Statistical problem of phase changes

We have already seen (chap. XI, 3) that the van der Waals equation of state can be employed to represent, in an approximate way, the isotherms of real gases and of liquids. In the two phase region it leads to isotherms analogous to those shown in figs. 16.2 and 16.3, containing regions both of instability and metastability. 

It is important to realize however that the problem of phase changes 

A general formulation of the conditions which determine the appearance of a new phase remains an important problem in theoretical physics which has not yet been completely solved. 

We shall now give a brief account of critical phenomena in the vaporization of a binary mixture. In this case it is convenient to consider the T, p diagram at constant composition (c/. fig. 16.5). For a pure substance we obtain simply the line AG which terminates at the critical point C. For a mixture of constant composition we have to consider two pressures, one corresponding to the liquid, and the other to the vapour at the same composition and temperature. These two pressures correspond to the points in fig. 13.6 where an ordinate at constant composition e.g. Xj FE) cuts the vaporization curve (G) and the condensation curve (H). (The vapour and liquid are not of course in equilibrium). As the temperature is raised the shape of the lenticular area of fig. 13.6 varies and finally decreases to zero. We thus obtain the curve FGKH of fig. 16.5 of which the branch from F to K corresponds to liquid and K to H to the vapour. The point K is the critical point at which the two phases are identical. Near to K there will also 

Two further interesting points emerge from a study of fig. 16.5. If the system is maintained at a pressure and the temperature raised, initially only liquid is present. When the liquid curve is crossed at G, A aporization begins. Now, in general, a horizontal line will cut the curve again at a point on the vapour branch of the curve, and this will correspond to complete vaporization. In this particular case, however, the line cuts the liquid curve again at D, between L and K, and at this point the vapour disappears. This phenomenon is known as retrograde 

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