Now we define two more functions called the Helmholtz free energy A and the Gibbs free energy G through the equations.
A = U – TS
(21.21
and
G = H - TS
(21.22)
Substituting for dU and dH, we obtain
dA = -SdT – PdV and
(21.23)
dG = - SdT + VdP
(21.24)
and applying eq. (21.17), we get
( S/V) T = ( P/ T) V and ( S/ P) T = - ( V/ T) p
(21.25)
A great advantage of eq. (21.25) is that the volume and pressure dependence of entropy can be obtained in terms of P/ T and V/T which can be very easily measured. Equation (21.18), (21.20) and (21.25) are referred to as Maxwell's relations.
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