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: Thermal Physics Relation

  1. Feb 24, 2008 #1
    1. The problem statement, all variables and given/known data
    Derive the following equation


    2. Relevant equations
    [tex]TdS = C_{V} \left( \frac{\partial T}{\partial P} \right)_{V}dP + C_{P} \left( \frac{\partial T}{\partial V} \right)_{P}dV [/tex]


    3. The attempt at a solution

    [tex] dU = \delta Q - \delta W [/tex]

    [tex] \delta Q = TdS [/tex] for a closed system

    [tex] C_{P} = T \left( \frac{\partial S}{\partial T} \right)_{P} [/tex]

    [tex] C_{V} = T \left( \frac{\partial S}{\partial T} \right)_{V} [/tex]

    I am not sure where to go from here.
     
  2. jcsd
  3. Feb 24, 2008 #2

    siddharth

    User Avatar
    Homework Helper
    Gold Member

    I think the trick here is playing around with the relations.

    If you consider S as a function of p and v as independent variables, then
    [tex] dS = \left(\frac{\partial S}{\partial P}\right)_V dP + \left(\frac{\partial S}{\partial V}\right)_P dV[/tex]

    But, [tex]\frac{\partial S}{\partial P}_V = \left(\frac{\partial S}{\partial T}\right)_V \left(\frac{\partial T}{\partial P}\right)_V [/tex], and so on.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook