The Principles of Thermodynamics

Magnetic Systems 169

Therefore, the Curie law gives, for the difference C

B

e

−C

M

,

C

B

e

−C

M

=

aV B

2

e

T

2

(8.79)

which agrees with eqn(8.28), on using Curie law.

As another check on the model let us compute



∂

C

B

e

∂

B

e



and



∂

C

M

∂

M



. Explicit

evaluation yields



∂

C

B

e

∂

B

e



=

2aV B

e

T

2

= T



∂

2

∂

T

2

M



B

e

(8.80)



∂

C

M

∂

M



=0=−T



∂

2

∂

T

2

B

e



M

(8.81)

In obtaining the second equation we used the fact that B

e

is linear in T when M is

held fixed. This is in accord with eqn.(8.21).

8.2.6 Equilibrium conditions

Now we briefly discuss the connection between the magnetic thermodynamic poten-

tials and the criterion for equilibrium for magnetic systems. As far as the Helmholtz

free energy is concerned, th