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

1. Sep 6, 2009

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$$\theta$$/R2)*(S3/NV)

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

2. Relevant equations

$$\mu$$= chemical potential
$$\partial$$U/$$\partial$$S = T
-$$\partial$$U/$$\partial$$V = P
$$\partial$$U/$$\partial$$Nj = $$\mu$$j

3. The attempt at a solution

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

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

Thank you.