(5%) 
These equations would also hold, if w, and u’, still depended 
on w, and y,, but then it would not be possible to express 7, and 
y, in w, and y,. Performing the substitutions mentioned we get: 
ik l—a,—y,  @, 
- RAE ae Sea ey av os, Nog EON 
P va Paths 
As it is however not only our aim to obtain the results, but as 
we also wish to interpret the equations given before, we return to 
equation IL in order to determine the line of equal pressure for the 
vapour phases. 
If we continue to use the index 2 for the vapour phasis, and the 
index 1 for the liquid phasis, but if we now apply equation II to 
the vapour phases, it assumes the following form: 
2 2 
5 5 
Vie dp == | (vw, — 2) jas an Kiel, Òz,dy, | ie 
5 5 
(v,—2,) Apes Se isd al Das | dy, d 
y 
B: 0v,0Y 4 J2 
As we may neglect wo, and uw’, for the vapour phases, we may 
also neglect the second derivatives of u; and we may put: 
02 N 12 d? 1 
SURT ETR pees : 
Om? wv, (l—a,—y,) 0x,0y, 1—e,—y, 
0? Td 
and SURT LE 
Oy,” nlt 
dv dv dv 
We have v,, = 7, —-v, — («,—2,) — (y¥,—y,)| —— | ;and| — 
de, p dy, d de, p 
dl) are zero for the vapour which we assume to follow the 
dy, Jp 
law of Boyle, and so to occupy the same volume, if the pressure and 
the number of molecules are constant. If we neglect moreover the 
volume v, of the liquid compared with v, the volume of the vapour, 
then we get after division by MRT: 
dp 1—1 Y,—Y, 
ea = Wer) ——— Ys ties ee kel da, + 
P 4 «(1—a#2,—y,) 1 Ts Us | 
Ld l—wz | 
af | ene ae ede) dy, 
Loy, : ve) 
For a binary system this yields the well known equation: 
‘dp Ld, 
P ave «,(1—«,) 
da 
