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Therefore
(1-2) dU = T dS ? P dV.
The differential of the accumulated internal energy in a fixed-composition, P dV ? work system is.
= dH = dU + d(PV)
(1-3) = dU + P dV + V dP.
Substituting equation (1-2) in equation (1-3), we obtain
(1-4) dH = T dS + V dP.
From the defining the Helmholtz function A we obtain
( 1-5) dA = dU ? d(TS) = dU ? T dS ? S dT.
Substituting equation (1-2) in equation (1-5)
(1-6) dA = -S dT ? P dV.
From the Gibbs Free Energy equation and equation (1.4)
(1.7) dG = -S dT + V dP.
We have in equations (1-2), (1-4), (1-6), and (1-7) expressed dU, dH dA, and dG
in terms of P, V, T, and S...
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