386 KEYES 



ART. J 



vanish, and application of the same condition to the last equation 

 leads to 



y^ = 2^ix = Axi = A^ + i:viRt = AE -i- m. (124) 



But this is the numerator of the expression (120) for the 

 derivative with respect to t of log kp, which is to be identified as 

 the heat of reaction at constant pressure subject to the condi- 

 tion that the specific heat capacities of the reacting gases are all 

 equal (i.e., 2viCi = 0). 



The temperature derivative of log kc, taken for constant 

 volume, is 



/ 8 log k,\ AE 



and AE is the heat of reaction at constant volume. From [86] we 



find { — ) = c and integrating at constant volume using [283] 

 \ot/v 



we have 



' ^ (126) 



= \aE+ jY^ViCidt 



which is the general equation for the energy at constant volume. 



The above is the equivalent, with some elaboration of detail, 



of the material of Gibbs, I, 180 and the first third of 181. 



It remains to note that since we have defined log kp and log kc 



as equal to 2j ^^ ^^^ P^i ^^^ Zj ^^ ^^^ ~' V — ^ — ~ ) ^^ ^^^° 

 and 



( d log fcA ^ ^ 



from (114) [309]. If, however, we set S vi log xi equal to log kx, 

 then from (114) [309] it follows that 



\ 8p 7, p 



\ dv ), V 



