Entropy solid-fluid equilibrium

In summary, we refer to Figure 5.5, which may be considered as the projection of the entire equilibrium surface on the entropy-volume plane. All of the equilibrium states of the system when it exists in the single-phase fluid state lie in the area above the curves alevd. All of the equilibrium states of the system when it exists in the single-phase solid state lie in the area bounded by the lines bs and sc. These areas are the projections of the primary surfaces. The two-phase systems are represented by the shaded areas alsb, lev, and csvd. These areas are the projections of the derived surfaces for these states. Finally, the triangular area slv represents the projection of the tangent plane at the triple point, and represents all possible states of the system at the triple point. This area also is a projection of a derived surface. 

We will examine this question in a particular case, in order to explain our approach. The most complete case may be examined in the future. We will consider first that there is no variation of the volumes of the solid and fluid phases. We will also assume that the exchange reaction between the solid and fluid phase is athermic and that there is no heat flux. In absence of other energy terms, we can thus set the problem at constant energy and volume. The chemical equilibrium between the solid and fluid phase is then expressed in the form dS /dc = dS /dc, where and S are the volumic entropies of the solid and the fluid respectively because the chemical potentials are here i = -T(dS/dc)... 

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