Statistical Mechanics · Problem 1.3

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · chemical-potential-energy-exchange

Problem

Two systems

A

and

B

, of identical composition, are brought together and allowed to exchange both energy and particles, keeping volumes

V_A

and

V_B

const. Show that the minimum value of the quantity

(dE_A/dN_A)

is given by

\frac{\mu_A T_B - \mu_B T_A}{T_B - T_A},

where the

\mu

and the

T

are the respective chemical potentials and temperatures.