Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.5-4

FIRST-ORDER PHASE TRANSITIONS

Physics — Statistical Mechanics · magnetic-heat-capacity-susceptibility

Problem

Show that

C_{B_e} - C_I = \frac{\mu_0^2 T}{\chi_T^2}\left(\frac{\partial I}{\partial T}\right)_{B_e}

and

\frac{C_{B_e}}{C_I} = \frac{\chi_T}{\chi_S}

where

C_{B_e}

and

C_I

are heat capacities and

\chi_T

and

\chi_s

are susceptibilities:

\chi_T \equiv \mu_0(\partial I/\partial B_e)_T