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Help with differentials

  1. Nov 10, 2008 #1
    1. The problem statement, all variables and given/known data

    I'm looking for [tex]\frac{\partial{P}}{\partial{V}}[/tex] at fixed T and fixed S.

    2. Relevant equations


    3. The attempt at a solution






    At constant T, I get this: [tex]\frac{dP}{dV}=-\frac{TS}{4V^2}+\frac{T}{4V}\frac{dS}{dV}[/tex]

    At constant S, I get this: [tex]\frac{dP}{dV}=-\frac{TS}{4V^2}+\frac{S}{4V}\frac{dT}{dV}[/tex]

    What do I do about the other differentials: [tex]\frac{dS}{dV}[/tex] and [tex]\frac{dT}{dV}[/tex]?

    Wouldn't this also be true?


  2. jcsd
  3. Nov 10, 2008 #2


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    Staff Emeritus
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    Gold Member

    Re: differentials

    You want to find [tex]

    and your second line is


    So.... you're done?
  4. Nov 10, 2008 #3
    Re: differentials

    Yes. That's at constant T and constant S.

    Is it the same if T is constant and S is not constant? Or vice-versa?
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