Subcritical temperature isothermal behavior

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. 

The PVT behavior of a pure substance may also be described on a pressure-volume diagram, as shown in Figure 1.2. The variation of volume with pressure at various fixed temperatures is represented by the isotherms. If temperature of the isotherm is above the critical, the pressure decreases continuously as the volume increases and no phase change takes place. The critical temperature isotherm is also continuous but has an inflection point at the critical pressure. On subcritical isotherms, the pressure of a liquid drops steeply with small increases in the volume until the liquid starts to vaporize. At this point the pressure remains constant as the total volume increases. 

T his chapter presents a new formulation of the equation of state for - -fluids at subcritical and critical temperatures, T < 1. Unlike many other equations of state, this equation of state is defined as a differential equation, and is designed to describe not only the behavior of isotherms on their stable vapor and liquid branches, but also in the two-phase transition region. Interesting insights concerning the nature of metastable and absolutely instable phases are obtained also. 

The essential features of vapor-liquid equilibrium (VLE) behavior are demonstrated by the simplest case isothermal VLE of a binaiy system at a temperature below die critical temperatures of both pure components. For this case ( subcritical VLE), each pure couqionent has a well-defln vapor-liquid saturation pressure Ff , and VLE is possible for the fiiU range of liquid and vsqior compositions X/ and y,. Figure l.S-1 illustrates several pes of behavior riiown by such systems. In each case, the upper solid curve ( bubble curve ) represents states of saturated liquid the lower solid curve ( dew curve") represents states of saturated vapor. 

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