IJY J. E. TREVOR
For the iz + 2 phases that coexist at a multiple point of an a-component system, Gibbs’s theory of theniiod) namic rquilibrium supplies the eqaations, I
J
- 1
where 72,
Zli,
ne,,
p2)
denote the voliiine, the entropy, and the inass and ciieinical potential of thej-th component, of the i-tli pliaseof the system ; and p , 8 the pressure and therniodynntnic temperature. On eliminating tlie corninoil dp’s bet\veen the si1ccessix.e pairs of equations, solvi n g the resulting equations for @,dB and for respectively, and adding, we find
&,+
’
J
,zx
where is the work absorbed in the transfer of unit iiiass from the m-tli to the it-th phase. It shoiild be noted, further, that we can successivel? eliminate d8 and d f l between the successive pairs of oiir initial linear equations. In the simple case of a one-component sj-stem, u e find 2,
71
djll
-
dP
ijl 7)tl
711
n'~li
712,
qr
4
'I,
'I1
dell
71,
:2
4
m,
i,
71ZL
zll
d~,, ((6
i
z-
712
( f j t
i,
vi
dP
112-
~r
" ~ 2 3
m , vi rI
z'
vi
i,
71171t,
+
+
(lP d0-,
dp-{ de
i',
74
n'jH
i'l
711
dP
71 7,
~ ' P I I
?)zj
1721
-
vi 71
r,
111,
i
111,
7 ,
=o,
j3)
- - ~ , (4)
dP dp
- 0 ,
(5)
- 0,
(6)
'1
,
dp
(io
eqiiations which are atlalogous in form to the foregoing fundamental equations of the triple point. If, iiow, equations ( 4 ) a i d ( 6 ) be multiplied through by 8 and -$, respectively, the> become :
like equations ( ~ nand ) ( 2 n ) above. T h e extension of these results to Yz-component systems is a simple matter. Coiwell Iicivemiiy.
