
Magnetic Systems 159
susceptibility
χ
S
. We could have introduced the magnetic analog of the coefficient of
thermal expansion as
α
M
=
1
V
∂
M
∂
T
B
e
. But we shall not do so to avoid a prolifera-
tion of symbols; instead we shall explicitly display the temperature derivative of M .
However, it is useful to eliminate
∂
B
e
∂
T
M
in terms of quantities already introduced.
∂
B
e
∂
T
M
= −
∂
M
∂
T
B
e
∂
B
e
∂
M
T
= −
1
V
χ
T
∂
M
∂
T
B
e
(8.23)
This allows us to simplify the magnetic TdS equations further:
TdS = C
M
dT +
T
V
χ
T
∂
M
∂
T
B
e
dM
TdS = C
B
e
dT + T
∂
M
∂
T
B
e
dB
e
(8.24)
Equating the two TdS equations one gets
0=(C
M
−C
B
e
)dT + T
∂
M
∂
T
B
e
1
V
χ
T
dM −dB
e
(8.25)
As in our discussion for the nonmagnetic case, ...