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11 Dec 2019

The canonical partition function of an N-particle, monatomic ideal gas is given by

Q(N, V, T) = 1/N! ( 2pimK_b T/h^2)^(3/2N)* (V^N)

Using the definition for the chemical potential ? of a single component system,

?? = ( ????/????) ??,V

find an expression for the chemical potential for a monatomic ideal gas. Then show that the same expression can be derived using the definition of the Gibbs free energy, ?? = ??/?? = 1/?? (?? + ????) where the Helmholtz free energy ?? = ?? ? ????.

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