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!

Thermodynamics, Helmholtz free energy, Legendre transformation

  1. Jan 4, 2012 #1
    1. The problem statement, all variables and given/known data

    The Helmholtz free energy of a certain system is given by [itex]F(T,V) = -\frac{VT^2}{3}[/itex]. Calculate the energy U(S,V) with a Legendre transformation.


    2. Relevant equations

    F = U - TS
    [itex]S = -\left(\frac{\partial F}{\partial T}\right)_V[/itex]


    3. The attempt at a solution

    We have [itex]U = -\frac{VT^2}{3} + TS[/itex]. S is given by [itex]S = -\left(\frac{\partial F}{\partial T}\right)_V = -\frac{2}{3}VT[/itex]. Then:

    [itex]U = -\frac{VT^2}{3} - \frac{2}{3}VT^2 = -VT^2 [/itex]

    Now I didn't end up with a function U that depends on S and V, but on V and T instead. Should I somehow describe T in terms of S instead? If so, how can I do that?
     
  2. jcsd
  3. Jan 5, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Check the sign of S: it is 2/3 VT .
    Having this relation between T, V and S, express T as function of S and V and substitute into the expression for U.

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




Similar Discussions: Thermodynamics, Helmholtz free energy, Legendre transformation
  1. Helmholtz free energy (Replies: 5)

Loading...