Statistical Mechanics · Problem 1.12

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · entropy-of-mixing-inequalities

Problem

Show that the various expressions for the entropy of mixing, derived in Sec. 1.5, satisfy the following relations: (a) For all

N_1

V_1

N_2

and

V_2

(\Delta S)_{1=2} = \{(\Delta S) - (\Delta S)^*\} \geq 0,

the equality holding when and only when

N_1/V_1 = N_2/V_2

. (b) For a given value of

(N_1 + N_2)

(\Delta S)^* \leq (N_1 + N_2)k\ln 2,

the equality holding when and only when

N_1 = N_2