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Working with Maxwell's equations

  1. Feb 9, 2015 #1
    Hello all - I've been trying to work out an example from a book, and I don't quite understand the math.

    show that (δT/δV)s = - (δP/δS)v

    solution (δ/δV (δU(S,V)/δS)v)s = (δ/δS(δU(S,V)/δV)s)v
    (δ/δV (δ(TdS - PdV)/δS)v)s = (δ/δS(δ(TdS-PdV)/δV)s)v
    (δT/δV)s = -(δP/δS)v

    I don't understand the substitution or the last step
     
  2. jcsd
  3. Feb 9, 2015 #2
    I don't understand the notation. The way I learned it is as follows:

    ##dU=TdS-PdV##

    We must also have that:

    $$dU = \left(\frac{\partial U}{\partial S}\right)_VdS+\left(\frac{\partial U}{\partial T}\right)_SdV$$

    Therefore, comparing both equations, we have:

    $$T=\left(\frac{\partial U}{\partial S}\right)_V$$
    $$-P=\left(\frac{\partial U}{\partial T}\right)_S$$
     
  4. Feb 9, 2015 #3
    Right I don't understand it either they've inserted the differential expression into a partial fraction I don't know how to work with it.
     
  5. Feb 9, 2015 #4
    So their notation in hinky. Can you get to the final result from my last two equations?

    Chet
     
  6. Feb 9, 2015 #5
    Sure no sweat.
     
  7. Feb 9, 2015 #6
    Ah I figured it out
     
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