A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 211

Since the chemical potential is expressed in P, and does not depend on

N, we can write

where and are reduced entropy and volume respectively.

Using the equation for the Gibbs free energy of a single-component system,

we can write

where we also used But from (S.4.92.1),

So finally

b) By definition the average number of particles in the grand canonical

ensemble is

where Now, from (a),

where N is an average number of particles:

where we have used