Thermodynamics-Free Energy

[astrozilla]

1. The problem statement, all variables and given/known data
What happens when the hemholtz free energy F of a system does not depend on the number of particles of the system?What does this mean for the chemical potential μ?

μ= U+PV -TS ,μ= F+PV


2. Relevant equations

F (OR A) F=U-TS

3. The attempt at a solution
I think the answer to this question requires deep understanding of the F

[Mapes]

Your definition of the chemical potential is a little off. It's G, the Gibbs free energy, that is equal to U+PV-TS. Once you correct the definition, you'll see what independence of N implies for μ.

[astrozilla]

change in Helmholtz free energy is given by :
dF = -SdT-PdV +μdN

μ is equal to zero

thanks