Guest Post by Willis Eschenbach
Since at least the days of Da Vinci, people have been fascinated by perpetual motion machines. One such “perpetuum mobile” designed around the time of the civil war is shown below. It wasn’t until the development of the science of thermodynamics that it could be proven that all such mechanisms are impossible. For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.
I bring this up for a curious reason. I was reading the Jelbring hypothesis this afternoon, which claims that greenhouse gases (GHGs) are not the cause of the warming of the earth above the theoretical temperature it would have without an atmosphere. Jelbring’s hypothesis is one of several “gravito-thermal” theories which say the heating of the planet comes from gravity rather than (or in some theories in addition to) the greenhouse effect. His thought experiment is a planet with an atmosphere. The planet is isolated from the universe by an impervious thermally insulating shell that completely surrounds it, and which prevents any energy exchange with the universe outside. Inside the shell, Jelbring says that gravity makes the upper atmosphere colder and the lower atmosphere warmer. Back around 2004, I had a long discussion on the “climateskeptics” mailing list with Hans Jelbring. I said then that his theory was nothing but a perpetual motion machine, but at the time I didn’t understand why his theory was wrong. Now I do.
Dr. Robert Brown has an fascinating post on WUWT called “Earth’s baseline black-body model – a damn hard problem“. On that thread, I had said that I thought that if there was air in a tall container in a gravity field, the temperature of the air would be highest at the bottom, and lowest at the top. I said that I thought it would follow the “dry adiabatic lapse rate”, the rate at which the temperature of dry air drops with altitude in the earth’s atmosphere.
Dr. Brown said no. He said that at equilibrium, a tall container of air in a gravity field would be the same temperature everywhere—in other words, isothermal.
I couldn’t understand why. I asked Dr. Brown the following question:
Thanks, Robert, With great trepidation, I must disagree with you.
Consider a gas in a kilometre-tall sealed container. You say it will have no lapse rate, so suppose (per your assumption) that it starts out at an even temperature top to bottom.
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
I say no. I say after a million collisions the molecules will sort themselves so that the TOTAL energy at the top and bottom of the container will be the same. In other words, it is the action of gravity on the molecules themselves that creates the lapse rate.
Dr. Brown gave an answer that I couldn’t wrap my head around, and he recommended that I study the excellent paper of Caballero for further insight. Caballero discusses the question in Section 2.17. Thanks to Dr. Browns answer plus Caballero, I finally got the answer to my question. I wrote to Dr. Brown on his thread as follows:
Dr. Brown, thank you so much. After following your suggestion and after much beating of my head against Caballero, I finally got it.
At equilibrium, as you stated, the temperature is indeed uniform. I was totally wrong to state it followed the dry adiabatic lapse rate.
I had asked the following question:
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
What I failed to consider is that there are fewer molecules at altitude because the pressure is lower. When the temperature is uniform from top to bottom, the individual molecules at the top have more total energy (KE + PE) than those at the bottom. I said that led to an uneven distribution in the total energy.
But by exactly the same measure, there are fewer molecules at the top than at the bottom. As a result, the isothermal situation does in fact have the energy evenly distributed. More total energy per molecules times fewer molecules at the top exactly equals less energy per molecule times more molecules at the bottom. Very neat.
Finally, before I posted my reply, Dr. Brown had answered a second time and I hadn’t seen it. His answer follows a very different (and interesting) logical argument to arrive at the same answer. He said in part:
Imagine a plane surface in the gas. In a thin slice of the gas right above the surface, the molecules have some temperature. Right below it, they have some other temperature. Let’s imagine the gas to be monoatomic (no loss of generality) and ideal (ditto). In each layer, the gravitational potential energy is constant. Bear in mind that only changes in potential energy are associated with changes in kinetic energy (work energy theorem), and that temperature only describes the average internal kinetic energy in the gas.
Here’s the tricky part. In equilibrium, the density of the upper and lower layers, while not equal, cannot vary. Right? Which means that however many molecules move from the lower slice to the upper slice, exactly the same number of molecules must move from the upper slice to the lower slice. They have to have exactly the same velocity distribution moving in either direction. If the molecules below had a higher temperature, they’d have a different MB [Maxwell-Boltzmann] distribution, with more molecules moving faster. Some of those faster moving molecules would have the right trajectory to rise to the interface (slowing, sure) and carry energy from the lower slice to the upper. The upper slice (lower temperature) has fewer molecules moving faster — the entire MB distribution is shifted to the left a bit. There are therefore fewer molecules that move the other way at the speeds that the molecules from the lower slice deliver (allowing for gravity). This increases the number of fast moving molecules in the upper slice and decreases it in the lower slice until the MB distributions are the same in the two slices and one accomplishes detailed balance across the interface. On average, just as many molecules move up, with exactly the same velocity/kinetic energy profile, as move down, with zero energy transport, zero mass transport, and zero alteration of the MB profiles above and below, only when the two slices have the same temperature. Otherwise heat will flow from the hotter (right-shifted MB distribution) to the colder (left-shifted MB distribution) slice until the temperatures are equal.
It’s an interesting argument. Here’s my elevator speech version.
• Suppose we have an isolated container of air which is warmer at the bottom and cooler at the top. Any random movement of air from above to below a horizontal slice through the container must be matched by an equal amount going the other way.
• On average, that exchange equalizes temperature, moving slightly warmer air up and slightly cooler air down.
• Eventually this gradual exchange must lead to an isothermal condition.
I encourage people to read the rest of his comment.
Now, I see where I went wrong. Following the logic of my question to Dr. Brown, I incorrectly thought the final equilibrium arrangement would be where the average energy per molecule was evenly spread out from top to bottom, with the molecules having the same average total energy everywhere. This leads to warmer temperature at the bottom and colder temperature at elevation. Instead, at thermal equilibrium, the average energy per volume is the same from top to bottom, with every cubic metre having the same total energy. To do that, the gas needs to be isothermal, with the same temperature in every part.
Yesterday, I read the Jelbring hypothesis again. As I was reading it, I wondered by what logic Jelbring had come to the conclusion that the atmosphere would not be isothermal. I noticed the following sentence in Section 2.2 C (emphasis mine):
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.
He goes on to describe the atmosphere in that situation as taking up the dry adiabatic lapse rate temperature profile, warm on the bottom, cold on top. I had to laugh. Jelbring made the exact same dang mistake I made. He thinks total energy evenly distributed per molecule is the final state of energetic equilibrium, whereas the equilibrium state is when the energy is evenly distributed per volume and not per molecule. This is the isothermal state. In Jelbrings thought experiment, contrary to what he claims, the entire atmosphere of the planet would end up at the same temperature.
In any case, there’s another way to show that the Jelbring hypothesis violates conservation of energy. Again it is a proof by contradiction, and it is the same argument that I presented to Jelbring years ago. At that time, I couldn’t say why his “gravito-thermal” hypothesis didn’t work … but I knew that it couldn’t work. Now, I can see why, for the reasons adduced above. In addition, in his thread Dr. Brown independently used the same argument in his discussion of the Jelbring hypothesis. The proof by contradiction goes like this:
Suppose Jelbring is right, and the temperature in the atmosphere inside the shell is warmer at the bottom and cooler at the top. Then the people living in the stygian darkness inside that impervious shell could use that temperature difference to drive a heat engine. Power from the heat engine could light up the dark, and provide electricity for cities and farms. The good news for perpetual motion fans is that as fast as the operation of the heat engine would warm the upper atmosphere and cool the lower atmosphere, gravity would re-arrange the molecules once again so the prior temperature profile would be restored, warm on the bottom and cold on the top, and the machine would produce light for the good citizens of Stygia … forever.
As this is a clear violation of conservation of energy, the proof by contradiction that the Jelbring hypothesis violates the conservation of energy is complete.
Let me close by giving my elevator speech about the Jelbring hypothesis. Hans vigorously argues that no such speech is possible, saying
There certainly are no “Elevator version” of my paper which is based on first principal physics. It means that what I have written is either true or false. There is nothing inbetween.
Another “gravito-thermal” theorist, Ned Nikolov, says the same thing:
About the ‘elevator speech’ – that was given in our first paper! However, you apparently did not get it. So, it will take far more explanation to convey the basic idea, which we will try to do in Part 2 of our reply.
I don’t have an elevator speech for the Nikolov & Zeller theory (here, rebuttal here) yet, because I can’t understand it. My elevator speech for the Jelbring hypothesis, however, goes like this:
• If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest air at the top and the warmest air at the bottom.
• This also is happening with the Earth’s atmosphere.
• Since the top of the atmosphere cannot be below a certain temperature, and the lower atmosphere must be a certain amount warmer than the upper, this warms the lower atmosphere and thus the planetary surface to a much higher temperature than it would be in the absence of the atmosphere.
• This is the cause of what we erroneously refer to as the “greenhouse effect”
Now, was that so hard? It may not be the best, I’m happy to have someone improve on it, but it covers all the main points. The claim that “gravito-thermal” theories are too complex for a simple “elevator speech” explanation doesn’t hold water.
But you can see why such an elevator speech is like garlic to a vampire, it is anathema to the “gravito-thermal” theorists—it makes spotting their mistakes far too easy.
w.
Joel Shore says: January 22, 2012 at 7:18 am
“What is the driving force?”
Joel, the driving force is the wind, which generates isotropic turbulence and forces air to move up and down, even against buoyancy resistance in the stable regime. Air forced down warms faster than ambient, acquiring an upward buoyancy. Its momentum (and local pressure gradients) keep it moving for a while (taking KE from the air). When it arrives it
diffuses heat to ambient; this is heat that has been pumped down against the gradient. The amount of heat is proportional (for a given motion) to the difference between the LR and the DALR. The effect is to drive the gradient toward the DALR, and the strength of the pump is proportional to (DALR-LR).
Upward motion pumps heat in the same direction (down).
When LR exceeds DALR, signs change; heat is pumped up, and KE is added to the air. This is the restoring mechanism you identified there. They are dual processes.
It’s like shovelling sand up a slope where it’s sliding down. If you can shovel hard enough you can maintain the slope. If not, the sand spreads until the slope reaches a lower value where the sliding matches your shovelling rate. Since the pump has finite power and its rate drops as LR ⇒ DALR, it can’t force LR all the way to DALR.
As the air thins, the effectiveness of the pump diminishes relative to conduction, so the actual LR gets further from DALR. The perturbing role of the heat source of absorbed insolation (and the sink of IR emission to space) also becomes relatively greater.
I can’t believe you guys are just continuing merrily to cruise along when I have ripped the fundamental foundation for Anthropogenic Global Warming right out of the ground. My latest amended proposal:
Bart’s Law:
It follows that surface temperature sensitivity to the addition of radiative gases is negative: the addition of more IR radiative gases will tend to lower the surface temperature. This is a sensitivity holding everything else equal – it does not preclude the possibility of feedback from other processes tending to resist the change, e.g., cloud albedo effects.
Bart’s Law is justified by the following line of reasoning:
What happens when you add additional IR gases, which are the lowest energy emitters, to the atmosphere? Without them, you would have continued increasing surface temperatures until higher energy emitters limited the surface temperature. Therefore, they have limited the temperature to less than it would have been. It follows that, if you add more of them, you will pin the surface temperatures down to a lower level.
IR emitters in the atmosphere do not heat the surface. They limit the surface to a lower temperature than otherwise would be the case. Adding more of them will further cool the surface.
Gravity can also concentrate heat with the use of photons. A photon gains energy when it travels downward in a gravity well. In fact, a black hole can prevent heat from escaping completely. It seems that gravity will concentrate energy more easily using particles with a high ratio of momentum to kinetic energy.
And other question, when you measure the radiation from a CO2 particle, how do you know if it participates to warming? The energy could have been previously absorbed from above. So this energy could be half of a reemission associated with a back-radiation to space(cooling). An example is the condensation of water vapor. If you have a lot of greenhouse gases between the condensation layer and the ground. Those gases with back radiate the energy to space. So the energy emitted to the ground is associated with a cooling by greenhouse gases.
To reinforce what David Hoffer Stephen Rasey are saying about what the Earths heat capacity and rotation does to maximumum and minimum temperatures.
The rotational effect is very pronounced here.
This is a new paper paper by Nikolov and Zeller
Posted on Tallbloke.
Have a look at the temperature /time graph of various locations on the Moon.
Eyeballing the graph and by removing the middle 27 Earth day periods we get an almost horizontal (little temperature variation) plot.
Pick say the temperature at the equator.
The explanation of the Holder inequality is worth a look
http://tallbloke.files.wordpress.com/2012/01/utc_blog_reply_part-1.pdf
@Nick Stokes: Nick, your heat pump idea made for something good to ponder while I was playing ultimate frisbee today…and I think I have a better understanding of it now. Let me put it into my own words and see if you agree that this is what you are talking about:
A heat pump / refrigerator / air conditioner pumps heat from cold to hot using an expansion-compression cycle. So, what you are saying is that the variation with pressure with height that occurs for an atmosphere in a gravitational field provides the setup for such a heat pump, with air at higher pressure at the ground and lower pressure further up. All that is needed is something to provide the actual “pumping” action. And, your point is that the pumping action will in practice be provided by any differential heating that occurs due to the diurnal cycle or the variation in insolation with latitude, presumably coupled with something like orographic effects to turn the horizontal motions into vertical motion.
Do I have the basic picture? If so, that’s pretty cool…and I have definitely learned something new! Have you thought about how important this effect is likely to be…E.g., it seems to me that, in the absence of greenhouse gases, an atmosphere will have a lapse rate somewhere between the isothermal distribution that is its equilibrium and the adiabatic lapse rate that is favored by this “heat pump” effect, but it is not clear to me where on that scale it is actually likely to fall.
By the way, for the benefit of those who want to violate the Laws of Thermodynamics: I will just emphasize a point that I am quite confident Nick will agree with, which is that whether or not there is a lapse rate is irrelevant to the average temperature (or really the average power emission) that a surface would have to have in the absence of a greenhouse effect. I.e., the constraint on the temperature has to be at the surface in this case because that is what is communicating (via radiation) with the rest of the universe.
Tallbloke;
I’ll be providing a mathematical proof of the misapplication of S-B on my site soon. Watch this space.>>>
To limit my misuse of time on the internet I long ago made a deal with myself to participate in one an one only forum. Please provide that mathematical proof as soon as you can and I will break my three year old deal with myself on the spot. My initial reaction to N&Z was that they were in dreamland. I had to let go of some long held beliefs, but I did so because their arguments make a ton of sense, and if the ONLY think that comes out of this discussion is that the misapplication of SB Law gets exposed and discredited once and for all, science will have made a giant leap forward.
Accepted Views of Their Time:
o the earth is flat
o the sun circles the earth
o bumps on your head determine your mental health
o disease can be cured by letting some of your blood out
o witches exist
o witches float
o warts are caused by touching toads
o volcanoes will cease erupting if your throw enough virgins into them
o the blackbody temperature of the earth is 255K
o the surface temperature of the earth is 288K
o the only mechanism by which a higher than “average” blackbody surface temperature of the earth can be achieved is through back radiation of GHG’s.
They all have one thing in common. They are wrong. Well…maybe not the part about witches because I believe I have a personal relationship with one and she does indeed float, though she disputes being a witch.
On a rotating uneven sphere under a single sun with a non GHG atmosphere there would be huge dayside and nightside temperature differentials producing very strong winds.All the energy exchanges between surface and atmosphere would be via conduction and convection involving ALL the molecules of the atmosphere whatever their radiative characteristics.
There would be enough mixing to bring warmed upper air down to the cold ground on the night side which would smooth out both heating and cooling around the planet.
The pressure at the surface would still combine with solar input to give the bog standard adiabatic lapse rate (or Atmospheric Thermal Effect) for a planet of that mass and atmospheric pressure. The air circulation of the planet would simply restructure itself around the ATE.
Just as every planet with an atmosphere of any composition always has done and always will do.
You see, an atmosphere structured around ATE is the only possible stable structure. Unless it achieves ATE then the situation is unstable and the atmosphere either boils off or congeals on the ground eventually.
The Ideal Gas Laws have never been falsified.
GHGs wholly unnecessary.
Robert Brown says at 1/22 8:04am:
“…one reference to a textbook (Caballero) has been offered that both derives/explains the adiabatic lapse rate…”
Replying succinctly as I chug thru my reading assignments, these are exact Caballero quotes you can text search for the rest of the context:
Caballero: 2.1: “Note that pressure is due to only to the local properties of the gas and not to anything going on far away.”, 2.1: “..if the gas as a whole is at rest…”, 2.11: “..an ideal gas with an isotropic velocity Distribution..”, in 2.2: “…we assume that the gas has no mean motion… yields the Maxwell-Boltzmann distribution…”
And so on. Under above assumptions, find non-g field gas column is isothermal. Don’t remember I ever wrote Willis’ premise cv gas would be stratified without presence of that inexplicable gravity (g) field. The gravity field is not consistent w/all the assumptions above, because now Willis’ GHG-free adiabatic tall gas column is not at rest, it is accelerating at g w/o an isotropic velocity distribution.
As I advised Willis upthread, I read down thru Cabellero Chapter 4 s-l-o-w-l-y. I scanned thru the rest of the chapters. Do not think I missed Caballero extending calculations to add explicit Willis premise including g unless Caballero was writing on the full atmosphere which he says must stratify in T (i.e. must have a lapse rate). If I missed it, you are more familiar with his work, please advise. It makes sense the full atmosphere should collapse to Willis’ premise with stratification of T inside his 1 cv of interest.
Robert continues:
“If MB statistics were not valid in gravitational fields, how would they ever have been discovered? Is there somewhere Maxwell or Boltzmann could go where they were absent?”
Thought problems like Willis’ premise have worked before! Thought problems did work pretty well for Einstein also. Here, Caballero tells us above that M-B distribution was discovered when “we assume that the gas has no mean motion… yields the Maxwell-Boltzmann distribution.” M-B has not gone on to apply to gas in gravity field in this work, maybe Tallbloke’s trip to the library will find a reference.
Of course, an accelerated gas will have a mean motion, special unaccelerated M-B is thus not applicable though it might be a subset of more general M-B and maybe that is where N&Z are going. Willis’ premise is extending at least my science understanding & in part, causing this thread length.
Robert continues:
“…and has as an explicit end of section homework problem to prove otherwise, and finally your answer is inconsistent.”
Found the jet & scuba diver, but need a more precise pointer to Willis’ cv problem here Robert and I’ll dig into my homework assignment.
And thanks again Robert, that Caballero ref. was great on 1st read and today’s second read – should be very useful again down thread.
Bart says:
Bart: Here is the elevator speech as to why your reasoning is wrong —
Greenhouse gases both absorb and emit radiation. However, for an atmosphere where the temperature decreases with increasing height (which is what the atmosphere will tend to when populated by greenhouse gases…and which convection can only partially cancel), the amount absorbed will be less than the amount emitted back out into space. This means that the net effect will be to allow the average surface temperature to exceed any possible average temperature that would produce radiative balance in the absence of an IR-absorbing atmosphere.
This is all well-understood stuff. You may be very smart but you are not quite as smart as you think you are (a statement alas true about a lot of people around here).
Bart,
I’ve got it in a sightly different form:
The atmosphere of any planet will restructure itself regardless of composition to produce the ATE determined by mass and solar input.
The critical thing to note about our hypothetical atmosphere is that it is at equilibrium. By definition, we cannot extract any additional energy out of this system provided that it is the lowest possible energy state. If it was not in the lowest possible energy state, we could be envisioning an atmosphere that is actually metastable. To clarify, consider a metastable atmosphere (dG = 0) where G = G1 and an alternative, attainable, and stable atmosphere (dG = 0) where G = G2. If G1 > G2, we could envision building a device that could extract energy from the system until it reached the lower energy state. Bear in mind, our hypothetical atmospheric system was initially at equilibrium dG1 = 0. And, at the end of the process, it is once again at equilibrium dG2 = 0. The key thing to note is that our ability to extract energy from the original system will cease once it reached the new equilibrium position. Hence, arguments for an isothermal atmosphere that are based soley on the ability to build a perpetual motion machine are non sequitur.
The challenge that we have is that our equation describing the equilibrium free energy of our system simply reads:
dG = -(CvlnT + Rln(RT/P) + Sm0)*dT + (RT/P)*dP + Mgdx = 0
In and of itself, this equation does not provide us with a definitive answer to the question. It does tell us that the free energy of the atmosphere must be uniform. However, there is no unique solution to this equation. There are a class of solutions if we (perhaps arbitrarily as a mathematician might view it) set dT = 0, dP = 0, or dT = dP = 0. We may even have a valid class of solutions where dT = dP or dT ~= dP. Of these five cases, the only absolutely safe bet is that dT = dP = 0 will not be a useful solution, since this trivial solution would imply the absence of an atmosphere. The other possible solutions are what I think form the basis for claims of the potential of a stable atmosphere which is not isothermal. From a purely mathematical point of view, we only know that the energy distribution must be uniform. Our equation does not dictate that the temperature must be uniform. This is about the point where I would anticipate a mathematician saying, “a solution to your question exists,” and immediately walk away.
As physical scientists, we immediately apply the temperature formulation of the zeroth law, because every system that we know of approaches an equivalent temperature state (e.g. Newton’s and Fourier’s law). In such a case, a valid solution to the equilibrium equation would be given as: P = P0*exp[-Mgx/(RT)]. This solution suggests that there will be a pressure gradient within an isothermal atmosphere. Paradoxically, every gaseous system not subject to a gravitational field also approaches an equivalent pressure state (refer to Figure 6-10 (b) of Klotz & Rosenberg:
Klotz & Rosenberg go on to describe a way to build a machine that will extract energy out of such a system. Hence, we could envision building a perpetual motion machine of the second kind to exploit the pressure differential in our hypothetical atmosphere. The resolution to this apparent paradox was realized by Clausius, who provided the most rigorous definition of the second law: “The energy of the universe is constant; the entropy tends toward a maximum.” In short, the application of the gravitational field may confound our intuition.
My scientific approach is best described as that of an empiricist. To quote Lord Kelvin, “when you measure you know.” It sounds like there are no definitive (non-thought) experiments addressing this question; if anyone knows of such experiments, please provide a link (or reference) to the original work. If not, then I would be intrigued by the results of the following experiment:
1. Place a gas in a thermally insulated cylinder of sufficient length,
2. Place this cylinder into a centrifuge,
3. Ensure that the gas is both isothermal and isobaric such that it has reached a state of equilibrium,
4. Turn on the centrifuge,
5. Allow a sufficient amount of time to pass to ensure that the system has achieved a new state of equilibrium.
The tricky part will getting an accurate measurement of the temperature distribution along the cylinder without disrupting the equilibrium state. We would also want to approach the equilibrium state from multiple directions to ensure that we did not happen to hit upon a metastable equilibrium. Assuming it is possible to devise such a system, the results will provide not only the answer the original question, but also validate (or refute) a fundamental law of thermodynamics when applied to systems subject to a gravitational field. The null hypothesis for this experiment is dT = 0. Any statistically significant deviation from dT = 0 would imply that the temperature formulation of the zeroth law is a limiting case. In short, a statically significant result would require a major paradigm shift. I’m not quite ready to discard what has been accepted for more than a century, so I’ll anticipate a result of dT = 0, even though it has a 1/inf (purely mathematical) probability of being the most thermodynamically stable energy state.
Bryan says:
January 22, 2012 at 2:25 am
I love folks like you, Bryan. They ask people to do their work for them.
But what the heck. I’ll bite let’s suppose the thermocouple has a resistance of Rt, and the connecting wire has a resistance of Rw. Let’s suppose that the thermocouple puts out a voltage V for a temperature difference ∆T
Now, the total resistance of a series circuit is R, + R2 + … + Rn. In this case the resistance is Rt + Rw.
Now Mr. Ohm comes to our aid with his famous E = I R equation. That tells us that Voltage = Current times Resistance.
The current flowing in the circuit under discussion is therefore
Now Bryan, I want you to notice something. As long as those variable have real values, A CURRENT WILL FLOW. It doesn’t matter if the wire is made out of steel and the voltage is tiny. Doesn’t matter if the silver wire doesn’t conduct much heat. If the components have real, non-zero values, a current will flow.
So the experiment is not “impossible” as you claim. There’s no reason to use real values, because the values don’t matter. It doesn’t produce much power, but that wasn’t Robert said. So your claim, that the experiment is “impossible” is falsified.
w.
Willis Eschenbach says
“Now Bryan, I want you to notice something. As long as those variable have real values, A CURRENT WILL FLOW. It doesn’t matter if the wire is made out of steel and the voltage is tiny. A current will flow. So the experiment is not “impossible” as you claim. There’s no reason to use real values, because the values don’t matter. It doesn’t produce much power, but that wasn’t Robert said. So your claim, that the experiment is “impossible” is falsified.”
Well Willis, I think you realise that if you put real values in, the current could not be measured.
So as far as Modern Physics is concerned if it cannot be measured you cannot say it exists.
So all you are left with is a conjecture..
Stephen Wilde says:
For the 1 millionth time: the lapse rate does not uniquely determine the surface temperature. You also need the temperature at one particular height. That height is the height from which radiation can successfully escape into space. For a planet without a greenhouse effect, said height is necessarily the surface of the planet.
Now, I have it. If the atmosphere is very thick in IR frequencies that interacts with CO2. Those photons do not travel a long distance. Let’s say this distance is 100m. It means a CO2 particle absorbs IR from 100m below and 100m above. Since the temperature is nearly the same over 200m, the emission of this CO2 particle is nearly as much a back radiation to the ground as a back radiation to space. It would not hold true at the top of the atmosphere because there is little radiation from above in the IR.
Trick, a coffee cup on a table is experiencing the force of gravity, but it is not moving in the table’s frame of reference, therefore it is not accelerating. (I’m not going to get into the Earth as a rotational frame of reference.)
A gas column will be stratified by density in a gravitational field, but at equibrium it is a statics problem where all forces cancel out and bulk acceleration is zero. Gravity can cause acceleration, but it doesn’t require it.
davidmhoffer says:
Sir, I have provided you with sample insolation curves and the blackbody calculations derived from them by doing the calculation over time and shown quite conclusively that it is easily possible to have a daily fluctuation of insolation from 0 to 850 w/m2 that averages 240 w/m2 and yields an average temperature over time of 140K. Your rebuttal amounted to screaming “that’s impossible”. Hardly a refutation.
You are attacking strawman arguments of your own devising. I have not said that it is impossible. I have said that the approximation that local temperature is determined by demanding radiative balance with the local insolation is a very poor approximation for the temperature of a planet with any significant atmosphere, rotation, etc.
But…It is also largely irrelevant. Let’s say I am wrong on this point and that an Earth without a greenhouse effect really would have such a dramatically broader temperature distribution that it would have an average temperature of 140 K. What does that prove? It proves nothing. You seem to think that we now have some much larger temperature discrepancy to explain, but the explanation for it is no big mystery to anyone but N&Z, you, tallbloke, and their other groupies: It is simply that lots of different temperature distributions with average surface temperature less than 255 K are compatible with the constraint that the surface must emit an average of 240 W/m^2.
Where? I am not going to search this whole thread.
O H Dahlsveen says:
January 22, 2012 at 9:17 am
I’d love to … but I’m banned from the talkshop for my evil ways. Is it posted anywhere else?
w.
davidmhoffer says:
January 22, 2012 at 8:39 am
The point is that if you arrive at the mean surface pressure of the various planets by another means, and plug those values into N&Z, you should either get the same results at they did, or, if you get different results, then either the way you calculated mean surface pressure is wrong, or the way they did is. Or I suppose, both could be wrong.
But I don’t see anyone jumping up and showing that the mean surface pressures of the various planets are appreciably different from what they calculated. Oddly, would that not be the easiest way to falsify at least that part of their work?
But allow me to suggest an alternative. If you understand what they are trying to get at over all, is there any reason they could not have used atmospheric weight (note that I said weight, not mass) instead of mean surface pressure?
We’re in agreement that there is a relationship of surface pressure to temperature. That was the point of the rest of my comment that you didn’t copy. However, it’s not useful to argue against the fact that they did use multiple free parameters or exact values. Instead, it’s better to look at those free parameters and argue that they really weren’t completely free and that the result of most of them should be testable (as you indicated).
Also, I still feel the presence of GHGs is most likely required. I feel it’s a non-issue as GHGs were present in all the atmospheres that were compared. The pressure-temperature relationship is the important one.
Read Nick Stokes comment above about turbulence and the relationship to the lapse rate. I think he’s on the right track and this is why the N&Z relationship exists.
@Joules Verne and tallbloke: The average surface temperature of the moon is the perfect debating point if your goal is to never resolve anything. You can debate this all day but unless you carefully define how the average is taken (e.g., are you looking at the first fraction of a mm or at the first meter of the surface), you’ll get all sorts of different answers!
And, this is precisely because there are lots of different temperature distributions having lots of different average temperatures that are all compatible with the moon being in radiative balance.
Misaplication of SB Law
Conventional calculation for “average” insolation of 240 w/m2 = 255K
Practical Application of SB Law in hourly increments over 24 hours beginning at midnight, the following insolation curve in w/m2 is illustrative:
0, 0, 0, 0, 0, 0, 100, 150, 350, 650, 800, 850, 850, 800, 650, 350, 150, 100, 0, 0, 0, 0, 0, 0
Applying SB Law to the hourly increments we arrive at equilibrium temperatures in degrees K of:
0, 0, 0, 0, 0, 0, 205, 227, 280, 327, 345, 350, 350, 345, 327, 280, 227, 205, 0, 0, 0, 0, 0, 0
Averaging both these series OVER TIME we arrive at:
“Average” insolation = 242 w/m2
“Average” SB Law equilibrium temperature = 144K
REBUTTAL
Since I already know the tune, I’ll play the next verse in advance. My detractors will immediately scream something to the effect that this is unrealistic and use the moon as an example where, even with a 14 “day” night and a 14 “day” daytime, extremes of either O or 350K are not achieved, hence there must be something wrong with my model as presented.
RESPONSE
Why of course! Did you think the heat capacity of the moon was zero?
Joel Shore;
Let’s say I am wrong on this point and that an Earth without a greenhouse effect really would have such a dramatically broader temperature distribution that it would have an average temperature of 140 K. What does that prove? It proves nothing. >>>
You mean other than attributing 33K to the GHE is totally and completely wrong? Other than demonstrating that the observed temperatures cannot possibly be achieved by GHE alone and that leaving heat capacity and time constant of the earth out of the equation is totally and completely wrong? Other than showing that much of the observed positive trend in temperatures globally can be attributed to the temperature of the earth becoming more uniform rather than the existence of an actual energy imbalance due to increases in GHG’s?
well, I guess if you skip all of those, then yup, it proves nothing.
“For a planet without a greenhouse effect, said height is necessarily the surface of the planet”
Irrelevant because energy still gets into the air via conduction and convection and back to the surface via convection and conduction for then radiating out. So there will still be a lapse rate and it must match ATE otherwise the system is unstable. If it doesn’t match ATE then the atmosphere will accumulate energy via conduction and convection indefinitely until it boiled away or lose energy to the ground via conduction and convection indefinitely until it congealed on the surface.
The true Perpetuum Mobile is the concept of a planet with an atmosphere that is not precisely in equilibrium with its ATE.
Any disequilibrium will either boil off the atmosphere or congeal it on the ground.Once congealed on the ground it would be lost via sublimation.
The radiative GHG theory is itself a Perpetuum Mobile because it proposes that changing the composition changes ATE. Thus a bit more human GHGs are amplified by more water vapour and that gives more GHGs which amplifies again ad infinitum.
The atmosphere and oceans would get hotter and hotter until they boiled away.
We would see lots more planet sized bodies with no atmospheres at all because a little change in atmospheric composition would have been enough to destabilise it.
IIf we were to reduce GHGs so that they changed the ATE lapse rate the other way then the Earth would get steadily colder until the oceans and air congealed on the ground.
The system won’t allow it. Any change in composition that might introduce a disequilibrium with ATE is neutralised by a reconfiguring of the circulation pattern.
If you could find one planet where the Gas Laws do not apply then you would have me. Where is it ?
davidmhoffer says:
Various things essentially borrowed from Postma and then…
You are wrong. Indeed, GLOBAL radiative balance requires that you do need GHGs. Giving local examples to illustrate why you think you don’t have to does not work…Yes, on a local scale, we can have energy storage and energy moved from one place to another. However, globally, we can’t have the Earth emitting 76.5 TerraWatts (150 W/m^2 times the surface area of the Earth) more than it is emitting day-in and day-out. If it were doing so, it would be rapidly cooling until it was no longer doing so. End of story.
davidmhoffer says:
No…It is not wrong. It is correct as a result of Holder’s Inequality.
We’re not leaving them out. Do you understand what an inequality is? It tells you that something can’t be bigger than something else. The temperature of a blackbody emitter receiving and average of 240 W/m^2 cannot be greater than 255 K. It can be less, depending on the temperature distribution. Is that such a hard concept to understand?
Joel,
Yes, I think that’s it. You can make a cycle – suppose hydrostatic atmosphere, LR=.5*DALR. Take a balloon with 1kg air, and pull it down 100m. T rises to ambient+0.5, and work had to be done against buoyancy. Hold it until T is back to ambient. 500J moved against gradient. Then pull it back up. It cools to ambient-0.5. Hold till ambient. 500J flows in.
I’ve done some quantification here, in entropy terms. The gradient produces a rate of entropy increase
E_V = (k/T^2) ∇T • ∇T
k=conductivity. The heat pump has to counter that. As the LR rises toward DALR, the pumping diminishes to zero, and the entropy production increases. Somewhere there is a balance point.
And yes, I do agree that without GHG the lapse rate is the same but irrelevant to heat balance and surface temperature. The air does not then interact with the outgoing heat flux. Though there is the possibility of liquefaction 🙁