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4 The Thermodynamics of Real Systems
We now obtain some additional useful equations. Equations (4.1-8) and (4.2-3) give
dA −SdT − PdV (closed system)
(4.2-15)
so that
∂A
∂T
V ,n
−S
(4.2-16)
∂A
∂V
T ,n
−P
(4.2-17)
A third Maxwell relation is
∂S
∂V
T ,n
∂P
∂T
V ,n
(a Maxwell relation)
(4.2-18)
Equations (4.1-13) and (4.2-3) give
dG −SdT + VdP (closed system)
(4.2-19)
so that
∂G
∂T
P,n
−S
(4.2-20)
∂G
∂P
T ,n
V
(4.2-21)
Our fourth Maxwell relation is
∂S
∂P
T ,n
−
∂V
∂T
P,n
(a Maxwell relation)
(4.2-22)
A mnemonic device for writing the Maxwell relations is to write a blank relation
∂ · · ·
∂ · · ·
···, n
∂ · · ·
∂ · · ·
···, n
and then to put P and V in opposite corners and T and S in the other opposite corners.
There are four ways to do this, giving the four Maxwell relations. In each relation the
independent variable in one derivative is held constant in the other derivative and n
is fixed in both of the derivatives. If T and V occur in the same derivative, attach a
negative sign to one side. Otherwise, the signs are positive.