144 



Trans. Acad. Sci. of St. Louis. 



dQ 



dT 



?=C' + 



C 



J{l—n) 



(5) 



Equation (3) may be considered as representing a projec- 

 tion on the P, V plane of a curve drawn on the thermodynamic 

 surface P, v, T. The equation of this surface is (1), and its 

 form is the well-known hyperbolic paraboloid shown in the 

 figure. 



Lines represented by (3), in 



the figure are wi, v, a line of 



constant volume, for which n 



= oc ; m, K, an isentropic line, 



C' 

 for which n =7t = l-^l = «; 



m, t, an isothermal line, for 

 which ?i = 1 ; and m, p, a line 

 of constant pressure, for which 

 n = o. The projections of 

 any of these lines, or of any 

 line represented by (3) inter- 

 mediate between these principal lines, on the three reference 

 planes, are represented by the equations, 



Fv" 



Tv"-i = 



A 



C 



(3) 

 (6) 





A 



(Jn 



(7) 



For hydrogen, (7 = 4.143 X 10^ and 6\ = 2.420. Putting 

 these values in (5), together with the value of J" = 4.19 X 10^, 

 and the specific heat of hydrogen, for various values of n is 

 computed as given in the following table. In the table the 



values 



- m. 



are computed for compression only. For 



the same value of n in expansion, the sign oi dT would be in 

 every case reversed. 



