
164 The Principles of Thermodynamics
This leads to the identification of the intensive parameters for the magnetic case as
T =
∂
U
∂
S
V,n,M
−P =
∂
U
∂
V
S,n,M
μ
=
∂
U
∂
n
S,V,M
B
e
=
∂
U
∂
M
S,V,n
(8.45)
The extensivity of U, as before, means U(
λ
S,
λ
V,
λ
n,
λ
M )=
λ
U(S,V,n,M ).The
magnetic analog of the Euler equation emerges exactly as in the nonmagnetic case:
n
μ
= U + PV −ST −B
e
M (8.46)
Thus in the magnetic case too the chemical potential equals the magnetic Gibbs
potential.
8.2.3 Counting the magnetic potentials
Thus, the magnetic case, as per our counting of chapter 9, corresponds to n =4,
including the number of moles . Therefore, there ought to be 15 thermodynamic
potentials ...