Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 16.1-3

THE CANONICAL FORMALISM; STATISTICAL MECHANICS IN HELMHOLTZ REPRESENTATION

Physics — Statistical Mechanics · canonical-formalism-entropy-partition-sum

Problem

Show that

S/k_B = \beta^2 \partial F/\partial \beta

and thereby express

S

in terms of

Z

and its derivatives (with respect to

\beta