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Problem on Thermodynamics

  1. Oct 14, 2016 #1
    1. The problem statement, all variables and given/known data
    Derive the equation
    ##U=-T(\frac{\partial A}{\partial T})_V##
    where ##U## is the internal energy, ##T## is the temperature, ##A## is the Helmholtz function.

    Reference: Heat and Thermodynamics, Zemansky, Dittman, Page 272, Problem 10.4 (a)
    2. Relevant equations
    ##dA=-PdV-SdT## ... (i) [##S## is the entropy]
    ##A=U-TS## ... (ii)

    3. The attempt at a solution
    As ##A(V,T)## is a state function,
    ##dA = (\frac{\partial A}{\partial V})_T dV + (\frac{\partial A}{\partial T})_V dT## ... (iii)
    Comparing (i) and (iii),
    ##(\frac{\partial A}{\partial V})_T = -P## ... (iv)
    and ##(\frac{\partial A}{\partial T})_V = -S## ... (v)
    Using (ii) and (v),
    ##U = A +TS = A- T(\frac{\partial A}{\partial T})_V##
    Any help would be appreciated.
     
    Last edited: Oct 14, 2016
  2. jcsd
  3. Oct 14, 2016 #2

    DrDu

    User Avatar
    Science Advisor

    I think your solution is correct while the problem as stated is wrong.
     
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