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: Finding chemical potential with given thermodynamic relation

  1. Nov 2, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose you are given the following relation among the entropy S, volume V , internal energy U, and number of particles N of a thermodynamic system, where A is a constant.:
    $$ S = A(NVU)^{\frac 1 3} $$
    Find the chemical potential μ(T,P)
    2. Relevant equations
    $$ \frac μ T = -(\frac{∂S}{∂N})_{U,V} $$
    U = TS - PV + μN
    3. The attempt at a solution
    $$ \frac μ T = -(\frac{∂S}{∂N})_{U,V} = \frac 1 3 A N^{-\frac 2 3} (VU)^{\frac 1 3} $$
    This only solved μ(U,V,N)
    Since internal energy is a function of N,V,T : U(N,V,T)
    $$ ∴ μ(U,V,N) → μ(T,\frac V N) → μ(T,P) $$
    However, I don't know how to carry out the above transform in this case. I don't know U(N,V,T)

  2. jcsd
  3. Nov 2, 2016 #2


    User Avatar
    Science Advisor

    Try to express p and T in terms of U, S and V, using dU=TdS-pdV.
    Then set up G(T,p,N)=U-TS+pV.
    Calculate mu from G.
  4. Nov 2, 2016 #3
    Oh! Thanks, I didn't think of that before
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted