FUNDAMENTAL EQUATIONS OF IDEAL GASES 343 



In many cases of interest in the application of Gibbs' theory to 

 gaseous equiUbria, the temperature of measureable reaction 

 rate and practically significant concentrations of the products 

 of the reaction are sufficiently high to enable an equation of 

 essentially the type of (VII), (Vila), to be used without involv- 

 ing too serious error -•'• ^^' ^^- ^^. Every purpose will be served in 

 what follows by omitting all terms in the brackets in (Vila) 

 following the one having the coefficient ai. 



7. Choice of Units of Mass arid Energy. The equations (II) 

 to (IV) of Gibbs refer to "a unit" of gas and the gram or gram 

 mol might equally well be employed. We will consider one 

 gram as the unit quantity in what immediately follows and 

 the gram mol in those instances where convenience is thereby 

 better served. The unit of energy will be the mean gram-calorie 

 equal to 4.186 abs. joules where practical applications require 

 specification of the unit. The temperature scale will be that 

 of the centigrade scale given by the platinum resistance ther- 

 mometer plus 273.16, and the pressure unit the international 

 atmosphere, volumes being taken in cubic centimeters per gram 

 or gram mol. 



8. Definition of Temperature. It is noted that the tempera- 

 ture is defined by the perfect gas (Gibbs, 1, 12-15) or quite simply, 

 if the heat capacity c is assumed an invariable constant, by the 

 energy equation. Taking equation [11] (Gibbs, I, 63) for the 

 energy, de = tdrj — pdv, temperature and pressure may be 

 expressed in terms of the energy e, the volume, and the appro- 

 priate constants. From (IV) and (II) there result 



€ - E 

 t = —^> (1) [257] 



V = ' (2) 258 



V c 



monia under the same conditions of temperature and pressure has a 

 pressure less than that given by (II) by one and one-half percent, and 

 in conformity with the modern theory of cohesive and repulsive forces 

 the bracketed expression on the basis of a van der Waals model be- 

 comes more complicated. However, in the case of dipole gases at ever 

 higher temperatures (VII) tends to a simpler form on account of the 

 diminishing relative importance of those terms arising from the presence 

 of the permanent dipole. 



