Background
As an extension of the conversation on the Competing Mechanism thread, Chic and I have been swapping e-mails behind the scenes. Over the course of the exchanges, some thought experiments have been proposed which I think warrant an article of their own, and Chic has given me permission to publish whatever portions of our private communications as grist for that mill.As some of these thought experiments get quite long, this will be a multi-part series. First thought experiment is an actual experiment ...
Centrifuge Tubes Full of Water
Test Tubes Full of Water
[Update 3/19/2015: Chic notes in comments that I erred thinking that Graeff's protocol involved spinning his tubes in a centrifuge, thus allaying some of my confusion below about his theoretical derivation.]Chic brings up a fellow called Roderich W. Graeff who penned a note in 2006 entitled, Measuring the Temperature Distribution in Columns of Liquids. I have not yet read it, so let's take a look.
His main finding appears to be:
Vertical temperature gradients:I'll skip over the derivation and discussion to give the final form:
The most important result is the temperature gradient value 1 of the inner axis of the glass tube 1, filled with water and glass powder, as shown as the lowest blue curve in GRAPH 2. It is quite stable around a value of about -0.034 K/meter, the minus sign indicating a lower temperature at the top than on the bottom. This value is close to the theoretical value of -.04 K/m as discussed below.
TGr = -g x H / (c/n)He doesn't give units, so I assume them:
- g is acceleration due to gravity in m s-2
- H is vertical distance (height) in m
- c is specific heat in m2 s-2 K-1
- n is number of degrees of freedom (unitless), which for water he gives as 18
-0.04 K/m = -g m s-2 / 4186 m2 s-2 K-1 * 18Eh? He's saying the experimental rate under centrifugal acceleration (which he does not specify) is the same as the rate under (roughly) Earth standard gravity? Did I miss something?
g m s-2 = 0.04 K/m * 4186 m2 s-2 K-1 / 18
= 9.3 m s-2
[Update 3/19/2015: yes I did, he did NOT spin his tubes in a centrifuge, so Graeff really is saying -0.04 K/m under 1 gee acceleration. As my next calculation demonstrates, this is a wildly implausible result.]
For some real-world perspective, the Challenger Deep in the Mariana Trench is between 10,898 and 10,916 m deep. I'll average the range as 10,907 m. Thus:
10,907 m * 0.04 K/m = 436.28 KOne of us has goofed somewhere. I'll drill into the note some more, starting with the ...
AbstractSo he confirms that this idea does not conform to how the Second Law is formulated. Clearly, simply appealing to it as presently stated isn't going to work for Chic as Graeff is saying he thinks it needs to be rewritten. Let's see if I can figure out why:
Measurements of the temperature distribution in vertical tubes filled with water under equilibrium conditions are being reported. They show a negative temperature gradient, cold at the top and warm at the bottom within an environment showing a positive gradient. This is explainable by the influence of gravity. The measured effect comes close to a theoretical estimation. The temperature difference so created can be used to produce work out of a heat bath. These surprising results, if confirmed, necessitate a rewording of many statements of the Second Law reflecting the influence of force fields.
INTRODUCTIONThe Wikipedia article on Loschmidt has this to say:
Late in the 19th century J. Loschmidt believed that a vertical column of gas or of solids in an isolated system would show a temperature gradient under the influence of gravity, cold at the top and warm at the bottom. L.Boltzmann and J.C. Maxwell disagreed. Their theories tried to prove an equal temperature over height. The temperature distribution in liquids was not discussed. The historical discussion between J.Loschmidt, L. Boltzmann and J.C. Maxwell is covered in [1], [2], and [3]. A. Trupp gives a good summary in [4]. The author reported for the first time in [5] and [8] about actual measurements of the temperature gradient in gas columns in isolated systems. They are critically discussed by Sheehan [10]. They seem to strengthen the position of Loschmidt.
Loschmidt and his younger university colleague Ludwig Boltzmann became good friends. His critique of Boltzmann's attempt to derive the second law of thermodynamics from kinetic theory became famous as the "reversibility paradox". It led Boltzmann to his statistical concept of entropy as a logarithmic tally of the number of microscopic states corresponding to a given thermodynamic state.The article does not go on to say whether Loschmidt came to agree with Boltzmann's statistical concept of entropy or not. However, Chic in comments at WUWT quotes Dr. Roy Spencer (my emphasis added):
The most celebrated gravitational second law challenge revolves around an unresolved dispute between Josef Loschmidt and the two thermodynamic giants, Maxwell and Boltzmann. Loschmidt claimed that the equilibrium temperature of a gas column subject to gravity should be lower at the top of the column and higher at its base. Presumably, one could drive a heat engine with this temperature gradient, thus violating the second law. This debate has remained unresolved for over a century.I'm dubious. Whenever a climate contrarian like Spencer says something remains unresolved, fair or not, I translate it as, "I'm not convinced that prevailing wisdom is correct".
Back to Graeff's note. Skipping over the experimental setup and to the results:
Vertical temperature gradients:A good scientist will always try to account for any confounding effects in an experimental apparatus. Graeff thinks of several, and rules them all out:
The most important result is the temperature gradient value 1 of the inner axis of the glass tube 1, filled with water and glass powder, as shown as the lowest blue curve in GRAPH 2. It is quite stable around a value of about -0.034 K/meter, the minus sign indicating a lower temperature at the top than on the bottom. This value is close to the theoretical value of -.04 K/m as discussed below. Going from the inner axis radially to the outside, the value 3 of the enclosing PVC tube – black curve PVC tube 1 - shows a slightly less pronounced gradient, but still being colder at the top than on the bottom.
- Exothermic reactions between the water and glass beads.
- Evaporation of water from the top of the tubes.
- Convection currents creating an adiabatic gradient.
- Measurement error.
- (Local) equilibrium conditions never being met.
[Update 3/19/2015: none of the following reasoning applies due to my error in thinking he used a centrifuge in his experiments.]
- The bottom of a centrifuge tube moves faster under rotation than the top. Nothing in the description of the experimental apparatus indicates that the runs were performed in near-vacuum conditions. Hence it is conceivable that greater airflows near the bottom of the tubes caused some additional heating which did not occur near the slower moving upper portions of the tubes.
- Even though centrifuges are constructed to rotate smoothly and without vibration, there is always a bit of wobble due to the drive, bearings, or masses in the tubes being out of balance. Typically it gets worse as RPM increases, but not always depending on any harmonic resonances. Such vibrations, however slight, might be expected to cause mechanical action (compression and rubbing) in the tubes. It is easy to conceive how such actions would be amplified in the bottoms of the tubes where centripetal acceleration, and therefore pressures, are greater.
- Water is a polar molecule, meaning that it has an electric dipole moment. Move water in a circular motion through a magnetic field (like that of the Earth's), and the motions will set up a slight electrical current. Faster the motion through the magnetic field, the more current generated. This is the theory behind how electromagnetic induction heating works, but instead of moving the mass to be heated through a magnetic field, the field itself is pulsed. The result is that electrical eddy currents set up, excite the molecules of the target object, and it warms up.
Graeff himself doesn't consider this a viable form of "free energy" ...
4. Consequences of the measured temperature gradients for the Second Law.... yet he considers his results significant enough to call for overturning the Second Law. I think he needs to revisit his logic. Very next paragraph:
The brown curve 5 shows the temperature differences at the top of tube 1 and tube 2 with an absolute average value of about .01 K. This temperature difference could be used to create work i.e. by creating electric power through a thermocouple, as it is actually continuously taken place during the test. The amount of energy so produced is, of course extremely small. It does not affect the equilibrium condition of the experiment as this small amount of energy taken out of the system is easily replenished from the heat bath of the environment.
But the fact that heat flows under the influence of gravity from a cold reservoir to one with a higher temperature contradicts today’s understanding and present day’s statement of the Second Law. It has to be restated addressing the influence of force fields like gravity.
5. Theoretical Value for temperature gradient TGrYeeessssss ... however for every molecule moving down is one being displaced upward. Unless the water is always falling in the tube, the net effect of molecules moving around in the gravity well and trading potential energy for kinetic and vice versa is going to be goose eggs.
No published treatise of calculating the vertical temperature gradient TGr in solids or liquids under the influence of gravity is known to the author. But the value of TGr can be calculated by equating the potential energy of the molecules with the increase of their speed on their downward path. Their speed represents their temperature. When bouncing off the bottom wall or from another water molecule, their kinetic energy is zero at the moment of impact. Though their loss of potential energy in their downward movement is totally converted to an increase of their average “temperature”. A heat transfer takes place between water molecule and the upper and lower wall of the tube until the wall temperatures equal the “temperature” of the impinging water molecules and equilibrium has been reached.
Conclusions
If I've done the math above correctly, and am not grossly misunderstanding Graeff's calculations and other arguments, I'm gonna call this one done.[Update 3/19/2015: I did grossly misunderstand that this was a 1 gee experiment, not a several hundred gee experiment. If you'll pardon the pun, the gravity of the disconnect between experiment and real world observation far outweighs my key misunderstanding of his protocol. This one is not just sunk, it was dead on arrival.]
Postscript -- Where There's Actually Something To This
I mentioned earlier that this notion of temperature increasing due to gravitational force works if the gas is, on balance, "constantly falling". Hang around this discussion long enough, and someone is sure to bring up Jupiter:Although Jupiter would need to be about 75 times as massive to fuse hydrogen and become a star, the smallest red dwarf is only about 30 percent larger in radius than Jupiter.[30][31] Despite this, Jupiter still radiates more heat than it receives from the Sun; the amount of heat produced inside it is similar to the total solar radiation it receives.[32] This additional heat is generated by the Kelvin–Helmholtz mechanism through contraction. This process causes Jupiter to shrink by about 2 cm each year.[33] When it was first formed, Jupiter was much hotter and was about twice its current diameter.[34]Shrinking by 2 cm/yr takes this out of the realm of a constant volume problem. The constant shrinkage can be seen as Jupiter's atmosphere constantly falling on balance ... in other words, being compressed and leading to heating such that it radiates out more energy than it absorbs from the Sun.
Details.
Note however that this does NOT mean that this process is the only thing which accounts for Jupiter radiating more than it absorbs.
Top marks for patience, BG.
ReplyDeleteThis seems to be another of CB's blind spots. That it should lead to '2nd Law is wrong' nonsense is unsurprising since it's a well-worn track into the Pit.
Good debunk on the Challenger Deep btw. Filched for future use ;-)
Thanks, BBD. I do get frustrated with Chic at times, but he's otherwise pleasant to talk to. The review from first principles continues to be a good exercise for me.
DeleteFilch away, glad to have been of some minor assistance. :)
Brandon,
ReplyDeleteWith the intention of resolving this gravito-thermal question in my own mind, I am compiling relevant documents. Double check the credits to your quotes. The one begining with "Introduction" and the second one after that beginning with "The most celebrated..." are from Chapter 6 of Capek and Sheehan's book "Challenges to the Second Law of Thermodynamics" "http://www.amazon.co.uk/Challenges-The-Second-Law-Thermodynamics/dp/904816768X/ref=sr_1_2?s=books&ie=UTF8&qid=1335653229&sr=1-2
Excerpts from the book can be found at https://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/ along with other links and comments.
While organizing the above, I stumbled on to four posts about Dr. Graeff's work at the talkshop by Lucy Skywalker. This is the link to part 4 which provideys links to the other three: https://tallbloke.wordpress.com/2012/06/28/graeffs-experiments-and-2lod-replication-and-implications/
I haven't read Lucy Skywalker's posts yet, but I know enough from reading the Graeff experiment paper to point out a misunderstanding in your analysis. The Graeff experiment you describe was not a centrifuge experiment. He just placed tubes at rest in a well insolated setup with thermisters located in various places so that the temperature gradient could be measured. So there's no need for a vacuum. Proposals to use centrifugation to test this hypothesis are out there and your concerns may apply to them. There is a device that does show a gradient can/will form under a centrifugal force.
More importantly, I think you misinterpret Dr. Graeff's interpretation of molecular "speed on their downward path" in his section 5. Theoretical Value for temperature gradient TGr.
"Yeeessssss ... however for every molecule moving down is one being displaced upward. Unless the water is always falling in the tube, the net effect of molecules moving around in the gravity well and trading potential energy for kinetic and vice versa is going to be goose eggs."
While Brownian motion will ensure that for every molecule moving up there will be another molecule moving down, gravity will create a temperature gradient. As one's eyeballs move from the top of the tube down to the bottom, the speed of the molecules increases. IOW the average kinetic energy of the water molecules at a given level increases going from the top to the bottom. No particular water molecule need go the distance. Since temperature is a measure of kinetic energy, a gradient results.
Chic,
DeleteBefore I delve into more references and discussions of theory, perhaps you could address my calculation based on Graeff's results for the Challenger Deep. 436.28 K temperature gradient seems an awfully untenable prediction for 11 km of water under 9.8 m s-2 gravitational force.
PS,
DeleteI replied to your comment on WUWT yesterday afternoon and it was not published; not even as a [snipped] comment. Short, to the point, no snark. It would seem that's no longer a place where you and I will be able to dialogue.
This is how I replied at WUWT to your comment which was inexplicably censored:
Delete"His main finding is a temperature gradient due to gravity alone. There seems to be some question about the theoretical value of 0.04 K/m. I calculated 0.0025 K/m and Graeff multiplies that by 18 degrees of freedom. Hmmm. Why?
Extrapolating to the deep ocean probably violates assumptions used in deriving the theoretical gradient equation from the hydrostatic equation. Plus if the sign is negative, the deep ocean should have boiled away by now!"
I don't know how much else to add to that. Obviously, the ocean gradient is of the opposite sign and the magnitude of the temperature difference unreasonable. The best way I can explain it is there is no equivalent of an ideal gas law governing liquids. But consider the purpose of the water experiments. Irrespective of any theoretical derivation, one would expect an isothermal gradient in a liquid same as for a gas. Certainly Maxwell and Boltzmann thought so. With minimal change in pressure and density in a 10 cm tube, you have to come up with a good reason why the experimentally observed gradient can't be right.
Also, Graeff also has data for air as well. He has been doing these experiments over and over trying to find problems with the set up. It seems to be robust.
The best way I can explain it is there is no equivalent of an ideal gas law governing liquids.
DeleteThe parsimonious explanation is that Graeff is wrong.
With minimal change in pressure and density in a 10 cm tube, you have to come up with a good reason why the experimentally observed gradient can't be right.
DeleteExperimental error. Who has replicated Graeff's experiment, and where is it documented?
Chic,
DeleteThe Graeff experiment you describe was not a centrifuge experiment. He just placed tubes at rest in a well insolated setup with thermisters located in various places so that the temperature gradient could be measured.
Ah, that explains my confusion. I'll correct the head post to reflect my error.
Extrapolating to the deep ocean probably violates assumptions used in deriving the theoretical gradient equation from the hydrostatic equation.
Graeff is asserting that this effect is a fundamental property of nature, and that his experimental results call for overturning the 2nd law of thermodynamics. When he writes that his results demonstrate that (net) heat can flow from a cooler reservoir to a warmer one, he is in effect arguing that water can also run uphill.
The reason we call these things "laws" is because there are no exceptions to them.
Plus if the sign is negative, the deep ocean should have boiled away by now!
I make the pressure to be 0.0961 atm/m * 10,907 m + 1 atm = 1049.53 atm.
Assuming 20 C surface temperature, I make Graeff's prediction at the same depth as 0.04 K/m * 10,907 m + 293.15 K = 729.43 K.
The critical point of pure water is 647.15 K at 218 atmospheres. Even though ocean water has a different phase diagram, I think the temperature/pressure involved at this depth predicts a supercritical fluid, not gas. This is all academic, as you say: "Obviously, the ocean gradient is of the opposite sign and the magnitude of the temperature difference unreasonable."
I suggest you stick with that thought.
With minimal change in pressure and density in a 10 cm tube, you have to come up with a good reason why the experimentally observed gradient can't be right.
No, Graeff needs to explain why his theory doesn't come anywhere close to matching real-world empirical observation. I'm with BBD on this one, I think the parsimonious explanation is that his results are due to experimental error and his theoretical explanation is deeply flawed.
IOW, he's a crank. Tallbloke et al. do themselves zero credit seriously entertaining his stuff. I think I may take my own advice and suggest we discuss something else.
"Graeff is asserting that this effect is a fundamental property of nature, and that his experimental results call for overturning the 2nd law of thermodynamics. When he writes that his results demonstrate that (net) heat can flow from a cooler reservoir to a warmer one, he is in effect arguing that water can also run uphill."
DeleteI can't speak for Graeff, but I don't think the 2nd Law needs overturning. The "heat flows" verbiage comes from early caloric theory that heat is like a fluid. I would rather interpret the results in terms of modern thermodynamic statement of the second law "the entropy of an isolated system never decreases." To establish maximum entropy, IOW thermodynamic equilibrium, the molecules with more potential energy higher up will have less kinetic energy than below. There is no net flow of energy in the tube other than what is required to obtain maximum entropy.
"No, Graeff needs to explain why his theory doesn't come anywhere close to matching real-world empirical observation."
Why should Graeff's experimental results, with negligible pressure and density changes in a 10cm tube of water, have to extrapolate to salt water at 277 K and 1000 bar? Do you expect the atmospheric lapse rate to extend beyond the troposphere? You need to explain why the temperature in the tube should remain isothermal. What theory do you base that on and where's your data? Unless your prepared to do the experiment yourself, claiming "experimental error" doesn't cut it.
P.S. the name-calling is childish. It's a sign you've lost the argument. Which is too bad, because the high road is getting to the scientific truth, not winning an argument.
Chic,
DeleteI can't speak for Graeff, but I don't think the 2nd Law needs overturning.
Yet that is the central argument he's making on the basis of his experimental results.
The "heat flows" verbiage comes from early caloric theory that heat is like a fluid. I would rather interpret the results in terms of modern thermodynamic statement of the second law "the entropy of an isolated system never decreases."
I don't see any way of getting around what the man explicitly states in his note:
But the fact that heat flows under the influence of gravity from a cold reservoir to one with a higher temperature contradicts today’s understanding and present day’s statement of the Second Law. It has to be restated addressing the influence of force fields like gravity.
He's essentially saying that heat has mass and that it "falls" under influence of gravity in fluids at rest at a constant volume.
To establish maximum entropy, IOW thermodynamic equilibrium, the molecules with more potential energy higher up will have less kinetic energy than below.
I'm going to invoke the baseball in a closed system vacuum thought experiment we were discussing offline. Starting position: one ball 10 km above the other, both balls are at rest and the system is at thermodynamic equilibrium, 1 standard gee gravity. The mechanism you propose implicitly says that the upper ball will necessarily be warmer than the lower one.
Now suppose that the upper ball is released so that it can freely accelerate under force of gravity. What happens to the temperatures of both balls as it falls?
There is no net flow of energy in the tube other than what is required to obtain maximum entropy.
That was not a condition of the experiment. Aside from the fact that it's impossible to make a truly closed system, it's all but impossible to keep sensible heat transfer from occurring in a fluid, especially one that is as good a thermal conductor as water.
Why should Graeff's experimental results, with negligible pressure and density changes in a 10cm tube of water, have to extrapolate to salt water at 277 K and 1000 bar? Do you expect the atmospheric lapse rate to extend beyond the troposphere?
That's kind of like asking why we should expect the speed of light in a vacuum as tested in the lab to be the same as the speed of light in intergalactic space everywhere else in the universe.
If you can't explain why Graeff's prediction fails in the oceans, you should be asking HIM to explain the discrepancy, NOT ME.
"I don't see any way of getting around what the man explicitly states in his note."
DeleteIsn't it possible that his results can be right and his interpretation of the 2nd Law wrong?
"He's essentially saying that heat has mass and that it "falls" under influence of gravity in fluids at rest at a constant volume."
LOL. I don't think you should be speaking for him either.
You're back with the ball analogy? This is it, last time I'm playing this game.
"The mechanism you propose implicitly says that the upper ball will necessarily be warmer than the lower one."
This is wrong for two reasons. First, you have the starting conditions backwards. A ball higher up has more potential energy and less kinetic energy and the reverse for the lower ball. Temperature is proportional to kinetic energy. Secondly, using balls as an analogy is inappropriate, because you can't get a temperature from only two entities. Temperature is a measure of the average kinetic energy of the molecules in the system. Now a baseball will equilibrate to the temperature of the molecules surrounding it, but this will take a long time--too long before the ball returns from its flight. Please don't mention baseballs again, it's a bad analogy unless you are using it simply to point out that potential energy increases with height and kinetic energy decreases. If it helps you to understand the principle involved here, then imagine a ball with an infinitely fast diffusion coefficient. In this case the ball will cool while losing kinetic energy as it rises and warm as it falls and gains kinetic energy.
"That was not a condition of the experiment."
The experimental setup was intended to prevent energy in or out, i.e. adiabatic conditions. Internal energy transfer such as potential to kinetic is allowed. IOW, the water molecules can move around just like air molecules.
"Aside from the fact that it's impossible to make a truly closed system, it's all but impossible to keep sensible heat transfer from occurring in a fluid, especially one that is as good a thermal conductor as water."
The walls of the tube are intended to insulate the water from its surroundings, making it a closed system. Assuming that some leakage occurred, why would that create a temperature gradient in the water the opposite of what it is in the surroundings? What explanation do you have for that?
"That's kind of like asking why we should expect the speed of light in a vacuum as tested in the lab to be the same as the speed of light in intergalactic space everywhere else in the universe."
No, I don't follow. What in space would make the speed of light different from what you would measure in the lab? On the other hand, the pressure and temperature differences at the bottom of the ocean are completely different from Graeff's lab. Having said that, I wouldn't discount the possibility of finding a different speed of light in the lab vs. space, but you would need a hypothesis to explain it. What is your explanation for why Dr. Graeff's experiments conform to his hypothesis and not yours?
"If you can't explain why Graeff's prediction fails in the oceans, you should be asking HIM to explain the discrepancy, NOT ME."
I did explain it. In the same way that a theoretically linear lapse rate does not hold over the entire atmosphere, because of uncontrolled for variables and loss of adherence to assumption of adiabatic conditions, similar assumptions valid for the Graeff experiment cannot be expected to hold from sea level to the bottom of the ocean.
What is your explanation for why Dr. Graeff's experiments conform to his hypothesis and not yours?
DeleteHe's wrong.
Ever heard of single-study syndrome, Chic? Or in this case, single unreviewed monograph syndrome?
Who has replicated Graeff's results and where is it documented?
I note that you have not come close to answering the question about the temperature in the abyssal deeps. You just wave it away, repeatedly. Bad faith.
So you have no evidence that over 800 experiments confirming a gravito-thermal effect are wrong. I don't know why others have not yet replicated his experiments or published their results if they have. I started searching for answers and will keep you posted. This is consistent with my interest in finding the truth as opposed to remaining blinded by faith, confirmational bias, or whatever else controls you.
DeleteMeanwhile your rebuttals to my arguments are all arguments by assertion, name-calling, obfuscation, etc. Specifically, I provided a reasonable answer to why these experiments showing a temperature gradient at close to standard temperature and pressure cannot be extrapolated over distances and pressures 10^5 and 10^3 greater, respectively. Your response? A false statement, devoid of scientific understanding.
A false statement, devoid of scientific understanding.
DeleteAmusing, coming from someone pushing crankery while wittering sententiously about searching for truth ' as opposed to remaining blinded by faith, confirmational bias, or whatever else controls you'.
So you have no evidence that over 800 experiments confirming a gravito-thermal effect are wrong.
DeleteAnd you have none that they are correct which was my original point. Yet you are convinced that this is 'the truth'.
Get a grip, Chic.
You've got nothing. GIGO. It's pathetic. You live in your own little closed system unable to think outside the box.
DeleteDo yourself a favor and read this interesting comment on related issues: http://wattsupwiththat.com/2014/08/18/monday-mirthiness-spot-the-troll/#comment-1711550
Try to avoid replies with unscientific dribble.
You've got nothing.
DeleteNo, Chic, *you've* got nothing. Except your blind faith and confirmation bias that CO2 is not an efficacious climate forcing. You *start* from a position of denial and attempt to find some kind of justification for it - even to the extent of perpetual motion crankery. So you do not get to pretend that you are the higher Galilean intellect here and I am a troll. Not when literally all the available scientific evidence shows that you are wrong. As I said, get a grip.
I am not surprised you came back with nothing but more unscientific drivel.
DeleteHi guys,
DeleteI think we should all be able to agree that our positions are essentially that the other guy is spouting unscientific drivel. It would please me if we take that as a given and focus on explaining why.
Note that I'm NOT asking any of us to be "nice", more that if you're gonna throw a punch, it would be better if it had the weight of argument behind it.
As I am a little weary of the topic, another option is let you two have at it as you will. I can go at least one more round though. On that note ...
Chic, I'm in the middle of stuff, don't have time to respond to your comments tonight. I hope to be able to get to them tomorrow.
Chic, part 1:
DeleteIsn't it possible that his results can be right and his interpretation of the 2nd Law wrong?
Possible but unlikely. More likely that his call for revising the 2nd law is correct, but his experimental results are off by several orders of magnitude on the high side. That was the point of me doing the calculations for the Challenger Deep.
By more likely, I really mean the barest fraction less than completely impossible imaginable.
LOL. I don't think you should be speaking for him either.
Fine. He's your reference, so if either of us is going to speak for him, or has call to ask him questions it's you.
You're back with the ball analogy?
I could use globs of Pla-doh if you prefer. Matter is matter. Phase of matter shouldn't matter.
First, you have the starting conditions backwards.
So flip it. But again, it shouldn't matter. The argument as I understand it is that absolute position in a gravity well is a determinant of temperature. Recall that total enthalpy in a system includes the energy required to bring the system to its current state, but since that's all but impossible to determine, what we normally do is calculate change in enthalpy as a function of work being done to or by a system.
A ball higher up has more potential energy and less kinetic energy and the reverse for the lower ball.
I agree, and have never disagreed since I first learned it.
Temperature is proportional to kinetic energy.
I agree with that as well.
Secondly, using balls as an analogy is inappropriate, because you can't get a temperature from only two entities. Temperature is a measure of the average kinetic energy of the molecules in the system.
If I know each ball's mass and velocity, I can tell you the average kinetic energy in the system.
If it helps you to understand the principle involved here, then imagine a ball with an infinitely fast diffusion coefficient.
Ok by me.
In this case the ball will cool while losing kinetic energy as it rises and warm as it falls and gains kinetic energy.
So, the rising ball implies a mechanism doing work to raise the ball, which introduces complications I was hoping to avoid.
Better is my original proposal where we have the intital state of a ball at altitude at rest. Then we drop the ball. You claim, in a vacuum, that the ball will warm as it falls.
What happens when it impacts the surface?
Think about the 1st law when you compose your answer.
Chic, part 2:
DeleteThe experimental setup was intended to prevent energy in or out, i.e. adiabatic conditions.
I understood that it was intended to be as close to a closed system as possible. I have a quibble about your use of adiabatic in this context, but I'm too tired to pursue it, and don't think it really matters.
Internal energy transfer such as potential to kinetic is allowed. IOW, the water molecules can move around just like air molecules.
Yes, I got all that. Additionally, some of the tubes were filled with glass beads to prevent macro movement in the form of convection. Look, it sounds like an elegantly designed experiment. My issue is not so much with how it was done, but with the results.
The baseball analogy was intended to be the same thought experiment, with the simplification of removing hydrostatic pressure. Otherwise, all other internal energy transfers allowed.
Assuming that some leakage occurred, why would that create a temperature gradient in the water the opposite of what it is in the surroundings? What explanation do you have for that?
Why should I have an explanation for it? It's not my experiment! Thermistors draw a current, yes? The tubes were resting on a lab bench, were they not?
What in space would make the speed of light different from what you would measure in the lab?
Exactly.
On the other hand, the pressure and temperature differences at the bottom of the ocean are completely different from Graeff's lab.
If the law doesn't account for temperature and pressure differences, it's useless.
What is your explanation for why Dr. Graeff's experiments conform to his hypothesis and not yours?
Because his calculated theoretical value -- not experimental value, his theoretical calculation -- is orders of magnitude higher than it can possibly be such that it requires highly controlled laboratory experimentation to detect.
I did explain it. In the same way that a theoretically linear lapse rate does not hold over the entire atmosphere, because of uncontrolled for variables and loss of adherence to assumption of adiabatic conditions, similar assumptions valid for the Graeff experiment cannot be expected to hold from sea level to the bottom of the ocean.
You're telling me that the real system has enough confounding factors to dissipate or otherwise transfer the energy of ... what is it ... a 475 K theoretical temperature differential. That's a tough nut to swallow.
Brandon,
DeleteRe the prelude to parts 1 and 2:
Are you weary because you don't want to agree with me or because you can't convince me to agree with you? Please understand I'm not trying to win an argument. Does anybody care what we think. What matters to me is being as confident as possible that what I think is actually true. No skeptic or consensarian has everything right. When you are confident you are right and I'm wrong, let me know and I'll go to another classroom.
Re part 1:
Delete"Phase of matter shouldn't matter."
In the context of the atmosphere and the propensity to form a temperature gradient, I think it does. When we are discussing kinetic energy and temperature of the atmosphere, we should limit ourselves to air molecules, not baseballs.
"The argument as I understand it is that absolute position in a gravity well is a determinant of temperature."
We haven't actually clarified that, but I do agree. More specifically, it is the average kinetic energy of the molecules at that position.
"...what we normally do is calculate change in enthalpy as a function of work being done to or by a system."
Who is we and in what context are we changing enthalpy? Enthalpy is a thermodynamic term representing the change thermal energy ("heat"), dQ, in an ISOBARIC change. dH = dU + d(pV) with U representing internal energy (potential + kinetic). If "we" limit ourselves to a constant pressure system, then dH = dU + pdV (Vdp = 0). dQ = dU + pdV, but dQ = dH only for isobaric conditions. This cannot apply to gravity discussions, because pressure will always be varying with altitude however we define our atmosphere.
"If I know each ball's mass and velocity, I can tell you the average kinetic energy in the system."
This is why I cannot tolerate any more ball analogies. When the balls are suspended or laying on the ground, they have zero velocity. Only when they are in play are they moving and they only move when energy is applied by an external source. Air molecules are moving all the time and do not require any new energy entering the system.
So no, not "Better is my original proposal where we have the intitial state of a ball at altitude at rest." I cannot follow where you are going with a fictitious mass with an infinite diffusion coefficient deprived of company, hence devoid of temperature, impacting the surface. The best I can do is surmise you wanted me to see that a ball in a vacuum can't warm as it falls.
"Think about the 1st law when you compose your answer."
I don't see where any energy disappeared.
Re part 2:
Delete"I have a quibble about your use of adiabatic in this context...."
Adiabatic: dQ = 0. dU = dW = pdV + Vdp. If our hypothetical system is closed, we could say V is constant and therefore dU = Vdp. This leads to dU/dz = Vdp/dz. From there we should be able to express dU/dz in terms of dT/dz and somehow get to a relationship describing how kinetic and potential energy change with respect to altitude.
"If the law doesn't account for temperature and pressure differences, it's useless."
By that logic, the ideal gas law is useless.
"Because his calculated theoretical value -- not experimental value, his theoretical calculation -- is orders of magnitude higher than it can possibly be such that it requires highly controlled laboratory experimentation to detect."
That is either wrong or misstated. His theoretical calculation was 0.04 K/m and his results were 0.012 and 0.050 K/m depending on whether the tube contained a convection suppressor.
"You're telling me that the real system has enough confounding factors to dissipate or otherwise transfer the energy of ... what is it ... a 475 K theoretical temperature differential. That's a tough nut to swallow."
Yes. There are plenty of examples to explain why you can't extrapolate a theoretical equation beyond the limits of the assumptions used to derive the equation. Should we abandon the dT = lamda x ln (C/Co) equation because it no longer applies at low concentrations of CO2?
I don't think we can get beyond pointless argumentation without agreeing on the validity of the theoretical hypothesis and the relevance of the available data. For my part, I have to show how the theoretical derivations claiming isothermal gradients are wrong. Your job is to explain why Graeff's experiments contradict the isothermal hypothesis. Just saying his results can't be extrapolated to near infinity doesn't cut it.
Addendum to part 1:
Delete"Think about the 1st law when you compose your answer."
Now I see where you were going. The ball is warming, so where is the extra energy coming from? There should be another ball going up and cooling so that the net internal energy change is zero.
Tallbloke! I knew it!
ReplyDeleteI almost said 'it'll be Tallbloke next'. Wish I had, now :-)
Lucy Skywalker is *insane* btw.
This is going from bad to worse.
Brandon,
ReplyDeleteIn my quest to get to the bottom of this gravito-thermal question, I came across an enlightening discussion on a thread at Climate Etc. https://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-651636
Commenter Peirre-Normand (P-N) initially cited several references pertaining to this issue. You can see his list near the top of the disussion. One of the papers (C&L 1985) describes the paradox (http://tallbloke.files.wordpress.com/2012/01/coombes-laue.pdf) and another one not on the list (VR&W 1996) corrects/amends it. https://tallbloke.files.wordpress.com/2012/01/s-velasco.pdf
These two papers and the exchange between P-N and Joe Born are highly relevant to our ongoing discourse. Before we continue, I would appreciate it if you could have a look at those references. I haven't yet worked out the calculus yet, but much of the discussion bears on the kinetic energy and temperature exchange we are having.
I think the comment from the same Climate Etc. post best expresses my view:
ReplyDeleteDavid Springer | December 8, 2014 at 9:48 am |
No, it’s not obvious [that the temperature in a closed atmosphere will be isothermal]. The isothermal gravity-confined column has a mechanical energy (PE + KE) gradient also called a potential temperature gradient. The existence of the gradient means the column is not at maximum entropy. PE and KE are freely interchangeable (no work required for the exchange) so the relaxed state of the column must be constant potential temperature not constant absolute temperature. The mental gymnastics required in any serious attempt to dispute this simple description of maximum entropy is astounding. Occam’s Razor alone is a compelling reason to question the isothermal argument.
I think this is just wrong.
DeleteThere is a perfectly insulated gas-filled cylinder in zero gravity. Gas temperature is the same as the room you are reading this in and isothermal within the cylinder.
At one end of the tube we have a gravity machine. When activated, it generates standard Earth gravity.
We turn on the gravity machine and wait. Gas density increases at the base of the cylinder and gradually decreases towards the top. This initial compression sets up a temperature gradient in the tube: warmer at the bottom; cooler at the top.
Now, wait a while and entropy renders the gas isothermal once again. The only way to re-establish a temperature gradient would be to turn the gravity machine up to >1g.
Well, not the only way. We could re-establish a temperature gradient by taking the wizard's hat off the top of the cylinder and admitting a radiative flux through its transparent end cap.
Dave Springer is a great one for making half-baked arguments from assertion and the above is a good example.
To be absolutely clear:
DeleteThe only way to re-establish a temperature gradient would be to turn the gravity machine up to >1g. [This would be a temporary gradient - an *initial* response to the increased gravity. It will be erased by entropy over time]
We could also re-establish a temperature gradient by taking the wizard's hat off the top of the cylinder and admitting a radiative flux through its transparent end cap. [This would last as long as the radiative flux is present. If the flux is sustained, the temp gradient will be maintained indefinitely]
Failure to conceptualise this properly results in perpetual motion errors.
First, bbd, I congratulate you on participating in a scientific discourse. The set up of your thought experiment is also commendable.
DeleteNow, at the point where the density, pressure and temperature gradients reached their semi-final values, ask yourself why doesn't the gradient(s) remain? And if entropy causes the temperature to equalize, why didn't entropy stop the gradient forming in the first place? Equations or a citation would be good here.
"Dave Springer is a great one for making half-baked arguments from assertion and the above is a good example."
I don't think you've shown this one half-baked. Any others?
Now, at the point where the density, pressure and temperature gradients reached their semi-final values, ask yourself why doesn't the gradient(s) remain? And if entropy causes the temperature to equalize, why didn't entropy stop the gradient forming in the first place? Equations or a citation would be good here.
DeleteExplained clearly above.
First, bbd, I congratulate you on participating in a scientific discourse.
I've said plenty about science to you on this blog. You either ignore or deny the scientific evidence presented. Stop lying and condescending.
In the model we are discussing there is no need to introduce radiation. We aren't debating AGW here.
DeleteSo if a gravitational force establishes only a temporary temperature gradient, what is the justification for an isothermal equilibrium which contradicts the Poisson formula T = To(P/Po)^(R/Cp) predicting a permanent temperature gradient due to a pressure gradient?
You can't claim perpetual motion errors without either an experiment or a rigorous thermodynamic proof. You have neither.
In the model we are discussing there is no need to introduce radiation. We aren't debating AGW here.
DeleteI can introduce what I wish by way of pointing out the role of radiation in establishing a temperature gradient. It's interesting that you snap instantly into denial mode when confronted by this.
Me: "...if entropy causes the temperature to equalize, why didn't entropy stop the gradient forming in the first place? Equations or a citation would be good here."
Deletebbd: "Explained clearly above."
I disagree. No equations, only hand waving, supposition, etc.
"I can introduce what I wish by way of pointing out the role of radiation in establishing a temperature gradient. It's interesting that you snap instantly into denial mode when confronted by this."
DeleteI call that moving the goal posts. I call invoking "denial mode" a sign of desperation.
I call that moving the goal posts.
DeleteI don't care what you call it. The facts are very simple: gravity does not create an enduring temperature gradient because entropy. Self-evident or it should be. You need radiation for that. I know why you don't like this.
Actually you never made the case for radiation "establishing" a temperature gradient. Daily recycling of solar energy perturbs the gradient which forms naturally as predicted by dT/dz = -g/Cp. Where is your evidence to the contrary. I can/have demonstrated this is NOT settled science other than in your mind. Your move.
DeleteCB
DeleteActually you never made the case for radiation "establishing" a temperature gradient.
Well, the standard position appears to be that gravity doesn't maintain a temperature gradient (Coombes & Laue) yet one exists. So, radiation must be required.
OK, this is progress. And did you notice that Velasco et al. have a different take on the “standard position?” Both papers apply assumptions which affect the validity of their derivations. The issue is far from settled.
Deletehttps://tallbloke.files.wordpress.com/2012/01/s-velasco.pdf
But let’s keep playing, without radiation for now.
Let's not. We already have the reference exchange at Judith's. I don't know what I could add to that and nor do you.
DeleteBBD,
DeleteThe facts are very simple: gravity does not create an enduring temperature gradient because entropy.
As stated, that reads to me as axiomatic. Which would normally be ok, except for the fact that Graeff is explicitly challenging the axiom. Why is note fails empirically is easy for me (Challenger Deep) but I'm flailing to describe theoretically why he has not "proven" the 2nd law (axiom) incorrect.
Self-evident or it should be.
Let me run through it if only to check my own understanding.
The Wikipedia article for Thermodynamic equilbrium begins:
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems. In a system in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, almost or perfectly exactly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.
A thermodynamic system in its own state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long range force field imposed on it by its surroundings.
In non-equilibrium systems, by contrast, there are net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, it is said to be in a metastable equilibrium.
Though it is not a widely named law, it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.
That all makes perfect intuitive sense to me. The final paragraph is where I was going with the baseball analogy: the starting position is at thermodynamic equilibrium, with the ball suspended above "ground level". Remove a partition and allow the ball to fall, it will not heat up until it impacts the surface. The only net quantity that changes is entropy, and it is an increase.
I don't see that there's any way to argue that the ball won't eventually return to its original temperature because temperature of a system cannot change unless internal energy of the system changes.
Did I screw up somewhere? Am I crocked?
Brandon
DeleteDid I screw up somewhere? Am I crocked?
Not that I can see. The problems lie with those who argue that gravity can maintain a temp gradient - something that violates the 2nd law.
I'm not like you. I have no real patience with deniers, here defined as those who deny scientific evidence (PETM strong evidence for GHG-forced hyperthermals; ~50Ma overall Cenozoic cooling trend only explicable in terms of CO2 forcing change; Graeff is obvious nonsense because the abyssal deep isn't hot; increasing IR atmospheric opacity *must* raise height of effective emission and so therefore reduce efficiency of radiative loss at TOA, creating radiative imbalance that warms climate system; entropy trumps gravity over time etc. etc.
And so, I'm not going to argue about this any longer:
A thermodynamic system in its own state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long range force field imposed on it by its surroundings.
When the deep boils, wake me :-)
BBD,
DeleteYou zeroed in on the same "other than temperature" clause in the Wiki article that I did. Everything I've ever read on this subject -- indeed, how it is taught -- points to that being true. Your frustration and impatience is fully understandable. The time I've spent on this thread has kept me from finishing articles on more interesting problems.
Equations or a citation would be good here.
ReplyDeleteSecond Law of Thermodynamics.
This really is childish. But I'll keep playing for fun.
DeleteWhich statement of the 2nd Law were you considering a penetrating insight into the intuitively vague?
Chic,
ReplyDeletePosting out of sequence for scroll.
Are you weary because you don't want to agree with me or because you can't convince me to agree with you?
If I'm to be held to only two choices, it would be more the latter. I'm weary of debating textbook physics in the context of the AGW debate. I'm less tired of that than I am debating the putative motives of climate scientists and activists. One reason why I generally enjoy our discussions is that you stick more to discussing the science and have helped me see places where I've been objectively wrong about something.
Please understand I'm not trying to win an argument.
I want to believe that, and long ago made a conscious decision to take you at your word. I like to win arguments, but accept on principle that discovering truth should be paramount.
Does anybody care what we think.
Who knows. It undeniably true that I'd like to make some difference in the world by writing this blog. Says so right in the About Me blurb. :)
When you are confident you are right and I'm wrong, let me know and I'll go to another classroom.
I have little doubt that the laws of thermodynamics are materially wrong and need to be rewritten. I'm far from confident that all my interpretations and applications of them are correct.
Egads, I'm batting 1.000 today: "I have little doubt that the laws of thermodynamics are NOT materially wrong and DO NOT need to be rewritten."
DeleteI wondered about that and didn't know how to respond. I do want to walk back my implication that nobody cares what we think. Some do, some don't. Some are interested in everyone coming to a consensus on the truth. Some are interested in being on the team with the most members.
DeleteSo how does that relate to the laws of thermodynamics? Truth-seekers will continue to investigate and understand the laws of thermodynamics phrasing them in the clearest and most correct way. Nature hasn't changed, only our understanding of it. However, if we are interested in being on the team with the most members, then we are interested in expressing the laws in ways that most people agree with.
Chic,
DeleteI don't think truth-seekers are bound to take an agnostic position on scientific issues that a "significant" number of other people deeply question. As an extreme example, you'll not catch me seriously entertaining the Earth is on the order of 6,000 years old just because a lot of people have challenged the consensus that it's actually several billions of years in age. Though science has been wrong in the past, and is must still be wrong in many ways today, I believe that consensus generally occurs because the consilience of evidence points more toward the truth. Yes, that's a heuristic, but one which I think overall leads to more productivity in advancing knowledge than less. This is because if one is constantly going to the other extreme and challenging "everything" it has the tendency to get bogged down.
I have a hard time condemning you for your approach when I approve of what you say in principle. In practice, I cannot abide by it either -- I simply don't have the time to work out every piece of scientific conventional wisdom from first principles.
"As an extreme example, you'll not catch me seriously entertaining the Earth is on the order of 6,000 years old just because a lot of people have challenged the consensus that it's actually several billions of years in age."
DeleteSo when the consensus said Earth was 6 ky old, you would have gone with the consensus? Were Copernicus and all the others wrong?
Consilience is faith, not truth-seeking. If you have more important things to work on, let it go. No one is forcing you to get bogged down considering the evidence against the majority opinion in this case.
Consilience is faith, not truth-seeking.
DeleteRubbish, and self-serving rubbish at that. Consilience of evidence is itself evidence that the explanation is likely correct. You seem to be conflating consilience with [scientific] consensus, which arises *from* consilience of evidence and is equally logical, not faith-based. Since you are about a micron away from telling us that 'AGW is a religion' just go for it. Say it out loud.
* * *
What a display of rope-a-doping this thread has been.
Yes, I could have said it better. Consilience of evidence is right up there with circumstantial evidence and concluding causation by correlation. Somewhere between possible and probable.
DeleteDo you believe there is a scientific consensus on AGW?
You don't have to play, if you don't want to.
Do you believe there is a scientific consensus on AGW?
DeleteOf course there is. And if you deny this, you will have placed yourself beyond the scope of reasoned discourse.
Consilience of evidence is right up there with circumstantial evidence and concluding causation by correlation.
DeleteMore rhetoric.
Consilience of multiple lines of evidence is stronger than circumstantial evidence or concluding causation by correlation.
After a few replies to my comments at ATTP, I learned that there would not likely be any reasoned discourse with you. Your faith is too strong.
DeleteYour faith is too strong.
DeleteEvidence-based reasoning. See above.
Chic, part 1;
ReplyDeletePosted out of sequence for scroll.
Note: I've previously been using the term "closed system" when what I've really meant is "isolated system" -- no mass or energy transfers in/out, and no external work being done to it or by it.
In the context of the atmosphere and the propensity to form a temperature gradient, I think it does.
I agree that phase changes are relevant there, but I was talking about a solid baseball in a vacuum specifically so that we can neglect temperature and phase changes.
When we are discussing kinetic energy and temperature of the atmosphere, we should limit ourselves to air molecules, not baseballs.
As I understand the laws of thermodynamics, they apply to all to all phases of matter and forms of energy.
"The argument as I understand it is that absolute position in a gravity well is a determinant of temperature."
We haven't actually clarified that, but I do agree.
Ok good.
More specifically, [temperature] is the average kinetic energy of the molecules at that position.
Yes, I'm good with that definition of temperature.
Who is we and in what context are we changing enthalpy?
"We" being anyone doing thermodynamics problems. My mistake, I had confused internal energy and enthalpy (not for the first time).
When the balls are suspended or laying on the ground, they have zero velocity.
A ball at rest still has kinetic energy due to its temperature.
Air molecules are moving all the time and do not require any new energy entering the system.
Sure. Since heat doesn't move in or out of an isolated system. I'm not proposing anything different with the baseball analogy.
The best I can do is surmise you wanted me to see that a ball in a vacuum can't warm as it falls.
Yes.
"Think about the 1st law when you compose your answer."
Now I see where you were going. The ball is warming, so where is the extra energy coming from?
Bingo.
There should be another ball going up and cooling so that the net internal energy change is zero.
The opposing movement constraint is only true of an isolated isochoric system containing a fluid. It might be productive to think of this in terms of LTE, with which I believe you agree. Why does LTE tend to spontaneous occur under adiabatic conditions?
"A ball at rest still has kinetic energy due to its temperature."
DeleteHmm. I really hate these ball analogies.
"The opposing movement constraint is only true of an isolated isochoric system containing a fluid."
Or a gas, which is what our mock atmosphere is, an isolated isochoric adiabatically-constrained system. And yes, I believe LTE would have to be the case. How could it not be if we have dQ = 0.
Chic,
DeleteSo my argument is thus: if LTE spontaneously evolves in an isolated system left to its own devices, and LTE entails a spatially homogeneous temperature distribution, it stands to reason that when the entire system is at thermodynamic equilibrium, the entire system must also be in thermal equilibrium with itself, i.e., must have a homogeneous temperature distribution.
Your logic is circular. LTE is local thermodynamic equilibrium, not necessarily spatially homogeneous temperature distribution. Otherwise everything would always be at the same temperature.
DeleteLTE means that at every level, the net energy in and out is zero. It doesn't mean that every level has to have the same energy. More importantly it doesn't always exist. For example when new energy enters a system, LTE is disturbed. Turning on gravity in a closed system will also disturb LTE, because potential and kinetic energy will be redistributed until a new temperature gradient forms where every level is again at LTE.
Chic,
DeleteYour logic is circular.
We'll see about that.
LTE is local thermodynamic equilibrium, not necessarily spatially homogeneous temperature distribution.
Well great, now you're challenging a central tenet of LTE, which is spatially homogeneous temperature.
Basically all bets are now off. I'll forge ahead regardless.
Otherwise everything would always be at the same temperature.
No, things are different temperatures because real world systems are hardly ever at thermodynamic equilibrium. LTE is how we break down parts of the system and assume approximate thermodynamic equilibrium for tractable analysis.
LTE means that at every level, the net energy in and out is zero.
Yes, that's one interpretation. Another is an adiabatic process, like an expanding/compressing gas entailing no other energy exchanges with the immediate environment. T changes near-instantaneously as a function of dP to establish a new LTE.
It doesn't mean that every level has to have the same energy.
Correct, because dPe/dz <> 0.
More importantly it doesn't always exist. For example when new energy enters a system, LTE is disturbed.
Obviously.
Turning on gravity in a closed system will also disturb LTE, because potential and kinetic energy will be redistributed until a new temperature gradient forms where every level is again at LTE.
You really don't see how you've just contradicted yourself, do you: "[LTE] doesn't mean that every level has to have the same energy."
"The meaning, and requirement, of LTE (local thermodynamic equilibrium) is often misunderstood.
DeleteIt does not mean that a body is at the same temperature as its surroundings. Or that a body is all at the same temperature (isothermal)."
http://scienceofdoom.com/2010/10/24/planck-stefan-boltzmann-kirchhoff-and-lte/
Chic, part 2;
ReplyDeleteAdiabatic: dQ = 0. dU = dW = pdV + Vdp.
I plead muddled thinking due to fatigue and retract my quibble.
By that logic, the ideal gas law is useless.
Buh? PV = nRT
P,V and T are pressure, volume and temperature respectively.
Graeff explicitly excludes pressure in his model, which is fine for a system with no macro-movements of matter. That's not where I think he messes up.
That is either wrong or misstated. His theoretical calculation was 0.04 K/m and his results were 0.012 and 0.050 K/m depending on whether the tube contained a convection suppressor.
Which puts the range of temperature differential between surface and bottom of Challenger Deep at 130.88 to 545.35 K. Even the low end of that range is wildly implausible.
Should we abandon the dT = lamda x ln (C/Co) equation because it no longer applies at low concentrations of CO2?
No, because it's not a law. It's a log-linear approximation (read: curve-fit) of model integrations over temperatures, pressures, densities and emissivities of varying atmospheric component constituents which by their very nature defy closed form solutions. It doesn't work for very high concentrations of CO2 either.
Graeff's theoretical derivation 100% rests on linear models of physical processes. They're definitional:
potential energy: Ep = -M x g x H
energy available: Eavail = M x cGr x T
potential energy = energy available: Ep = Eavail = M x g x H = M/cGr * T
solve: T = g x H / cGr = TGr
.... waaaaait a tick, shouldn't that be: -M x g x H = M x cGr x T ?
solve: T = -g x H / cGr = TGr
Yes, that's better, and what he uses later. Next he writes:
cGr is not the normal specific heat of the liquid in question as the acceleration through g affects only the vertical speed of the molecule. The potential energy is converted only into an increase of their speed in their lateral downward direction while no energy is used or distributed in accordance with the equipartition of energy to the other degrees of freedom like the additional two lateral directions left to right and front to back or towards the rotational energy in molecules with more than one atom. Therefore
cGr = c / n
with c = specific heat; n = number of degrees of freedom
We therefore get
TGr = -g x H / cGr = -g x H / (c/n)
With this formula we can calculate the value for water as
No. of degree of freedom for water 18
TGr -0.04 K/m
Now it seems to me he's forgetting that a molecule accelerating downward due to g in an isochoric system must be exactly balanced by a molecule accelerating upward against g. So we MUST write:
TGr = [-g x H / (c/n)] + [-g x H / (c/-n)]
We don't even need to know the values of the parameters to find the answer.
Your job is to explain why Graeff's experiments contradict the isothermal hypothesis.
Because even in the single-body solid baseball problem, ΔU = ΔEₖ. Always. Gross infidelity with real-world observation is the icing on the cake.
Errata: "ΔU = ΔEₖ. Always."
DeleteShould be ΔU = -ΔEₖ, hence ΔU + ΔEₖ = 0. And I should probably stipulate that "always" means in an adiabatic process, e.g., an object on a ballistic trajectory in a vacuum in thermal equilibrium with its container.
I'm now off to soak my head in a bottle of bubbly.
There you go again with the Challenger Deep nonsense. Come up for air. You can't expect the theoretical relationship predicting a thermal gradient to apply over every range of every variable. If you insist on that, then you have to throw out the ideal gas law and the hydrostatic equation, because both are involved in the derivation of a temperature gradient due to gravity. And from the temperature profile of the whole atmosphere, you can see the linear lapse rate only applies to the lower troposphere. Why do you think that is?
DeleteRe: U = E, are you saying U is another symbol like E to define internal energy or do you mean to make a distinction? Some subscripts or superscripts may not be showing up on my screen.
DeleteRe Graeff's derivation and your comment, "Now it seems to me he's forgetting that a molecule accelerating downward due to g in an isochoric system must be exactly balanced by a molecule accelerating upward against g. So we MUST write:
DeleteTGr = [-g x H / (c/n)] + [-g x H / (c/-n)]
We don't even need to know the values of the parameters to find the answer."
The discussions at Climate Etc. and elsewhere indicate the upward and downward velocities of molecules may not balance. This would be more of an assertion than a fact. There is lot I need to learn, eg., about equipartition principle and virial theorem, before I can sort out the calculus involved. It will be awhile.
Comparing lower troposphere to Graeff's experiment and the oceans is apples and oranges. You already should already know why I think lapse rate happens in the lower atmosphere, gas expansion/compression due to solar-driven convection. Such vertical movements in the oceans below the thermocline are relatively slow, and in any case would not be expected to create compressive heating/cooling like we see in gasses. Graeff's lab results and theoretical derivation suggest that the gravito-thermal effect should be significant, if not dominant, over diffusive and convective heat exchanges in the lower ocean. Clearly, they are not. I see your come up for air comment with get your head out of the sand, sir.
DeleteI have to pop out for an hour, when I get back I'll dig into your other more substantive comments elsewhere. Cheers.
You can't expect the theoretical relationship predicting a thermal gradient to apply over every range of every variable.
DeleteCome off it. You can expect an observational result that is at least in line with the hypothesis. But observations flatly contradict Graeff's stuff.
Chic,
DeleteRe: U = E, are you saying U is another symbol like E to define internal energy or do you mean to make a distinction? Some subscripts or superscripts may not be showing up on my screen.
I'll keep in mind that your browser may not do Unicode. dU = -dEk, thus dU + dEk = 0, where dU is change in potential energy and dEk is change in kinetic energy.
The discussions at Climate Etc. and elsewhere indicate the upward and downward velocities of molecules may not balance.
Indeed.
There is lot I need to learn, eg., about equipartition principle and virial theorem, before I can sort out the calculus involved.
This is how I've intuitively sorted it for the moment. If average downward and upward velocity are not equally distributed, the system cannot possibly be staying at a constant volume UNLESS the pressure gradient is constantly changing. Neither case is compatible with an isolated system at rest, in thermodynamic equilibrium with itself.
Obviously I can't change your minds on the inappropriateness of extending a controlled experiment to test a hypothesis to an uncontrolled system at conditions wildly different from the controlled experiment. And apparently it is too much to ask that you explain why we should accept the ideal gas law when it doesn't apply to the whole atmosphere and the hydrostatic balance equation when it doesn't apply to the whole ocean.
Delete"Graeff's lab results and theoretical derivation suggest that the gravito-thermal effect should be significant, if not dominant, over diffusive and convective heat exchanges in the lower ocean."
Nobody said anything about dominance! You are making too much out of this. I sense fear that if the gravito-thermal effect is shown to be correct, your whole support system will collapse. Relax, it doesn't mean convection isn't dominant and that increasing CO2 doesn't raise the EEL and all the rest. All Graeff's experiments show is that a temperature gradient forms in a 10 cm tube of water in gravitational field apparently without the need of energy input or convection. Your arguments are not scientific because you have no data to the contrary and, unless you are hiding something, like me you haven't vetted the several papers that claim an isothermal gradient.
Brandon,
I was under the impression that U is internal energy which is the sum of PE and KE. The whole discussion rests on this. Please let me know your source, if I'm wrong.
Also I have been considering volume constant in our hypothetical atmosphere and the real atmosphere. We should make a distinction when volume needs to change. I know that some of the discussions have compared the difference between "capping" a column of air and leaving it open. When considering systems with no energy flux, I can't see where volume needs to change. The gradient is either isothermal or its not.
Chic,
DeleteObviously I can't change your minds on the inappropriateness of extending a controlled experiment to test a hypothesis to an uncontrolled system at conditions wildly different from the controlled experiment.
Nothing in Graeff's paper suggests that wildly different temperature or pressure would make a whit of difference. My arguments don't only rest on the disconnect between lab and real-world observation, but also the fact that his theoretical derivation ...
TGr = [-g x H / (c/n)]
... effectively turns gravity into a source of energy because he leaves out ...
+ [-g x H / (c/-n)]
Not accounting for the fact that in a fluid at rest at constant volume, 1/2 of molecules are moving UP is a fatal flaw. IOW, Graeff is challenging the 2nd law by (apparently unwittingly) violating the 1st law. It's a glaring error, and I'm a bit embarrassed I didn't catch it right off.
And apparently it is too much to ask that you explain why we should accept the ideal gas law when it doesn't apply to the whole atmosphere and the hydrostatic balance equation when it doesn't apply to the whole ocean.
Firstly, the ideal gas law is (or should be) taught with the explicit understanding that ideal gasses don't actually exist. Secondly, your argument seems tangential to me because it's not at all clear how it relates to Graeff. Thirdly, I must have missed the discussion about where hydrostatic equilibrium breaks down when applied to the whole ocean.
Nobody said anything about dominance!
I thought I made it clear that it's my expectation based on having done the math and pointing out that the predicted temperature differential between deep ocean and surface is on the order of hundreds of K.
I sense fear that if the gravito-thermal effect is shown to be correct, your whole support system will collapse.
Bollocks. Who wouldn't want such a "free" energy source to be real? Especially one such as I looking for alternatives to fossil fuels??
I was under the impression that U is internal energy which is the sum of PE and KE.
Apparently I got my symbols confused, so I'll rewrite it thus:
dPe = -dKe, dPe + dKe = 0.
When considering systems with no energy flux, I can't see where volume needs to change.
I agree. To be absolutely clear, that is what I thought I have been arguing. Your previous statement ...
The discussions at Climate Etc. and elsewhere indicate the upward and downward velocities of molecules may not balance.
... demands that either volume has changed, or that the pressure gradient is changing.
The gradient is either isothermal or its not.
When average velocity at all levels is constant, an isothermal gradient can be the only result since temperature and velocity are proportional.
“I must have missed the discussion about where hydrostatic equilibrium breaks down when applied to the whole ocean.”
DeleteNo, I just didn’t bother to check! My bad. Pressure is proportional to depth all the way down.
I don't know of anyone else who has a problem with Graeff's derivation. It's only the result that people don't get.
"[upward and downward velocities of molecules not balancing]... demands that either volume has changed, or that the pressure gradient is changing."
DeleteNo, the up/down differential is precisely the mechanism which would cause an isothermal system to form a gradient in a gravitational field.
"When average velocity at all levels is constant, an isothermal gradient can be the only result since temperature and velocity are proportional."
Temperature is proportional to velocity squared, no? What does this have to do with the average velocity changing from one level to next once a temperature gradient has been formed in a gravitational field?
Chic,
DeleteNo, the up/down differential is precisely the mechanism which would cause an isothermal system to form a gradient in a gravitational field.
Yes of course. But a velocity differential only happens when:
1) Volume is changing
2) Volume is constant, but hydrostatic equilibrium has not been achieved.
Neither one of those cases represents an isolated constant-volume system at rest.
What does this have to do with the average velocity changing from one level to next once a temperature gradient has been formed in a gravitational field?
My argument is that if average velocity is not the same for any given level, work is being done to or by the system, and it is therefore not in thermodynamic equilibrium with itself.
"But a velocity differential only happens when:
Delete1) Volume is changing
2) Volume is constant, but hydrostatic equilibrium has not been achieved."
That makes sense. I "intuit" at least both are possible.
"My argument is that if average velocity is not the same for any given level, work is being done to or by the system, and it is therefore not in thermodynamic equilibrium with itself."
That is a circular argument. I can just as easily argue that if the temperature gradient is initially isothermal and the average velocity is the same at every level, gravity will change the velocity distribution and the temperature gradient until the system establishes its normal equilibrium temperature gradient.
Unless, you have a burning issue to resolve, I think it would be a good time to take a break. There are too many equations, conditions, and assumptions to sort out in papers cited on Climate Etc that are new to me.
Re a ball at rest has kinetic energy: Feynman says, "We already have one of the theorems of statistical mechanics, namely, the mean value of the kinetic energy for any motion at the absolute temperature T is kT/2 for each independent motion, i.e., for each degree of freedom." http://www.feynmanlectures.caltech.edu/I_40.html
ReplyDeleteThe implication here is there are more than one object moving with a kinetic energy = mv^2/2. On average, all the objects are moving and their kinetic energy proportional to T. However, a single object at rest is not moving and therefore no kinetic energy. It does have energy defined by MCpT.
Chic,
DeleteHowever, a single object at rest is not moving and therefore no kinetic energy.
Read your Feynman quote again: "We already have one of the theorems of statistical mechanics, namely, the mean value of the kinetic energy for any motion at the absolute temperature T is kT/2 for each independent motion, i.e., for each degree of freedom."
Even in solids, molecules have degrees of freedom to move. And they do by way of vibration. Were it not so, all solids would be at absolute zero. IOW, Cp is (at least partially) determined by the mean DoF of the atoms/molecules in a given material for ANY phase of matter.
It helps me to think about this in terms of frames of reference. Temperature is proportional to kinetic energy of an object relative to itself. We don't need another object in the system for that definition to work.
OK, I give up. Now how does this relate to your "Gas in a closed system" post again?
DeleteI may be losing track of the relevance myself. I'm kidding. Mostly.
DeleteWhy should a block of ice have a different amount of potential energy due to gravity than an equal mass of liquid water at the same altitude?
It should not. But as you have previously schooled me, their average kinetic energies are different due to their different temperatures even though their bulk volumes are not moving.
DeleteI think I see the point. You are questioning a difference in potential energy due to temperature. I don't believe there is. But there is a difference in kinetic energy which is a direct proportionality. So the simplest argument in favor of a temperature gradient is the presence of energy gradients: dU/dz = dPe/dz + dKe/dz. There is no change in temperature with dPe/dz. There is a temperature decrease as kinetic energy decreases with altitude.
I’m at a loss to see how the virial theorem applies to the gravito-thermal question. From Wikipedia:
ReplyDelete"The significance of the virial theorem is that it allows the average total kinetic energy to be calculated even for very complicated systems that defy an exact solution, such as those considered in statistical mechanics; this average total kinetic energy is related to the temperature of the system by the equipartition theorem. However, the virial theorem does not depend on the notion of temperature and holds even for systems that are not in thermal equilibrium."
So with our system being a gas or liquid exposed to gravity and isolated from net energy flux, knowing the kinetic energy of the whole system does not help. How the kinetic energy of the top differs from that of the bottom is the question we are investigating.
The same objection applies to the equipartition theorem. Again from Wikipedia:
"The equipartition theorem makes quantitative predictions. Like the virial theorem, it gives the total average kinetic and potential energies for a system at a given temperature, from which the system's heat capacity can be computed. However, equipartition also gives the average values of individual components of the energy, such as the kinetic energy of a particular particle or the potential energy of a single spring. For example, it predicts that every atom in a monatomic ideal gas has an average kinetic energy of (3/2)kBT in thermal equilibrium, where kB is the Boltzmann constant and T is the (thermodynamic) temperature. More generally, it can be applied to any classical system in thermal equilibrium, no matter how complicated."
Now that I understand these theorems, I should be able to follow the discussion at Climate Etc. It seems that there are at least two ways to approach the problem. One is to find the change in kinetic energy of the system from top to bottom and determine whether it differs from zero. Another approach would be to divide the system into two parts and determine whether the top has less kinetic energy than the bottom. This assumes that the temperature at any point is equal to the average kinetic energy of the molecules at that altitude or height in a 10 cm tube of water.
If I remember correctly, some of the online discussion involves comparing the upward and downward velocities of the molecules. Seems to be a more complicated approach.
Chic,
ReplyDeleteIf I remember correctly, some of the online discussion involves comparing the upward and downward velocities of the molecules. Seems to be a more complicated approach.
It seems the simplest approach to me. If up/down velocities are not equal at any level, either pressure or volume must be changing.
There IS a pressure gradient forming/formed due to gravity. There is no need for volume to change. Non-sequitur.
DeleteThe reason I said the velocity approach is more complicated is because it requires so many assumptions and deep calculus. I am working on an alternative argument with less complicated integration.
Chic,
DeleteThere IS a pressure gradient forming/formed due to gravity.
Let me try to clear this up again. In an isolated fluid at rest, pressure at any given level will remain constant. That does NOT mean that dP/dz <> 0.
The reason I said the velocity approach is more complicated is because it requires so many assumptions and deep calculus.
It's quite intuitive for me without having to write out the calc. If average velocity up <> average velocity down, we don't have a hydrostatic equilibrium. In a gas, you bet your life that dT/dz <> 0 in that circumstance -- it's no longer a system at rest, and the only way for it to sustain that state perpetually is if it's no longer a closed system and has a perpetual input of energy.
"In an isolated fluid at rest, pressure at any given level will remain constant. That does NOT mean that dP/dz <> 0."
DeleteThe pressure at any level remaining constant doesn't constrain the gradient. It could be isobaric or not. Is that what you mean?
"If average velocity up <> average velocity down, we don't have a hydrostatic equilibrium."
It may be intuitive to you, but I don't know if the average velocity means the same number of molecules up and down have the same average kinetic energy or if few molecules with greater velocity in one direction balance the greater number of slower molecules going the other way. I suppose it has to be the former otherwise the mass balance would violate the hydrostatic equilibrium. That still doesn't mean that the system is isothermal as the atmosphere clearly is not isothermal ever and the hydrostatic equation would apply in either case, would it not?
"and the only way for it to sustain that state perpetually is if it's no longer a closed system and has a perpetual input of energy."
Your argument is an assertion without proof. There is a week's worth of similar discussion on Climate Etc. on this. I can't really respond properly in any case because I don't know what you mean by <>. Use English.
Chic,
ReplyDeletePosted out of sequence for scroll.
It should not. But as you have previously schooled me, their average kinetic energies are different due to their different temperatures even though their bulk volumes are not moving.
Assuming their temperatures are different of course.
I think I see the point. You are questioning a difference in potential energy due to temperature. I don't believe there is.
For good reason, as kinetic and potential energies are quite independent of each other: kinetic energy being a function of temperature (and/or bulk motion relative to an external reference frame) and potential energy in this context is a function of vertical distance from some external reference point along the gravity axis.
And yes, this is a central point.
So the simplest argument in favor of a temperature gradient is the presence of energy gradients: dU/dz = dPe/dz + dKe/dz.
I agree with that relationship, but not with the conclusion that it argues in favor of a temperature gradient. See just below.
There is no change in temperature with dPe/dz.
BINGO!
Back to the falling ball example, dU/dz = 0 in free-fall. dT = 0 until the ball impacts some other object. At any given point in the ball's trajectory until impact, dPe/dz = -dKe/dz. That cannot be true if dT <> 0 because dKe = 3/2 * R/Na * dT (where R is the gas constant, and Na is Avogadro's number).
A free-fall situation is non-reversible and you'll have heat lost to the surroundings. It's just not a good proxy for the abiabatic atmosphere we are considering. I can't comment on ball analogies anymore.
ReplyDeleteIs <> less than or greater than, but not equal to?
Chic,
ReplyDeleteIs <> less than or greater than, but not equal to?
Correct. Many computer programming languages use <> to mean "not equal to", as do spreadsheet programs. I sometimes forget not everyone programs computers.
Over on Brandon's "Difference Beteween Fraud and Farce, Reflux" post, BBD challenged me to a game of gotcha on the gravito-thermal effect. I think it started with this comment:
ReplyDeleteThe flaw in the gravity argument is that constant gravity cannot create energy. It can only redistribute it. And in time, entropy will unpick that redistribution.
Those familiar with the GTE should realize it doesn't propose that gravity creates any new energy. This is a construct created in BBD's fertile mind. It does propose that an isothermal column of air subjected to a gravitational field will orient itself with a temperature gradient so that entropy will be maximal.
So without further ado, I'll put the ball back in BBD's court and see if wants to start over, continue where he left off, or just pack it in.
To review the gravito-thermal effect (GTE) history, Loschmidt claimed that the equilibrium temperature of a gas column subject to gravity should be lower at the top of the column and higher at its base, whereas his contemporaries Maxwell and Boltzmann, argued the column would have to be isothermal. Apparently, no one reported an experimental test of the GTE until Dr. Roderich Graeff in 2007. Brandon's post and the subsequent comments above discuss those results and their consequences. Meanwhile several discussions erupted in the climate blogosphere over papers more or less based on GTE theory. This link provides a keyhole to those papers:
ReplyDeletehttps://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/
Prof. Robert G. Brown presented his version of the Maxwell/Boltzmann argument here:
http://wattsupwiththat.com/2012/01/24/refutation-of-stable-thermal-equilibrium-lapse-rates/
Judith Curry dedicated a special post on it here: https://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/
Some, as Brandon demonstrates above, see GTE as a violation of the 2nd Law of Thermodynamics. Others base their objections on conceptual arguments. For my part I'm still trying to work out the various approaches with a mathematical explanation. I have the benefit of drawing on the work of several others. What is common to all their papers is a detailed explanation of the system being modeled. Obviously there is a volume of gas in a gravitational field and the pressure/density gradient that comes with it. Additionally the system can be constrained in several alternative ways. It can be an adiabatic system which has by definition no net heat transfer, but could be defined with or without a constant flow in and out. Others have applied isoentropic and isoenergetic constraints, as well. So it was not surprising to me to see so much confusion over the matter. Anyway, back to the game.
See https://www.researchgate.net/publication/337915638_Understanding_Josef_Loschmidt's_Gravito-_Thermal_Effect_and_thus_Why_the_Radiative_Forcing_Greenhouse_Hypothesis_is_False
ReplyDelete