EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 169 



If we denote by fa and fa the volumes (determined under standard 

 conditions of temperature and pressure) of the quantities of the gases 

 G l and G 2 which are contained in a unit of volume of the gas G s , we 

 shall have 



/-I AI Ot-i j / AoOto /OA/3\ 



fa - -, and /3 2 = ^ % (306) 



3 3 



and (302) will reduce to the form 



& nnrt -nj3i+/3o-l n n ^ n t* ^ ' 



a 3 a 3 



Moreover, as by (277) 



^v=(a 1 m 1 +a 2 m 2 +a 3 m 3 X, (308) 



we have on eliminating v 



A . B', , C /O AA\ 

 T = log* -- 7, (309) 

 - ] 



where B / = \c l -i-\c z c^-\-\ l a l +\ 2 a 2 a^ (310) 



It will be observed that the quantities fa, fa wl ^ always be posi- 

 tive and have a simple relation to unity, and that the value of 

 fa+fa 1 will be positive or zero, according as gas G 3 is formed 

 of G, and G 9 with or without condensation. If we should assume, 



1 4 



according to the rule often given for the specific heat of compound 

 gases, that the thermal capacity at constant volume of any quantity 

 of the gas 6r 3 is equal to the sum of the thermal capacities of the 

 quantities which it contains of the gases G l and 6r 2 , the value of B 

 would be zero. The heat evolved in the formation of a unit of the gas 

 Gr 3 out of the gases G t and G 2 , without mechanical action, is by 

 (283) and (257) 



or Bt + C, 



which will reduce to C when the above relation in regard to the 

 specific heats is satisfied. In any case the quantity of heat thus 

 evolved divided by a B t 2 will be equal to the differential coefficient of 

 the second member of equation (307) with respect to t. Moreover, 

 the heat evolved in the formation of a unit of the gas G 3 out of the 

 gases G 1 and G 2 under constant pressure is 



which is equal to the differential coefficient of jbhe second member of 

 (309) with respect to t, multiplied by a^t 2 . 



It appears by (307) that, except in the case when fa+fa = I, 

 for any given finite values of m 1 , m 2 , m 3 , and t (infinitesimal values 

 being excluded as well as infinite), it will always be possible to 

 assign such a finite value to v that the mixture shall be in a state 



