80 Prof. H. L. Callendar on the Thermodynamical 



then takes the form c/Y = constant, or ^?/0 n+1 = constant, or 

 p n (v — b) n+1 — constant. 



In the case of steam the constancy of the specific heat, 

 and the accuracy of the value found by experiment, may be 

 further verified by calculating the values of the total heat and 

 saturation pressure as follows : — 



Adopting the assumption S u = constant, it is possible to 

 express the thermodynamical properties o£ any imperfect gas 

 or vapour in terms of c by means of very simple formulae : 

 •thus we find 



Entropy, <£ = S log c 0— R \og e p — ncplQ + A, . (58) 



Energy, E = * o 0-nc/> + B, ...'.... (59) 



in which A and B are indeterminate constants of integration. 

 The values of the other thermodynamic functions follow 

 immediately from those of E and <f>. Thus we find for the 

 total heat 



F=E+pt>=8o0— (w+l)<y + ftp + B; . . . (60) 



and for the thermodynamic potentials at constant pressure and 

 volume, 



G=F-00 = S o 0(l-log e 0)-R01og eP -(c-%-A0 + B, (61) 

 J = E-00 = * O 0-So0log c 0-R01og ei p-A0 + B. . . . (62) 



Observing that the difference of the total heats of the liquid 

 and vapour at any temperature is equal to the latent heat L 

 and the difference of the entropies equal to L/0 (or equating 

 values of G for the liquid and vapour), we obtain the equation 

 for the saturation-pressure, 



Rlog e ^ = A'-B70-^-S o )log e 0+( c -%/0, . (63) 



in which the specific heat s' of the liquid is assumed to be 

 constant. A' is a constant to be determined by the obser- 

 vation of the boiling-point ; B' is the difference of the con- 

 stants B in the expressions for the total heats of the vapour 

 and liquid, which may be determined by the observation of 

 the latent heat at the same point. 



It should be observed that the equations for the thermo- 

 dynamic potentials and for the vapour-pressure are inde- 

 pendent of the assumption that c varies inversely as the nth 

 power of the temperature, and are generally true provided 

 that c — b is a function of the temperature only; but the 

 assumption c = c {) (0 o /6) n satisfies RegnauhVs observations of 

 the saturation-pressure very accurately. 



