Liquid-vapor, generally critical point

At ihe critical point the molar volumes of the liquid and of the gas become equal. In general a critical state is characterized by the fact lhal the two coexistent phases (here the liquid and Ihe vapor) are identical. 

A gas existing below its critical temperature is generally referred to as a vapor because it can condense. If a pure gas is maintained at a constant temperature below its critical temperature and the pressure is increased, eventually the gas begins to condense into a liquid. This procedure can be reversed by decreasing the applied pressure and the liquid will be transformed back to its gaseous state. In our discussions, the term vapor will be used to refer to a gas below its critical point in a process where the phase change is of interest. The terms gas and noncondensable gas will refer to a gas above the critical point or to a gas that cannot condense. 

Studies of liquid-vapor coexistence are, generally, best addressed in the framework of an open ensemble thus the state variables here comprise both the particle coordinates r and the particle number N. A path with the appropriate credentials can be constructed by identifying pairs of values of the chemical potential p and the temperature T which trace out some rough approximation to the coexistence curve in the p—7 plane, but extend into the one-phase region beyond the critical point. Once again there is some circularity here to which we shall return. Making the relevant variables explicit, the sampling distribution [Eq. (26)] takes the form... 

Referring to Table XVI-1, let us first, consider the latent heat of fusion. We observe that in practically every case it is but a small fraction of the heat of vaporization. That is, the atoms or molecules are pulled apart only slightly in the liquid state compared with the solid, while in the vapor they are completely separated. Of course, this holds only for pressures low compared to the critical pressure near the critical point, the heat of vaporization reduces to zero. To be more specific, we notice that in the metals the heat of fusion is generally three or four per cent of... 

The great attraction of this equation is that it contains just properties of the pure species and therefore expresses K-values as functions of T and P, independent of the compositions of the liquid and vapor phases. Moreover, and 4> can be evaluated from equations of state for the pure species or from generalized correlations. This allows K-values for light hydrocarbons to be calculated and correlated as functions of T and P. However, the method is limited for any species to subcritical temperatures, because the vapor-pressure curve terminates at the critical point. 

The Kellogg and DePriester charts and their subsequent extensions and generalizations use the molar average boiling points of the liquid and vapor phases to represent the composition effect. An alternative measure of composition is the convergence pressure of the system, which is defined as that pressure at which the K values for all the components in an isothermal mixture converge to unity. It is analogous to the critical point for a pure component in the sense that the two... 

The critical point of a binary mixture occurs where the nose of a loop in Fig. 10.3 is tangent to the envelope curve. Put another way, the envelope curve is the critical locus. One can verify tliis by considering two closely adjacent loops and noting what happens to the point of intersection as their separation becomes infinitesimal. Figure 10.3 illustrates that the location of the critical point on the nose of the loop varies with composition. For a pure species the critical point is the highest temperature and highest pressure at which vapor and liquid phases can coexist, but for a mixture it is in general neither. Therefore under certain conditions a condensation process occurs as the result of a reduction in pressure. 

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