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Exact differentials

  1. Feb 13, 2012 #1
    1. The problem statement, all variables and given/known data
    Given that [tex] \mathrm{d}U = T\mathrm{d}S - p\mathrm{d}V [/tex]

    find a function [itex] G [/itex] such that [tex] \mathrm{d}G = V \mathrm{d} p - S \mathrm{d} t [/tex].

    I'm not sure where to start - how are the two related? Could someone please give me a clue of how to start this off?

    3. Attempt at the solution
    I was thinking this looks too much like the quotient rule to be a coincidence...

    With very many thanks,

    Froskoy.
     
    Last edited: Feb 13, 2012
  2. jcsd
  3. Feb 13, 2012 #2

    lanedance

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    [tex] dG = VdP - SdT [/tex]

    adding a few terms gives
    [tex] dG = (VdP - SdT) + (VdP-VdP)+(TdS-TdS) [/tex]

    rearranging
    [tex] dG = (VdP+PdV)-(SdT-TdS)- (PdV-TdS) [/tex]
     
  4. Jun 7, 2012 #3
    So, what is the function G?
     
  5. Jun 7, 2012 #4
    Do you know an expression for the function U in terms of T,S,P,V?

    If so, think about what you could add or subtract to U in order to get the differentials to work for G.
     
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