Thermodynamic Properties of Air. 25 



The variations of the specific heat c p , as revealed by these 

 tables, have been represented in a graphical form on PL II. 

 It will be remarked that with increasing pressure the specific 

 heat increases, the more considerably the lower the tempe- 

 rature of the corresponding isothermal. In the vicinity of the 

 critical temperature these increments are largest, and in the 

 critical state itself the specific heat tends to infinity. This 

 might have been anticipated, on the ground of equation (2), § 2, 



because zj- = in the critical state, whilst c and ^7 remain 

 finite. 9b ; ' d< 



The most interesting feature of the diagram (Plate II.) is 

 that at temperatures above the critical the specific heat rises 

 with increasing pressure only to a maximum value, corre- 

 sponding to a certain limiting pressure (which is a function of 

 the temperature). Under pressures exceeding this limiting 

 value the specific heat remains nearly constant, with but a 

 slight tendency to decrease. The lower the temperature, the 

 smaller is this limiting pressure, and the more marked the 

 transition from increase to approximate constancy of the 

 specific heat. It would seem as if these pressures marked a 

 limit between truly gaseous states and a gaso-fluid condition 

 of matter, in which the intrinsic pressures attain a prepon- 

 derance against which the external pressure has but little 

 influence. It is interesting to note that the curves of the 

 coefficient of expansion a, under constant pressure (Part I., 

 plate i.), show similar bends for pressures which are not 

 much different from the limiting pressures of the specific-heat 

 curves. We shall see that neither the curves of the specific 

 heat at constant volume, nor those of the coefficient of expan- 

 sion at constant volume, show any trace of bends of this sort. 



§ 13. It is a more difficult matter to calculate the variations 

 of the specific heat at constant volume. At first sight it would 

 seem easiest to apply the equation (3), § 2 : — 



~&v Jm ~dt 2 



But we shall see that the variations of pressure at constant 

 volume are so nearly proportional to those of the temperature, 

 that the calculation of the second differential coefficient 



—-f is practically impossible. 



In order to find the variations of pressure of air of any 

 density kept at a constant volume, I shall refer once more to 



