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[itex](\frac{\partial U}{\partial P})_T[/itex] derivation

  1. Dec 3, 2015 #1
    1. The problem statement, all variables and given/known data
    Capture.PNG

    2. Relevant equations
    Maxwell relations

    3. The attempt at a solution
    Here is how I proceeded. Am I allowed to go from line 1 to 2? It almost seems too simple.
    [tex]
    dU=TdS-PdV \\
    (\frac{\partial U}{\partial P})_T=T(\frac{\partial S}{\partial P})_T-P(\frac{\partial V}{\partial P})_T \\
    \text{We know that}-(\frac{\partial S}{\partial P})_T=(\frac{\partial V}{\partial T})_P \\
    (\frac{\partial U}{\partial P})_T=-T(\frac{\partial V}{\partial T})_P-P(\frac{\partial V}{\partial P})_T \\
    (\frac{\partial U}{\partial P})_T=-[T(\frac{\partial V}{\partial T})_P+P(\frac{\partial V}{\partial P})_T]
    [/tex]
     
  2. jcsd
  3. Dec 3, 2015 #2
    This seems fine, as long as you are allowed to use the "we know that" equation, which comes from the Maxwell relations.
     
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