FUNDAMENTAL EQUATIONS OF IDEAL GASES 385 



This is the form adopted by Gibbs.* We proceed to examine a 

 few properties of this equation. 



The equation of state of the gas mixture is assumed to be 

 pv = Rt(ni + 712), where ni is the number of mols of NO2 and ria 

 the number of N2O4, which permits the equation to be expressed 

 as 



rii 



AE 



log — = - — + /. 



n^v Rt 



(119) [309] 



Setting p — equal to kp, and — equal to kc, and differentiat- 

 X2 ThP 



ing (118) [309] with respect to t at constant pressure gives the 



equation 



'd log kp\ AE + Rt 



c- 



dt /p Rf 



But equation [89] on differentiation and substitution of 



(120) 



'(|),* + 'va(/. 





dp + Cpdt for de + pdv, 



where Cp is the heat capacity at constant pressure, gives 



dx = Cpdt — 



.dt, 



— V 



dp, 



(121) 



and 



®r'- ©. = -['©.-"] 



'dVT 



— ' (122) 



where r = t"^. The summation principle [283] leads to the con- 

 clusion, however, using the first of the above pair of equations, 

 that 



X = [S I'lXi + 2 viCp,dt]p. (123) 



In (118) [309] the heat capacity terms have been assumed to 



* See paragraph beginning line 4, Gibbs, I, 180. 



