379 



phases at low temperatures, i. e. for infinitely low values of T^ 

 They are determined by the relations y>, = />, ^ />,,,„. and Z, = Z, 

 (the index 1 referring to the condensed condition, the index 2 to 

 the dilute gaseous state) which for small values of 7' are capable 

 of great simplifications. In fact at low temperatures y, ditfers infinitely 

 little from the limiting volume bli„^, that isiv, — ^ is infinitely small; 

 «1 is infinitely large; v^ is infinite and pcoex. infinitely small; 

 assuming .further that «^ ditfers infinitely little from 1, as confirmed 

 by the result, and neglecting infinitely small terms, the conditions 

 of coexistence become: 



_RT _RT 



Pcoex — 



1 k bun 1 



^ Urn. 



and 



RTlog (1 +e-^^) -f — (1 - ey=z RT log (1 -^,>-Xo)_ 



In order that «j may be infinite and «^ ^^^J fliffer infinitely little 

 from 1, according to (12) e^\ must be infinite and t;-^!! infinitely small ; 

 the second condition of coexistence becomes as follows 



EH a 



log t' = 1- 1 -I (1 — t)' + . . . . . . (24) 



•^ " RT R. ^ RTbii,a ^ ' ^ • ^ ^ 



hence 



log p,oë, =logRT--^ + ^-l- -^^— (1-e)^ + • • • (25) 



and 



a (1— «)' 



«^ = 1 _|_ i^"^6~^ _^ ., .^ (26) 



12. The heat of evaporation at low temperature is found to be 

 (vid. equation 19) 



;. = T (S—S,) = RT log v, + TH, — T (H^—H) =, 



T 



= ^(l-ey + E,i-{C,+R)T-^f/\(T)dT^...^) . (27) 



Olim J 







a 

 Putting Ao = — (1 — ey -f E„, i. e. the heat of evaporation at 



^) This expression is also arrived at, if one starts from the relation 



dlogp X 



~^Ta' which holds for low pressures, i. e. for low temperatures, or from 



dl 

 the relation -yy, — Cp — C repeatedly used by Nebnst. 



25* 



