390 KEYES 



ART. J 



Performing the operations indicated in [338] the following 

 equation is deduced : 



Accordingly the right hand member of the latter vanishes for a 

 substance whose (dp/dt)v coefficient is constant, and the con- 

 clusion follows that Cy is a function of temperature only. But 

 no restriction has been put upon whether (dp/dt).^ is to be taken 

 at high pressures or low, for perfect or imperfect gases, and 

 therefore c^ is the same whether the fluid is of great density or 

 of vanishing density. A fluid following van der Waals' equation 

 would possess the latter quality. Comparison of the heat 

 capacity c» of ether, for example, in the liquid phase and the 

 gaseous phase will show that the heat capacities are equal for 

 the substance in the two phases. This, however, is not to be 

 taken as an indication that ether follows van der Waals' equa- 

 tion. As a matter of fact, however, {dp/dt)v is remarkably 

 independent of temperature in the case of many substances, 

 (in both the gaseous and liquid phases) •^■* particularly non- 

 polar substances in the dielectric constant sense of the term. 

 Assuming the gases NO2 and N2O4 to be ideal the equation of 

 state may be written pv = Rt (ni + ^2) where rii and ^2 denote 

 the number of mols of the two gases. Assume that one mol of 

 N2O4 is dissociated to the extent a, the fraction dissociated. 

 The quantity Ui will be then given by 2a and 712 by (1 — a) 

 whence pv = Rt(l + a). On the other hand [333] in terms of a 

 becomes 



or 



log p : ^ Ao+ Bologt - 



i — (X I 



Ao' t^o e « -' (136) 



1 — a^ p 



where Ao, Bo and Co are constants related to similar ones 

 appearing in [333]. By means of the latter an expression for p 



