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Maxwell's relation Thermodynamics

  • Thread starter hasibme2k
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  • #1
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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.
 
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Answers and Replies

  • #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?
 
  • #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.
 
  • #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.
 
  • #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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