524 Dr. F. A. Lindernatm and Dr. F. W. Aston on the 



Distillation and Chemical Separation. 



dA 

 The second law of thermodynamics A— U==T— may be 



written -£ = -, ^rvfr ? where p is the pressure of the satu- 



di {v— v)l 



rated vapour, v its molecular volume, V the molecular volume 



of the liquid, A/ the latent heat of evaporation, and T the 



temperature. At reasonably low pressures v= — and v is 



large compared with V. One may therefore write 



d log p _ A' 

 dT "~ RT* 



Now 



•/ o Jo 



where Cp is the molecular heat of the vapour at constant 

 pressure, and Cp the molecular heat of the solid or liquid. 

 Therefore 





const., 



the latent heat of fusion of course being included in 



(C p — c p )dT if the temperature is above the melting- 



point. 



If p> is small C p is constant so that 



" Ut + ft. lo &' V J J[if2 1 O^T + const. 



RT R 



Q 2 r P 



Now. Cp = Gu+ - — , where v is the atomic volume, « the 



K 



expansion coefficient, and k the compressibility, whilst c v , 

 the atomic heat at constant volume, is given in the terms of 

 the atomic frequency in the solid v m by 





Therefore 

 16 



=^7™ 1 - — - dT + constant. 

 RPJ u 



