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Maxwell relations with heat capacity.

  1. Feb 28, 2008 #1
    Maxwell relations with heat capacity. Solved.

    1. The problem statement, all variables and given/known data
    Use the Maxwell relations and the Euler chain relation to express (ds/dt)p in terms of the heat capacity Cv = (du/dt)v. The expansion coefficient alpha = 1/v (dv/dt)p, and the isothermal compressibility Kt = -1/v (dV/dp)T. Hint. Assume that S= S(p,V)

    2. Relevant equations
    dQ(rev) = Tds
    The maxwell relations
    Euler Chain relation

    3. The attempt at a solution

    Alright, my attempts at this involved trying find common partial derivatives from the information already given. I couldn't find anything. But then looking at the hint I thought that there might be a way to express the change in entropy with respect to pressure and volume. I get this ds = (dU + PdV)/T assuming constant pressure. I am really not sure what I am suppose to do. I especially don't get what the expansion coefficient and thermal compressibility has to do with anything, but that might be because I can't see the big picture with this problem.

    A step by step explanation would be greatly appreciated.

    For anyone who cares about the answer... ds = (ds/dp)T dp + (ds/dT)p dT. Then you use the euler chain relations on both.
    Then you use maxwell's relations for the denominator of both. Then you can simplify the partial derivative. After that, you euler's chain relation again..... At this point it is easy to see what else you have to do. It would have been impossible for me to solve this problem had I not finally figured out that the hint was really really REALLY important, and I just euler chaining everything I saw.
     
    Last edited: Feb 29, 2008
  2. jcsd
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