Stability Analysis for a Single Component

The basic derivations for the stability analysis of a single-component system are similar to Haase s presentation (1956) with certain changes. 

Stability criteria based on entropy Let us consider a single-component single-phase system with molar internal energy u and molar volume [j 

The expression for the entropy change, AS, between the two states can be written as 

Based on the Second Law, the single-phase state is stable if AS 0 the entropy of the original single-phase state is greater than the entropy of the two-phase state for the isolated path. The constraints of the isolated path are 

The Taylor s series expansions are based on the assumptions that Au, Av, A°u, and A t are small. Note that in Eqs. (4.91) and (4.92), the partial derivatives are evaluated at the original single-phase state. From Eqs. (4.88) and (4.89), 

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