348 KEYES ART. J 



The latter equation for /x is, as it should be,* identical with 

 (10) [264], since at/p is equal to v/m. 



/H - c \ , /c\ 

 By setting I ~ ^) ^^^ V / ~^ ■'" ^^^^^ ^^ ^^^ constants 



Ki and K2, (15) [268] may be written 



n - E 



p = a ■ e' f' e "' , (16) [270] 



or the density p is given by 



p = e'^t^-'e "' . (17) [270] 



12. X Function for an Ideal Gas. The equation for xt is 

 likewise readily formed from equations (II) and (IV). Thus 



X = e + py = m(c + a)« + mE, (18) [89] 



and on differentiating this equation there results, using [86], 



dx = tdv -\-vdp-^Z udm, (19) [90] 



showing that the independent variables are the entropy, pressure 



X — fnE 

 and mass. From (18) [89] there is obtained t = —, — ; — r, and 



w(c + a) 



using the total differential of [89], with tdr\ replacing de. + pdv, 



we have 



X — mE X — mE adp 



dx = "7 I ^ • d'O + 



mic + a) (c + a) P 



or 



m(c + a) ;; = ^77 + am — , (20) 



X - mE p' 



which on integration, and using the entropy constant H, gives 

 [271], or 



* See equations [104], Gibbs, I, 89. 



t This quantity is frequently referred to as the "total heat," a 

 somewhat misleading term. It is also often designated by the symbol, H. 



