary physics on its head.
Sorry, but no (not for now anyway, show me some extraordinary proof first like producing a perpetual motion machine that works and explaining how your gravity works with solids and liquids). Lunacy seems an apt description.
Robert Brown wrote:
I should point out that this is my real interest at the moment — the philosophy of knowledge and the basis of science — and I am happy to cite you chapter and verse.
It’s a subject I have an interest in as well. Perhaps we can discuss it over a beer some time, should you find yourself so inclined.
“Robert Brown says:
January 24, 2012 at 8:31 pm
Oh, sweet Jesus.
Tell you what. The next time you cook, you be sure to put the food on the bottom of your pan and heat the top.”
You have misunderstood the point I was making. I had already clarified at
son of mulder says:
January 24, 2012 at 2:41 pm.
Your answer does not address the physical paradox implicit in my first post and explicit in my second.
Anyone disputing Jelbrings hypothesis needs to prove that gravity does not provide a minimum heat/energy level in matter when that matter is being held back from falling further through the gravity field by the electro-magnetic and strong forces of the atoms in the rocks at the surface of the planet. The matter is still being pulled through the gravity field, it is just being stopped by the other forces in the atoms of the rocks/liquid.
OMG. Seriously, dude. First of all, none of this has anything to do with Jelbring’s hypothesis, which basically consists of the following:
1) There exists this thing called the DALR, that I read about somewhere.
2) It exists in isolated gases ideal gases in stable thermal equilibrium in a gravitational field.
3) Therefore, it is responsible for why the surface is warmer than the top of the atmosphere.
1) is true without question, although it isn’t simple or uniform.
2) is false — that’s the point of my proof. The rest of your list of absurd assertions is utterly ignorable. We actually understand gravitational heating in brown dwarfs and stars and so on. We understand why falling asteroids release a lot of heat. We understand why you can stand on the surface of the planet at rest until hell freezes over and gravity ain’t gonna give you no heat! Take a physics class or two or get out of the game.
3) Given that 2) is false, 3) is not a valid conclusion. In fact, it is sort of half-true. The Greenhouse Effect is responsible for the DALR, which is a convective manifestation of differential surface warming and upper troposphere cooling. Although probably more complicated than “just” that.
But I don’t care about 1) or 3) — I’m just concerned with 2) and Jelbring says nothing about bizarre electro-magnetico-gluonic-gravitonic energy transfers that are responsible for breaking the second law of thermodynamics, any more than he talks about the invisible Maxwell Demon Fairies that sort out the hotter molecules in the gas and send them all down to the bottom.
It doesn’t matter how a lapse rate happens. No lapse rate that isn’t maintained by external input of energy or work is thermodynamically stable — if it were it would violate the second law.
rgb
Re,
Ed Caryl says:
January 24, 2012 at 7:36 am. I agree with you Ed, also living at some altitude. I do not believe that the surface at altitude receives less radiation than at sea level, in fact it should receive more because it passes through less atmosphere.
Which is why the following quote from Wikipedia seems to make no sense, if the conductive source is at say 3000 metres and is heated from the same source, the Sun, then the lapse rate should start from there at the same temperature as that at sea level.
“In the lower regions of the atmosphere (up to altitudes of approximately 40,000 feet [12,000 m]), temperature decreases with altitude at a fairly uniform rate. Because the atmosphere is warmed by conduction from Earth’s surface, this lapse or reduction in temperature (is?) normal with increasing distance from the conductive source.” from Wikipedia, ”Lapse Rate”
No, this is not proven since it is in direct conflict with what Caballero in the link in the Perpetuum Mobile thread proves in Sec. 2-3 – the real world gas column is non-isothermal w/gravity and the device in figure 2 will not run forever with a real non-perfect insulator.
Sure, Trick. Just like a 100% efficient heat engine with friction isn’t a violation of the second law, because look, it isn’t really 100% efficient.
As I said, put the damn wire into the container and give it up. Where’s the heat going to go now? It still flows from the bottom to the top, and then flows back down. If it flows (slowly) out the sides of the wire, who cares? Gravity still sends all of the faster molecules down and all of the slower molecules up, to maintain the lapse, right? So heat will flow up the wire forever. Or a dippy-duck will dip forever. Personally, I like the dippy duck. I should have made that my example.
rgb
Not so fast DP… sounds tempting, but surely the G force will NOT be constant throughout the cylinder. It will increase with the radius. Now there… any of the smart people here want to start some new convoluted thought experiments and circular reasoning based on that? C’mon.. we have only had 2 weeks (well it feels like 10) of that here.. /sarc
Just cannot believe that the simple issue of energy balance vs temperature balance can cause so much angst, so many futile thought experiments and so much isoteric maths and mis-applied physics to see the light. Not to mention the emergence to prominance of so many clearly educated beyond their intelligence. Luckily I consider myself educated well below my intelligence, so I can safely say that Jelbring and what has followed on that makes elegant and intuitive sense to me, unlike the other c**p that I have been diligently following to exhaustion here. Even for my 40 year old physics it hits the sweet spot, perhaps because I only remember the principles, not the maths. So much easier to see the wood in spite of the trees. And gosh, are these recent threads crowded with trees!
Rant over… Sorry, but I felt driven to it.
Off in anticipation to see the the second paper at Tallblokes’ if its there….
Gabriel van den Bergh (So you know who I am… I’ll be waiting…)
I’m not sure if I did this right, as it’s not normally the type of electrical calculations I do, but:
The mistake is in doing the computation at all. No (net) electrons move “up the wire”.
rgb
Is this not exactly the basis for astrophysics?. gas collects by gravity, warms up, gets denser, then warms enough to become a star!!!!!!
Sure, but that is not a stable state. The gas heats while it collapses. When it stops collapsing, it stops heating. The Earth and its atmosphere are not collapsing, so the process exists, and is irrelevant to the discussion.
rgb
I am just coming back from the shed having constructed my first Perpetium Mobilae. This is how it works: I have attached a copper wire to the bottom of my adiabatic container and a silver wire to the top. They nearly meat in the middle. The thermal conductivity in these metals is such that the wires are practically of uniform temperature so that the copper end is a warmer then the silver end. I have therefore a thermocouple in the middle producing energy out of nothing since gravity, without doing any work will restore the resulting termperature changes inside the adiabatic container.
Now I’m off to the shed to see how much energy I can produce. I’ll let you know: you’ll read about it in the newspapers.
Hint: sell your oil stocks, that’s so passee!
But I have to say, I can to the realization mostly on my own, and not because of anything anyone said here. Maybe this is the nature of the blogging medium, or maybe my learning style is not conducive to learning from blogs, but many of the responses to my line of thinking were more of the condescending variety [“Open a standard introductory physics textbook. Learn what temperature is. Then return.”] and not of the collegial variety [“If what you say is true, then how does the theory of equipartition hold in the presence of a temperature gradient with no work being done on the gas?”] and this had the effect of turning me off to contributing here again. ‘Tis mostly my loss, I suppose, but I wonder how many others feel the same way?
That was probably me, and my bad. I wasn’t trying to be condescending; I’m just answering several hundred comments, in detail, and I’m feeling a bit rushed. Also I admit my patience gets a bit tried by some of the “rebuttals”. As Willis noted, there are people conflating force with energy with power, LOTS of people who want to include gravity (somehow) in the list of degrees of freedom for a molecule in a gas in spite of the fact that direct measurements of the specific heat show — no gravity contribution (for perfectly understandable reasons). As I also noted elsewhere, you get an A+ for the day because you did go out and educate yourself. Doing a bit of work to learn something new is laudable. More readers and participants should take a lesson.
rgb
Just where is the proof that there is not a large radioactive core at its center, similar to what Earth has, but at 10 to 1000 times its size? Everyone making the claim that gas compression is responsible for Jupiter’s IR signature is making the same mistake Lord Kelvin made in estimating the age of the Earth.
Dunno. I was citing prevailing wisdom, not holy writ. Jupiter is too small for fusion AFAIK, but maybe fission.
rgb
Hey, I hope you mean Francis Weston Sears. I have only superficially followed this discussion, but I feel your pain.
It’s Frank Zappa: “Is that a real poncho or a Sears poncho?”
rgb