Since (dU) VTdS and (dH)PTdS, eq.(21.30a) and eq.(21.30b) become respectively
(dA) T,V 0
(21.31)
(dG) T,P 0
(21.32)
The above two equations have extensive applications in chemistry. Note that the equalities apply to equilibria and inequalities in eqns (21.27), (21.28), (21.29), (21.31) and (21.32) apply for spontaneous or irreversible processes