Statistical Mechanics · Problem 3.40

The Grand Canonical Ensemble — R. K. Pathria

Physics — Statistical Mechanics · heat-capacities-constant-field-magnetization

Problem

(a) Show that, for any magnetizable material, the heat capacities at constant field

H

and at constant magnetization

M

are connected by the relation

C_H - C_M = -T\left(\frac{\partial H}{\partial T}\right)_M \left(\frac{\partial M}{\partial T}\right)_H.

(b) Show that for a paramagnetic material obeying Curie's law

C_H - C_M = CH^2/T^2,

where

C

on the right-hand side of this equation denotes the Curie constant of the given sample.