FUNDAMENTAL EQUATIONS OF IDEAL GASES 391 



as a function of a and t is found and, using the equation for pv, 

 another equation giving v in terms of a and t. These are 



1 - a2 _Co 



p = — Ao't^ e ' ' (137) 



a 



a 



1 - 



2 Co 



1 -B 



a 



Ao" r - ^° e ' ' (138) 



R 



where Aq" is -j-,. From the equations it is clear that (dp/dt)v 



cannot be independent of temperature except in the strict hmit 

 oi p = or t = CO , for 



/dp\ R ^ ^ Rt /da\ 



[Vtl = ; (1 + «) + 7 [m): 



Equation [342] is the Gibbs-Dalton rule, p = 2pi, applied to 

 the case of binary mixtures assuming equilibrium to subsist at 



Rt , 

 all times. It is equivalent to the equation p = — (1 + a) 



where mols are used instead of masses. The equation for v 

 above corresponds to [345]. Since the entropy and energy 

 conform to the summation rules, [282], [283] may be easily 

 formed in terms of mols from the foregoing, while the calcula- 

 tion of the specific heat capacity of the equilibrium mixture may 

 be carried out by differentiating the energy equation [346] of 

 Gibbs with respect to temperature at constant volume. 



VI. On the Vapor-densities of Peroxide of Nitrogen, Formic 



Acid, Acetic Acid, and Perchloride of Phosphorus 



(Gihhs, /, 373-403) 



This section comprises material examined with a view to 

 demonstrating the applicability of [309] or (114) [309]. Since 

 1879 a quantity of new density data for these substances has 

 appeared, but no new facts or inferences can be gleaned by 

 repeating Gibbs' treatment. In the case of the N2O4 —> 2NO2 

 reaction Verhoek and Daniels' work, already referred to, has 

 shown that the perfect gas laws are not sufficiently valid to 



