FUNDAMENTAL EQUATIONS OF IDEAL GASES 381 



In general the heat capacities are known over a Hmited range 

 of temperature, for H2 is the only gas whose heat capacity is 

 known at low temperatures. The question of whether the 

 heat capacity approaches 3/2 R or vanishes at zero Kelvin is, 

 moreover, not yet settled. In the case of water vapor values of 

 C3 are available to temperatures where water vapor is detectably 

 dissociated. Such values must, however, be corrected for heat 

 absorbed due to dissociation; a correction evidently impossible 

 to obtain until the dissociation data can be correlated, and then a 

 final and exact result is only possible by successive approxima- 

 tion. Above zero degrees the heat capacities of most gases 

 increase rather slowly, and in the absence of a generally appli- 

 cable theory of heat capacities of gases linear expressions, or at 

 most quadratic expansions, may be used. On this basis the 

 heat capacity terms become, when the linear form is used, 



2^1 / c,*dt = ^v,a, {t - to) + SV (^' - ^0')' (116) 



J to 



2)"! / ci*dt/t = ^via,\og{t/to) + ^vA (t - to). (117) 



J to 



The present custom is often to integrate the linear terms 

 between zero Kelvin and t, but such practice, as is frequently 

 the case, had its origin in the earlier erroneous belief that 

 the heat capacity dependence on temperature was as simple 

 below the ice point as it appeared to be above. Note should be 

 taken also of Gibbs' decision to express the reaction pressure- 

 temperature function in terms of the energy constant £"1, a 

 choice very likely induced by the somewhat simpler treatment 

 possible when non-ideal gases are involved. 



When Zi'i vanishes in (114) [309] the mol fraction function 

 Si'i log xi becomes a function of temperature alone, and thus 

 pressure is without influence on the numbers of the different 

 kinds of molecules so long as the gases are ideal. A further 

 simplification would result if the terms 



/ J vi I Ci*dt and 2j 



vx \ Ci*dt/t 



