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: Thermo heat capacity proof: cp - cv

  1. Apr 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that for a general (but simple) substance,



    v* is the specific volume
    p is the pressure
    c[itex]_{p}[/itex] is the heat capacity when p is const
    c[itex]_{v}[/itex] is the heat capacity when v is const
    Q is heat
    T is temperature in K

    2. Relevant equations

    Standard Maxwell relations. Suppose to use jacobian to manipulate

    c[itex]_{p}[/itex] = ([itex]\frac{∂Q}{∂T}[/itex])[itex]_{p}[/itex]
    c[itex]_{v}[/itex] = ([itex]\frac{∂Q}{∂T}[/itex])[itex]_{v}[/itex]

    3. The attempt at a solution

    I started by inserting the above equations for specific heat in terms of heat (Q). Then I plugged the partial derivatives into the equation dQ = dE + p dv* which left me with


    Next I rewrote the partial derivatives using dE = -TdS-pdV, but clearly at this point I'm just going around in circles. I think I'm missing some simple step to combine the partials, but I'm not sure what it is. Your help would be appreciated.
    Last edited by a moderator: Apr 20, 2012
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted