1. Not finding help here? Sign up for a free 30min 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!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Thermal Physics Relation
  1. Thermal Physics (Replies: 1)

  2. Thermal physics (Replies: 1)

  3. Thermal Physics (Replies: 3)

  4. Thermal Physics (Replies: 3)

Loading...