144 



Trans. Acad. Sci. of St. Louis. 



dT~ ^'^ 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 m, v, , a line of 



constant volume, for which n 



= Qo; m, AC, an isentropic line, 



6\ 

 for which n ^tt = 1-41 = k, ; 



m^ ^, an isothermal line, for 

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

 of constant pressure, for which 

 n = 0. 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, 0= 4.143 X 107 and 6^ = 2.420. Putting 

 these values in (5), together with the value of •/ = 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 of 



(dQ\ 



are computed for compression only. For 



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

 every case reversed. 



