Imperfections of classical thermodynamics

by Jarek Duda
Tags: classical, imperfections, thermodynamics
 P: 2 Here is simple counter example to 2nd law of thermodynamics - converting heat into work. Everything is in vacuum, without gravity: Take a tube with interior covered with mirror. Fix two transparent separators inside and place hot gas between them. Now place two mirrors on both sides, which can freely move inside the tube. Some of thermal infrared photons will be bounced by a mirror - giving part of own momentum, thanks of momentum conservation law. The heat of the gas will be slowly converted into momentum of mirrors, which can be converted into work. Finally after infinity time temperature will drop to zero and there will be no photons. Above example uses that despite that kinetic energy of molecules behave randomly, each one has specific movement/oscillation, which energy can be changed into ordered one - electromagnetic oscillation of photon. Thermodynamics of photons is very 'simplified' - they don't interact with each other, so they don't equilibrate their energies, increase their randomness. They also vanish when their energy goes to 0. Are there any problems with this counter example? The real question is if it can be used in practice - there are made nanoantennas to catch thermal infrared: www.physorg.com/news137648388.html Can it be changed into electricity without difference of temperatures? The problem is with diodes which looks like Maxwell's demons...
 P: 2,141 Converting heat completely to work is possible if there is a heat reservoir at temperature 0K. For your example to work, you have to assume that everything is kept at zero temperature, so there is no contradiction with the second law.
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Imperfections of classical thermodynamics

 Quote by Jarek Duda Here is simple counter example to 2nd law of thermodynamics - converting heat into work.
As Count Iblis has pointed out, this is not a counterexample. If one's cold reservoir is at 0K, as it is in your thought experiment, then the Second Law predicts 100% efficiency at extracting thermal energy in the form of work.

 Quote by Jarek Duda With time the temperature of gas reduces also asymptotically to 0, so it's entropy is reduced.
I'm going to disagree with this. You could just as well argue that since each photon heads off into the void, the number of possible microstates (= entropy) goes to infinity. The Second Law predicts that entropy tends to increase, and there's no reason to disbelieve that here.

If you're going to assert that the Second Law is incorrect, the place to do it is the Independent Research forum; this forum is for discussing issues of consensus physics.
 Sci Advisor P: 7,408 You did not prove that all the heat is converted into work. Is it possible that some of the thermal photons actually end up heating the mirrors instead? Once the mirror starts heating up, it will also start to give off thermal photons, some of which will be reabsorbed by the gas.
P: 7,408
 Quote by Jarek Duda For such idealized models we can assume that mirrors are perfect separators for photons - doesn't absorb heat, but thanks of momentum conservation they absorb some momentum and so energy as kinetic energy.
Because the thermal photons are random, you won't be able to predict the exact speed and direction in which the mirror will move, so you will not be able to extract work with 100% efficiency from the mirror's momentum.
 Sci Advisor P: 7,408 Your overall framework is correct (in classical mechanics). If we were God and knew the position and momentum of every molecule with absolute precision, there would be no thermodynamics. Why Maxwell's demon doesn't work is a deep question with partial solutions given by Szilard and Brillouin, and solved completely only about 50 years ago by Landauer and Bennett. It turns out that Maxwell's demon can violate the second law as long as he does not erase information. But if the demon runs out of memory and erases information, then entropy increases.
P: 303
 Quote by atyy Because the thermal photons are random, you won't be able to predict the exact speed and direction in which the mirror will move, so you will not be able to extract work with 100% efficiency from the mirror's momentum.
As the distance between the source and the mirror increases, the direction of the incident photons becomes less random. At infinity, the radiated energy would essentially be a plane wave as far as the mirror is concerned.

Regards,

Bill
P: 7,408
 Quote by Antenna Guy As the distance between the source and the mirror increases, the direction of the incident photons becomes less random. At infinity, the radiated energy would essentially be a plane wave as far as the mirror is concerned. Regards, Bill
At infinity, your mirror must be infinitely large for it to absorb all the incident plane wave. So it will be infinitely heavy, and will not move, and cannot be used to do work.

Or if it is not infinitely large, it will not absorb all the heat from the gas, and so you will not be converting all the heat into work.
P: 303
 Quote by atyy At infinity, your mirror must be infinitely large for it to absorb all the incident plane wave. So it will be infinitely heavy, and will not move, and cannot be used to do work. Or if it is not infinitely large, it will not absorb all the heat from the gas, and so you will not be converting all the heat into work.
Correct on all counts. I did not mean to imply that the mirror would receive all of the radiated energy - just that what energy it did receive (at infinity) would all be propogating in essentially the same direction relative to the mirror (hence, plane wave).

Regards,

Bill
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 Quote by atyy Your overall framework is correct (in classical mechanics). If we were God and knew the position and momentum of every molecule with absolute precision, there would be no thermodynamics. Why Maxwell's demon doesn't work is a deep question with partial solutions given by Szilard and Brillouin, and solved completely only about 50 years ago by Landauer and Bennett. It turns out that Maxwell's demon can violate the second law as long as he does not erase information. But if the demon runs out of memory and erases information, then entropy increases.
I'll step in again here to defend the Second Law, which only says that entropy tends to increase. We shouldn't consider a temporary, unsustainable decrease in entropy to be a violation, just a temporary, unsustainable decrease in entropy.
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