- #1
Mayan Fung
- 131
- 14
Homework Statement
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)
Homework Equations
$$ \frac μ T = -(\frac{∂S}{∂N})_{U,V} $$
U = TS - PV + μN
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)
Thanks!