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Homework Help: Thermal Phys: Show (du/dP)|t = Pkv - (cp - cv)K/B

  1. Sep 28, 2009 #1
    For some reason this proof in thermal is tripping me up.

    1. The problem statement, all variables and given/known data

    Show that (du/dP)|t = Pkv - (cp - cv)K/B (problem 4-4 in Carter or 1.14 in Cheng)

    2. Relevant equations

    B = 1/v(R/P) = 1/T
    k= -1/v(-RT/p^2) = 1/P

    3. The attempt at a solution

    Start with 1st law dq=(du + Pdv) and substitute...eventually:
    Get to du/dP|T dP - (du/dt)|p dt - PBvdT +PkvdP
    Divide by dP

    Now is where I'm stuck....
  2. jcsd
  3. Sep 28, 2009 #2


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    Science Advisor
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    Gold Member

    You want to prove this generally, not just for the case of the ideal gas. Do you know the definitions of [itex]C_P[/itex] and [itex]C_V[/itex]?
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