100 



On a change in T the liquid therefore traverses a curve in a 

 concentration diagram ; this is also the case with the correlated 

 vapour. We will call these curves the saturation and vapour saturation 

 curves of F -\- F' under their own vapour pressure, or also the 

 liquidum and the vapour curve of the four-phase equilibrium 

 p j^ l^' j^ Zi J^ Q, The relation between pressure and temperature 

 will also be represented by a curve in a P, 7^-diagrani. 



In fig. 4 this P,T-curve is represented by LSDE; in fig, 1, 2 

 and 3 a c is the liquidum and a^c^ the vapour curve of the system 

 p J^ ]7" J^ L J^ Q. Point a of the curve ac therefore represents a 

 liquid saturated at a definite P and T with F -\- F' ; j)oint a' 

 indicates the correlated vapour. 



Let us represent the composition, the entropy, the volume and 

 the 5 of F by: n,^, 1 — «— i?; % v and C, 

 that of F' by : a/ 3', 1— «'—,?', n' v' and ?' 

 that of the liquid by : .r, y. 1— -f — ?/, H, V ami Z 

 that of the vapour by: .Tj, //i, 1 — x^—y^, //,, V^ and Z^. 



The conditions of equilibrium then are: 



()Z dZ ^ 



z-{.v «)-r -C'/-^)'A =^^ 



dZ dZ 



Z-(,v-a'y^-{y-^')—=^' 

 Oil' oy 



) (1) 



dZ^ dZ, ^ 



dZ_ dZ, dZ_dZ^ 



d.v d.v^ dy dy. 



Hence, we have five relations between the six variables 

 X, y, .%\, ?/i, P, and P, so that we can consider the vapour pressure 

 of the system and the composition of L and G as functions of the 

 temperature as stated above. If we differentiate the equations (1) 

 and eliminate clc^ and dy^ we obtain : 



[{x-a) r + {y -/i) s] civ + [{.v-ft) x + (y—i^) t] dy = AdP-BdT (2) 

 \{x—i^) r + {y -iï) xj d.v + [(a--«') .s + 0/— /3') t] dy = A'dP-B'dT (3) 

 \{cc,-x) r -{- {y,-y) s\d,v + [{.v,-,v) s + {y,-y) t] dy = CdF-DdT (4) 



A, B, C and D have herein the values indicated in communication 

 II; A' and B' are found from A and B by substituting in the 

 latter u, j:?, v and i], by n', ii', v' and >/. If we eliminate dx^w&dy 

 from (2), (3) and (4) we get: 



dP n 1] + n' ?/ + m H + m^ H 



dT n V -\- rt! v' -\- m V -\- 7n^ V^ 



(5) 



