Two-phase equilibrium in binary and ternary systems VII. Calculation of latent heats and some other similar properties

Abstract

Exact thermodynamic expressions are derived for the principal latent heats of binary mixtures, which enable these quantities to be calculated in terms of other properties. These expressions are in each case the sum of two terms, which are designated the 'direct’ and the 'indirect’ terms respectively. In the past certain authors appear to have considered the quantities, which are here designated ∆ S (L) and ∆ S (G) and which are defined by equations (16) and (17), as being the differential latent heats of the first and last drops in the distillation of a liquid phase. It is now shown that ∆ S (L) and ∆ S (G) are only the direct terms; the full differential latent heat requires the addition of an indirect term as well. Since ∆ S (L) and ∆ S (G) can be calculated by a general method given in equations (30) and (29), and since the indirect terms can normally be obtained without difficulty, the latent heats of the first and last drops can themselves be calculated. Calculation of the latent heats of the first and last drops is only a special case of the more general calculation of the latent heat of any drop. To carry out this calculation it is first of all necessary to obtain a general expression for the total change in entropy when any drop is distilled, in terms of the composition of the drop and of the properties of the phases (equations (1) and (2)). It is also necessary to find an expression for the composition of the drop in terms of the changes in composition of the phases (equations (11) and (13)). Combining all these results it is possible to obtain expressions for the various latent heats of any drop in terms of the equilibrium phase data, and of the properties and masses of the individual phases. Three of these latent heats are treated in detail (equations (24), (34) and (35)). Exact integral latent heats are obtained by the integration of the differential latent heats. A numerical example is worked out. The general method of calculation has also been applied to the evaluation of the Joule-Thomson coefficient in the two-phase region of a binary system.