890 
1—a—f is in equilibrium with a liquid Z of the composition «, 4 
and 1—«—y and with a vapour Z of the composition ,, y, and 
1—x,—y,. We call the volumes of these phases v, V, and V,, 
their entropies 9, H, and H,, their thermodynamic potentials 5, 7 
and Z,. 
As equilibrium conditions we find : 
\ 
\ 
OZ 0Z 
Z — («—a@) en (y— B) an eee | 
ÒZ. OZ 
ee) Ss (Bye eG eae tok ule hae ioe (19) 
Ow, Oy, 
DAZ, 0Z 02, 
nT ee 
From this we find: 
[(e—a) r + (u—B8)s] dx + [(a—a)s + (y—p)t| dy = AdP—BdT . (2) 
[(@,—a@)r, + (u, - B)s,] de, + [(e,—a)s, + (y,—p)t,] dy, = A,dP - B‚dT(3) 
dV, AV ee 0H 
en | 
rde + sdy = rd, + s,dy, + Ee a RT dT (4) 
®, ki ©, ; 
| dV, Ol 0H, ÒHN\ 
sde + tdy = sd, + t,dy, + (| — — — |dP— | —— df (5) 
5 Oy, oy ; 
If we only want a relation between dv, dy, dP, and d7’ then 
from the previous equations we deduce: 
[(@—a)r + (y B)s] de + |[(y—a)s + (y—p)t|dy = AdP—BdT . (6) 
[(7,—a)r of (y,—y)s|da in [(7, — x)s + (y,—y)t}dy = CdP—DadT . (7) 
In this: 
OV OV 0H 0H 
eG BA + eo Oo 
Ow Ov Ow Oy 
Sipe OV OV 0H 0H 
en a aoe eee a) a dt (oa ee 
Ou Oy Oa Oy 
e 
In order to obtain the saturation line of the solid substance # 
under its own vapour pressure we call in (6) and (7) d7'=0; we 
then obtain : 
(ee — a)r + (y — 8B) sl dw + [(w — a)s + (y —)t|dy = AdP (8) 
(eer + (y,—y) 8] de + [ry ee (yy) t]dy = CaP (9) 
The correlated vapour line is obtained by interchanging in these 
relations the quantities relating to vapour and liquid. In order that 
the pressure in a point of the saturation line under its own pressure 
may become maximum or minimum d/ in (8) and (9) must be = 0. 
Hence : 
~ 
56* 
