76 
THERMODYNAMIC METEOROLOGY 
The conditions of equilibrium for the maximum entropy are 
uniform temperature, T — T\ = T 2 = T 3 , and uniform pressure, 
Pl = P2 = Ps. 
Hence we have by selection, 
(309) r 2 = Ti (Si — S 2 ) = A {Ui — U 2 ) + Pi (®i — v 2 ) for vapor 
and liquid. 
(310) r 3 = T 2 (S 2 — Sz) = A (Ui — U 3 ) + P 2 (v 2 — Vs) for liquid 
and solid. 
Specific Heats 
A third example of a reversible cyclic process is given in the 
specific heats, Ci for vapor, C 2 for fluid. From the first law by 
(234), we have, 
(234) 
dP d.A P d.Cv 
dT dT dv 
Develop these terms successively by substitutions. 
Differentiate the last form of (293), dividing by d v, 
, * ,.d.AP M dr 2 _ r 2 M d (vi - v 2 ) 
bm) u; dT - Vi _ V2 - dT (vi-v 2 ydT 
rdn r 2 d (vi — v 2 )-i M 
Ld T (vi — v 2 ) d T J V\ — v 2 
The specific heat of the mixture is, by (136), 
(312) Cv = C 2 (M—Mi)+Ci M\—r 2 Hence, by (289), 
(313) 
(314) (2) 
Cv = Ci(M-Mi)+CiMi- 
r 2 d[Mi Vi + (M—Mi) v 2 ] 
(vi + v 2 )dT 
(315) 
dCv 
dv 
C 2 dMi CidMi 
~v 
r 2 
dv 
d v 
rd Vi — d v 2 ~[ 
(®i + v 2 ) L dT J 
dCv 
~d 
-= r 
v L 
C 2 + Ci - 
r 2 d (vi — v 2 ) 
A M 
J (vi - Vi). 
A< £ = {¥i+ C >- C ') 
'dr 2 
(vi + Vi) dT 
Subtract (1) — (2). 
M 
Vi - v 2 
(316)