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Imperfections of classical thermodynamics

  1. Sep 6, 2008 #1
    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

    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:
    Can it be changed into electricity without difference of
    The problem is with diodes which looks like Maxwell's demons...
  2. jcsd
  3. Sep 6, 2008 #2
    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.
  4. Sep 6, 2008 #3
    Yes everything besides hot gas all the time has T=0.
    They will appear photons, but they will vanish asymptotically.
    With time the temperature of gas reduces also asymptotically to 0, so it's entropy is reduced.
    So after infinite time photons vanishes - we have only gas between separators with T=0 and two mirrors with kinetic energy - the entropy of this system achieved minimum - is smaller than initial by entropy of heat of initial gas.
    Entropy should change continuously, so there exists finite time for which entropy would be already smaller.
    In other words we've changed the energy stored in heat of the gas into ordered kinetic energy of mirrors, which can be easily changed into work.

    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.


    If You don't like idealized unpractical models, there are also two very practical: one for us and one for organisms which lives hundreds of meters below and have extremely weak access to chemical energy, but they have plenty of energy around in heat (and tectonic vibrations...).

    Both of them uses microscopic mechanisms.
    Usually released microscopic energy quickly escape and change into heat.
    We can use that sometimes these releases are spatially localized, so local 'mechanisms' can help to put this energy into more stable form like potential energy of electron in a circuit or chemical energy of some molecule (like ATP).

    The first example uses that thermal infrared can not only be emitted/absorbed by single molecules, usually using their vibrational/rotational energy, but also for example by a free electron in a circuit - by nanoantenna.
    The energy of this electron when it absorbs photon is relatively huge - it's highly improbable that it gain this energy thanks of thermal energy only and emit a photon - absorption will dominate here.
    The problem is to rectify this electricity, but we can use that it is highly localized.
    This electron will naturally equilibrate its energy with environment, but this process is relatively slow, require some length of way through circuit.
    So the nearer electron is to the antenna, the higher average energy it statistically have.

    The whole electricity generator could look like (parallel):
    and electrons should more likely go left, because after absorbing a photon, they equilibrate their energy while going through conductor.
    If the antennas are printed as in the work of prof. Novack I've linked, required threshold could be just narrowing/ gap.

    Before going to the second example, let's think about crystallization.
    It obviously increases ordering (reduce entropy), but total entropy doesn't decrease because the binding energy (difference between energy of the molecule in solution (larger) and after binding (smaller) ) is stored in unstable form of energy (kinetic/vibration/rotation energy) that quickly equilibrate its energy with environment, increasing heat/entropy.
    But what if this binding energy would be stored in stable form, like chemical energy (ATP)/conformation ? Such energy stored in ATP can be used in order way to create work (for example using myosin).
    Remember that joining to growing 'crystal' is localized reaction - could use help of an enzyme as catalyst, which additionally stores part of binding energy in stable form like in ATP.

    The second example uses just two molecules instead of whole crystal.
    Let say that we have two molecules(A,B) which has larger total energy
    separated(E1) than when they are bind (E2
    Additionally there is energy barrier between these states (as usual).

    Now when they are bind in solution, their thermal energy statistically
    sometimes exceed the barrier and they split, taking require energy from heat -reducing temperature!
    But to bind them back, they not only have to reach the barrier, but
    they have also to find each other in the solution - it's not very
    likely, so statistically concentration of AB is relatively small
    comparing to concentration of separated molecules.

    Now we will need a catalyst which reduce the barrier, but then use the
    energy difference for example to bind ADP and phosphate.
    For example it catches all required molecules and uses just gained energy or energy stored in own structure to take A and B closer, to make them reach the top of the barrier, then use energy they produce to bind ADP + P and restore own energy.

    I know - this enzyme would work in both directions, but concentration
    of AB should be relatively small, it doesn't have to use whole binding energy, such that the wanted direction should dominate.
    Organisms can enforce required optimal concentrations.

    Returning to thermodynamics - it's derived averaging local behaviors.
    It's kind of mean field approximation - forgets about correlations ... which can give very different behaviors/interactions ... like different stability of stored energy.
    I agree that it can pass simplified models or tests like Maxwell's demon, but it's far from being proved to be universal property.

    Remember that 2nd law is not required to forbid machine which creates work for infinity, conservation of energy/momentum already forbids it.
    2nd law forbids only ordering energy stored in chaotic thermal movement.
    But if this law isn't always true, there would be other counter intuitive implications, like that computation could need no energy...
    But remember that quantum computation would theoretically also offer it - computation is invertible - doesn't use energy. Energy is requiredonly to read result.
  5. Sep 6, 2008 #4


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    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.

    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.
  6. Sep 6, 2008 #5


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    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.
  7. Sep 6, 2008 #6


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    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.
  8. Sep 6, 2008 #7


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    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.
  9. Sep 6, 2008 #8
    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.


  10. Sep 6, 2008 #9


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    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.
  11. Sep 6, 2008 #10
    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).


  12. Sep 7, 2008 #11


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    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.
  13. Sep 8, 2008 #12


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    I'll back up Mapes here. Entropy of the universe will always increase. That's why it has the word Law in the name. Therefore, as soon as the surroundings of your system are included, you'll see the entropy increase (at best it would theoretically stay the same assuming a reversible process but we all know they don't exist in reality).

  14. Sep 8, 2008 #13
    Light can cause pressure on an object. So light bounces from 1 place to the other which keeps exerting pressure forever back and forth causing some infinitely small amount of measurable energy. It never stops... until the reflector breaks.

    I love playing the devil's advocate to see how good others can argue what they learned.
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