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Find Cv as a function of V & T (or P & T) given G(P,T)?

  1. Feb 29, 2016 #1
    1. The problem statement, all variables and given/known data
    The function G is given in the question: [tex]G(P,T) = \frac{-aT^2} {P}, [/tex]
    where a is a positive constant.
    2. Relevant equations
    [tex] dG = Vdp - SdT, [/tex]
    and probably [tex] S(V,T) = (\frac{\partial S}{\partial T})_V dT + (\frac{\partial S}{\partial V})_T dV [/tex]
    3. The attempt at a solution
    [tex]C_v dT = TdS, [/tex]
    ∴​
    [tex](\frac{\partial S}{\partial T})_vdT = \frac {C_v}{T}[/tex]
    .. and that's about as far as I got.

    I could find C_p by taking a partial derivative of G with respect to T and get [tex](\frac{\partial S}{\partial T})_pdT = \frac {C_p}{T}[/tex]
    , which turned into something like [itex] \frac{-2aT}{P} [/itex] but I don't know how I would find [itex]C_v[/itex] without being given a starting function of V and T like Helmholt's energy. Because I'm looking for [itex]C_v[/itex] I'm 90% sure that the function will be a function of V & T, not P & T.

    Pls help thx
     
  2. jcsd
  3. Mar 2, 2016 #2
    In order to get Cv, you are going to have to get U. U can be obtained from knowledge of H and PV. Do you know how to get H if you know G(P,T)? Do you know how to get V if you know G(P,T)?

    Chet
     
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