1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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,

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


    User Avatar
    Homework Helper

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

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

    [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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook