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Thermo: chemical potential as a function of T,V, and N

  1. Sep 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the three equations of state for a system with the fundamental equation

    U =(vo[tex]\theta[/tex]/R2)*(S3/NV)

    For this system, find chemical potential as a function of T,V, and N.

    2. Relevant equations

    [tex]\mu[/tex]= chemical potential
    [tex]\partial[/tex]U/[tex]\partial[/tex]S = T
    -[tex]\partial[/tex]U/[tex]\partial[/tex]V = P
    [tex]\partial[/tex]U/[tex]\partial[/tex]Nj = [tex]\mu[/tex]j

    3. The attempt at a solution

    T= 3(vo[tex]\theta[/tex]/R2)*(S2/NV)
    P = (vo[tex]\theta[/tex]/R2)*(S3/NV2)
    [tex]\muj[/tex]= -(vo[tex]\theta[/tex]/R2)*(S3/N2V)

    If the above is correct, is it sufficient to write [tex]\mu[/tex]= T dS/dN - P dV/dN - dU/dN?

    Thank you.
  2. jcsd
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