( 124 ) 



To that purpose we sliall begin with tlie (liseussioii of the tension 

 of the saturated vapour o\er liquids at low temperatui-e. From tlie 

 conditions for coexisting [)liases of a sini})lc substance, that luimelj 

 p, T and the thermodynamic potential are the same in both phases, 

 follows : 



{pc —ipdv)^ — (pc — I pdc)^ 



or 



j,v liT 



J^-Vi 



— h 



V 



-Si 



h 

 — h 



If we put h = constant i. e. h independent of the volume, then the 

 latter equation assumes the well known form : 



pc 



RT Lo<) {v—l>) 



pc — 



RT IcHi {c—h) 



Properly speaking this equation is not suitable for the direct calculation 

 of the coexistence pressure; it must be considered to give a relation 

 between the specific volumes and so also between the densities of the 

 coexisting phases. At lower temperatures, however, for which the 

 vapour phase, which we lia\e indicated by means of the ijidex 2, is rare 

 and may be estimated not to deviate noticeably from tlie gas-laws, 

 tlie equation becomes suitable for the calculation of the pressure of 

 the saturated vapour. In this case it assumes the following form : 



pL\ RT loq {c, — h) - RT z=z RT loa ^— . 



i\ " ' RT 



We fijid after successive deductions wliicli are too simple to require 

 special discussion : 



a{v^—],) 



pt\ 



+ 



h 



/> + 



a a 



(v,—0) = RTlog 

 — RTlorj 



PJ'^-i-^) 

 RT 



P 



P + 



,.-- + 



—b 



[RT-p{v,-b)] 



— P 



v,iv,-2b) 



RT 



+ 



= RT loq 



P 



a 



P + — 



z=z log 



P 



P + 



