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Maxwell's relation Thermodynamics

  1. Oct 22, 2013 #1
    How can I prove the following relation
    T(∂p/∂T)v,N +(∂T/∂V)u,N =p(∂T/∂U)v,N

    where p= pressure, V= volume, U=internal energy, T= Temperature. I tried by fundamental relation and Maxwell's relation but couldn't able to prove it.

    I would appreciate if anybody helps me out.
     
    Last edited: Oct 22, 2013
  2. jcsd
  3. Oct 22, 2013 #2

    UltrafastPED

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    Are those partial derivatives? If so use "advanced" so we can be sure. Is t the same as T?
     
  4. Oct 22, 2013 #3

    vanhees71

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    ...and you also need to tell which variables are kept constant when taking the partial derivatives like in, e.g.,
    [tex]C_V=\left (\frac{\partial U}{\partial T} \right )_{V,N}[/tex]
    to define the specific heat at constant volume.
     
  5. Oct 22, 2013 #4

    dextercioby

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    That's the trick with thermodynamics. Partial derivatives always come from maths with something extra: which variables specifically you are keeping constant when calculating the limits of a multivariable function.
     
  6. Oct 22, 2013 #5

    Philip Wood

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    I think the relationship is wrong. The dimensions of the first term are those of pressure, but the dimensions of the other two terms are those of temperature divided by volume.
     
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