( 750 ) 



Physics. — "The shape of the empiric isotherm f or the condensation 



of a binary mixture". By Prof. J. D. van der Waals. 



Let us imagine a molecular quantity of a binary mixture with a 

 mass equal to m x (1 — x)-\-m,x l at given temperature in a volume, 

 so that part of it is in the liquid state, and the remaining part in 

 the vapour state. Let us put the fraction which is found in the 

 vapour state equal to y. The point that indicates the state of that 

 mixture, lies then on a nodal curve which rests on the binodal 

 curve. Let the end of the nodal line which rests on the liquid branch 

 be denoted by the index 1, and the other end by the index 2. Let 

 us represent the molecular volume of the end 1 by v x , and the 

 molecular volume of the other end by v„ then when v represents 

 the volume of the quantity which is in heterogeneous equilibrium : 



v — v x (l—y)-\- v ,y 

 the constant quantity x being represented by : 



x — x, (1 — y) + x,y. 

 From this we find : 



dv = (v,— v,) dy -f (1—3/) dv x -f y dv, 

 and 



= (#,— # x ) dy + (1 —y) dx x -f y da:,. 



By elimination of dy we obtain the equation : 



V — V ( I 



— dv — — Ul—y) dx x + y d.v a )\ — (l—y) dv,— y dv,. 



x,—x x [ ) 



Now in general dv =-. ( — j dx -f- ( — I d P- Let us a PP ] J tllis ecjua- 



\dssj p V'rJs 



tion for the points 1 and 2 of the binodal curve, and let us take 



the course going from i\ to v t -\- di\ and from v, to v^ -f dv, on 



the surface for the homogeneous phases. Then : 



and 



/dv.\ fd v i\ , 



do 1 = [-—\ dx, + — dp, 



dsS x J p \dp J horn 



dv. \ _ fdv,\ 



dv,=l-±)dx, + (-±\dp. 



dSB,Jp \dp J horn 



The quantities ( — - J and ( — - ) must then be taken along an isobar. 

 \dxj p \dx,J p 



If we substitute the values of di\ and dv, in the equation for dv, 



it becomes: 



