FUNDAMENTAL EQUATIONS OF IDEAL GASES 341 



(-f) 



is also well known ^-^ to proceed to a finite limit for 



p — > 0. The quantity is in fact never zero except at a unique 

 temperature, characteristic of each pure substance (Boyle — 

 point). It follows, therefore, that (pv — Rt) vanishes at all 

 temperatures when p — * 0.* 



4. Constancy of Specific Heat. The justification for defining 

 a perfect gas by means of equations (II), (III) and (IV) is 

 complete except as regards the absolute constancy of specific 

 heat. Experiment has proved to a high degree of precision 

 that the constant-volume heat capacities of monatomic gases, 

 at low pressures, are independent of temperature. Thus c for 

 argon is very closely 2.98 from below zero degrees to about 

 2000°C. However, in the case of diatomic gases the tem- 

 perature dependence, while small at ordinary temperatures, is 

 significant and the modern quantum theory is eminently satis- 

 factory in the account it provides of the course of c for hydrogen 

 from a value of 2.98 at low temperatures to a value of 4.98 at 

 room temperatures. Molecules of a higher order of complexity 

 have a correspondingly large positive temperature coefficient 

 above zero centigrade. 



6. Concluding Statement. We may therefore sum up the 

 present position with respect to the validity of the relations 

 (II), (III) and (IV) by stating that (II) may be assumed to 

 have been abundantly shown by experiment to correspond 

 with reality as a limiting law for computing pressures for all 

 pure gases. The independence of c with respect to tempera- 

 ture is, however, only true on the basis of present experience for 

 monatomic gases, and the magnitude of the temperature coef- 

 ficient of the heat capacity for all higher order molecules is large 

 according to the order of complexity. 



6. Comment on Gas Law for Real Gases. A discussion of the 

 section might be carried forward from this point without 

 explicit reference to an equation of state of greater complexity 

 than (II). Gibbs has, however, adopted a definite hypothesis. 



* It should be understood that temperatures greater than absolute 

 zero are referred to throughout in the considerations above. 



