FUNDAMENTAL EQUATIONS OF IDEAL GASES 359 



beginning eleven lines from the bottom of 156 and ending at the 

 corresponding point on 157 comprises material and inferences 

 following quite directly and simply from equations [273] to 

 [278]. The last sentence is significant. "It is in this sense, 

 (equations [282], [283]) that we should understand the law of 

 Dalton, that every gas is as a vacuum to every other gas." 

 The statement that Gibbs' relations [282] and [283] are "con- 

 sistent and possible" for other than ideal gases refers evidently 

 to the belief that the relations in question, taken quite generally 

 and without reference to the idealized gas laws, might lead to 

 better accord with fact than would be possible with the latter. 

 Thus the pressure of the individual gases composing the sum 

 in the first of equations [282] may be any function of volume 

 and temperature. By the use of (VII) for example, the total 

 pressure would be written, 



Saitnii 

 The energy, entropy and i/' function then become 



+ Y^m.E,, (53) 



V = 2j'^i= 2jm^ J^ ci* - + 2j^,a, log ^^ 



\l/ = //Wi / Ci*dt + / jTUiEi — f /.mi / Ci* dt/t 



•^-\ V — Binii -^^ 

 — t / jMiai log — t / jViiHi. (55) 



Equation (53) may be established by starting with either 

 of the equations 



\dv)t \dt). 



p, (56) 



