144 



Trans. Acad. Sci. of St. Louis. 





(5) 



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

 tion on t'he 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 m, v, a line of 

 constant volume, for which n 

 = OD ; m, K, an isentropic line, 



O 

 for which 7i ^tt ^= 1-41 



«; 



m, ^, an isothermal line, for 

 which n = l; and m, ^, 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. 



(3) 

 (6) 



(7) 



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

 these values in (5), together with the value of e/ = 4.19 X 10*7, 

 and the specific heat of hydrogen, for various values of /i is 

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



values 



^ «^ idr)^ 



are computed for compression only. For 



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

 every case reversed. 



