Phase behavior qualitative representation

Consequently, the continuous variation of specific volume of the vapor-liquid mixture at fixed temperature and pressure is a result of the continuous change in the fraction of the mixture that is vapor. The conclusion, then, is that an isotherm such as that shown in Fig. 7.3-2 is an approximate representation of the real phase behavior (shown in Fig. 7.3-3) by a relatively simple analytic equation of state. In fact, it is impossible to represent the discontinuities in the derivative dP/dV)T that occur at and v with any analytic equation of state. By its sigmoidal behavior in the two-phase region, the van der Waals equation of state is somewhat qualitatively and crudely exhibiting the essential features of vapor-liquid phase equilibrium historically, it was the first equation of state to do so. 

Qualitatively correct and occasionally also quantitatively satisfactory representation of LLE for binary and ternary polymer-solvent systems is achieved, especially for the UCST-type phase behavior. A single investigation for SLLE also shows good results. 

The Differential Equation of State 1 provides not only a good qualitative description of isothermal behavior at subcritical temperatures T < 1, but also yields accurate quantitative representations of experimentally measured data. It describes not only the stable vapor and liquid branches, but also the two-phase transition region, additionally yielding information on the nature of metastable and absolutely unstable phases. A complete and simple description of the vapor-liquid-phase transition and the critical point also is provided by the differential equation of state. 

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