If Helmholtz free energy doesn't depend on particle number, what is μ?

[astrozilla]

Homework Statement

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

Homework Equations

F (OR A) F=U-TS

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