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Thermodynamic Potentials in Proper Variables

  1. Nov 19, 2015 #1
    1. The problem statement, all variables and given/known data
    A solid has energy (for one mole):

    ##U_1 =\frac{S^2}{a_1}+b_1V(V-2V_0)##

    Write H, F, and G in terms of their proper variables.

    2. Relevant equations

    Maxwell's relations and

    3. The attempt at a solution

    H, for example:

    I have tried writing dV as a sum of partial derivatives times total differentials:

    ##dV=\frac{\partial V}{\partial S}dS+\frac{\partial V}{\partial P}dP##

    I have no idea how to get V in terms of S and P.

    I have similar problems for the other cases.

    Thanks for any help!
  2. jcsd
  3. Nov 19, 2015 #2


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    Under relevant equations you mentioned Maxwells equations.
  4. Nov 19, 2015 #3
    Maxwell's relations. I still don't know how that gives anything concrete.
  5. Nov 19, 2015 #4


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    Well, probably the first step is to find pressure as ##p=-\frac{\partial U}{\partial V}|_S## and an analogous relation for temperature. For the rest, you don't even need differentials.
    Last edited: Nov 19, 2015
  6. Nov 19, 2015 #5
    How did you find that?
  7. Nov 19, 2015 #6


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    Sorry, I was already thinking in temperature when writing down this. I corrected the expression in #4.
  8. Nov 19, 2015 #7
    Thanks sir! Your response helped me solve the problem.
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