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First Law of Thermo

  1. May 9, 2010 #1


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    1. The problem statement, all variables and given/known data

    First law can be written dU = TdS - PdV where the internal energy U may be written in terms of any two of T,P,V,S.

    I have to show that (DT/DV)s = -(DP/DS)v

    where D is partial d, and the subscripts s and v mean hold those constant..

    2. Relevant equations

    3. The attempt at a solution

    Not really sure how to proceed at all?
  2. jcsd
  3. May 9, 2010 #2


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    Gold Member

    This is one of the Maxwell relations.
    If you have a function
    [tex]f(x,y)=\left( \frac{\partial f}{\partial x} \right)_y dx + \left( \frac{\partial f}{\partial y} \right)_x dy = A dx + B dy[/tex]
    then, according to
    [tex]\frac{\partial}{y} \left( \frac{\partial f}{\partial x} \right) = \frac{\partial}{\partial x} \left( \frac{\partial f}{\partial y} \right)[/tex]
    you have
    [tex]\left( \frac{\partial A}{\partial y} \right)_x = \left( \frac{\partial B}{\partial x} \right)_y[/tex]
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