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: First Law of Thermo

  1. May 9, 2010 #1


    User Avatar

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

    First law can be written dU = TdS - PdV where the internal energy U may be written in terms of any two of T,P,V,S.

    I have to show that (DT/DV)s = -(DP/DS)v

    where D is partial d, and the subscripts s and v mean hold those constant..

    2. Relevant equations

    3. The attempt at a solution

    Not really sure how to proceed at all?
  2. jcsd
  3. May 9, 2010 #2


    User Avatar
    Gold Member

    This is one of the Maxwell relations.
    If you have a function
    [tex]f(x,y)=\left( \frac{\partial f}{\partial x} \right)_y dx + \left( \frac{\partial f}{\partial y} \right)_x dy = A dx + B dy[/tex]
    then, according to
    [tex]\frac{\partial}{y} \left( \frac{\partial f}{\partial x} \right) = \frac{\partial}{\partial x} \left( \frac{\partial f}{\partial y} \right)[/tex]
    you have
    [tex]\left( \frac{\partial A}{\partial y} \right)_x = \left( \frac{\partial B}{\partial x} \right)_y[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook