Chemical potential different for different systems?

[pivoxa15]

Homework Statement

For a given phenomena of macroscopic particles.

If we model it using the canonical ensemble then we get a certain chemical potential u.

But if we model it using the Grand Canonical system, we get a varying chemcial potential that depends on the average number of particles in the system.

So two different chemical potentials for the two systems. But in the thermodynamic limit of n-> infinity, both u equals each other.

That sounds right dosen't it?

 

[cepheid]

Yeah, you're basically right.

In any of the systems in the canonical ensemble, the chemical potential is given by

\mu(T,V,N)

whereas in any of the systems in the grandcanonical ensemble, it's given by

\mu(T,V,\langle N \rangle)

Now, in the "thermodynamic limit" as you have called it, the number of particles in any of the grandcanonical systems is *MUCH* more likely to be equal to \langle N \rangle than to any other number. So it's equivalent to having a closed system with a fixed number of particles \langle N \rangle.

If I have an open system and I want it to be equivalent to a closed system with a particular number of particles N_0 [/tex], I&#039;d have to somehow <b>pick </b> or <b>set</b> the value of \mu [/tex] such that \langle N \rangle = N_0 for that system.