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Thermodynamic Postulates

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider relationship for a thermodynamic system:

    S=A[UVN]^d , where A is a constant and d a real number.

    I need to explain why d=1/3 is the only allowed value consistent with the postulates of thermodynamics.

    3. The attempt at a solution

    I'm having a hard time determining why this is the case from the postulates.
     
  2. jcsd
  3. Sep 5, 2013 #2
    You should start by writing down the postulates you think could be relevant.
     
  4. Sep 5, 2013 #3

    berkeman

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    Staff: Mentor

    Please check your PMs. You must write out the relevant equations and show your attempt at solving this problem.
     
  5. Sep 5, 2013 #4
    This is a problem involving units. The units on both sides of the equation must match.
     
  6. Sep 10, 2013 #5
    I don't have an attempt because I'm completely stumped.

    The units on the left hand side are J/K, and on the right they are J^(1/3) m - which don't match.

    I can't see anything in the postulates that helps either:

    P1 - There exist equilibrium states characterised completely by U, V, N.
    P2 - There exists a function of the macroscopic variables, the entropy, which is maximised when a constraint is removed
    P3 - Entropy is additive over subsystems, and is a continuous and differentiable and increasing function of the total internal energy U
     
  7. Sep 10, 2013 #6

    vela

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    Considering you don't know the units of A, it's pointless to match units between sides.

    Can you give an example of what the third postulate means?
     
  8. Sep 10, 2013 #7
    While you can't match units directly because of the A term you can still make progress by requiring that the entropy be extensive.
     
  9. Sep 11, 2013 #8
    This is important.
     
  10. Sep 11, 2013 #9
    U, V, N, and S are all extensive properties. So, if you double U, V, and N, what has to happen to S?
     
  11. Sep 11, 2013 #10
    I know that for a constant:

    S(kN,KV,KU)=kS(N,V,U)

    But I'm not sure how that restricts the power to a third.
     
  12. Sep 11, 2013 #11
    Substitute kU, kV, and kN, and kS into your thermodynamic relationship, and see what you get.
     
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