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XXXVIII. On Vapour Pressures and the Isothermals of 

 Vapours. By J. H. Shaxby, B.Sc, Lecturer in Physics 

 and Director of the Viriamu Jones Research Laboratory, 

 University College, Cardiff*. 



§ 1. A LARGE number of: empirical formulae have been 

 JTjl. proposed to express the vapour pressure of a fluid 

 in terms of the temperature and certain "constants" for the 

 substance in question. Many of them, e. g. those of Dal ton, 

 Roche, Biot, Kirchhoff, and van der Waals, are of logarithmic 

 or exponential form. 



This at once recalls Dietericrs Equation of State 



RT _ A 

 p = ~~j e vRT , 



in which p is the external pressure upon a fluid of specific 

 volume v at absolute temperature T, R being the gas con- 

 stant and A and b constants for the particular substance. 



In obtaining this equation Dieterici makes use of a quantity 

 A', the work done per unit mass against the forces of 

 cohesion in removing molecules from the fluid ; A' is pro- 



A 



portional to the density of the fluid and is replaced by — . 



On similar lines, let us examine the relation between the 

 total internal pressure, II b in the liquid phase of any sub- 

 stance, and that, U 2 , in its vapour phase. The work done in 

 the transfer of unit mass from liquid to vapour may be 

 equated, following Dieterici, to twice the kinetic energy lost 

 during this transformation of high speeds (of the liquid 

 molecules which escape) into average speeds of these same 

 molecules on their arrival in the vapour. This loss of 

 kinetic energy per unit mass is \ s 2 , where s is the critical 

 value of the component normally towards the surface of the 

 velocity of a liquid molecule, i. e. the smallest value com- 

 patible with escape into the vapour. Now, .s 2 ==2RTlog e ^- , 



where Nj, N 2 are the numbers of molecules per unit volume 

 in liquid and vapour respectively. Thus, in the case of a 

 substance which is not dissociated either in liquid or in 

 vapour form, 



s 2 = 2RTlog/ii, 



where d Y -= density of liquid, d 2 of vapour. 



* Communicated bv Prof. A. W. Porter, F.K.S. 



