4.2 Maxwell's relations

Write Eq. (3.160) in the following form:

(4.14)

Denote by x and y two variables which are any pair of the four quantities p, v, T and s.

From Eq. (4.14) we obtain:

(4.15)

and

(4.16)

Differentiating the first of the two equations with respect to y, and the second with respect to x, we obtain, respectively:

(4.17)

(4.18)

Equating the right-hand sides of these equations, we obtain:

(4.19)

Substitution into Eq. (4.19) of p, v, T and s for x and y permits a number of relationships to be obtained.

Substituting into Eq. (4.19) p and s for x and y, we get:

Inasmuch as and and since, of course, and , we obtain:

Substituting in Eq. (4.19) v and s, p and T, v and T for x and y, we obtain, respectively:

(4.21)

(4.22)

(4.23)

These four differential equations (referred to as Maxwell's relations) will be often used below.