Problems and Solutions on Thermodynamics and Statistical Mechanics

144 Problems d Sdutio~ on Thermddynam'ca €4 Statiaticd Mechanica

where L = T(S - S') is the latent heat of phase transition. At the two ends
of the curve: He(T,) = 0 at T = T, gives L = 0; dHe/dT = 0 at T = 0
gives L = 0 also.

(b) From the above equation, we have

S' - s = - VH,. dH, -

41r dT *

As C = T(dS/dT)

At T = T,; He = 0, we have

At T = 0, He = H,, we have

AC=-H,[F] VT d2H, =o

47r T=O

1146

A simple theory of the thermodynamics of a ferromagnet uses the free

energy F written as a function of the magnetization M in the following

form: F = -HM + FO + A(T - Tc)M2 + BM4, where H is the magnetic

field, Fo, A, B are positive constants, T is the temperature and T, is the

critical temperature.

(a) What condition on the free energy F determines the thermody-

(b) Determine the equilibrium value of M for T > T, and sketch a

(c) Comment on the physical significance of the temperature depen-

namically most probable value of the magnetization M in equilibrium?

graph of M versus T for small constant H.

dence of M as T gets close to T, for small H in case (b).

( Wisconsin)