FUNDAMENTAL EQUATIONS OF IDEAL GASES 363 

 (v — BiiTii). Equation [280] now becomes 



c = 





11 



+ higher terms in 7 and ~' (72) 



t V 



19. Ideal Gas Mixture in a Potential Field. The paragraph 

 beginning Gibbs, I, 158, last line, is introduced to emphasize 

 the fact that in a mixture of gases, as in the atmosphere, each 

 gas may be assumed to react to the gravitational field inde- 

 pendently of the presence of the other gases". The point 

 is made use of by Lord Rayleigh to investigate the work of 

 separating gas mixtures and the reader is referred to Vol, I p. 

 242 of Scientific Papers, Lord Rayleigh, Camb. Univ. Press, 1899; 

 Phil. Mag., 49,311, (1875). 



SO. Vapor Pressure of a Liquid under Pressure from a Neutral 

 Gas. The subject of the effect of an insoluble and neutral gas 

 on the vapor pressure of a liquid has been discussed earlier, 

 making use of [272] in connection with the comments on 

 the additive law of vapor pressures. The treatment taking 

 account of a finite solubility of the neutral gas in the liquid is 

 given in Gibbs, I, beginning p. 160, last paragraph. It will be 

 seen that the phenomena connected with Henry's law con- 

 stitute a special case of a binary mixture. Thus with carbon 

 dioxide at zero degrees the pressure may be increased to 34.4 

 atm. at which point carbonic acid would liquefy since this is the 

 saturation pressure. The temperature of the system may also 

 be above the critical temperature of the neutral gas as with 

 carbon dioxide above 31°, and in the process for separating 

 helium from the natural gas in Texas. 



The general equations for the case of a two-phase binary 

 mixture are 



— v' dp + r]' dt + mi 'dtii ' -j- m^ 'd^i ' = 0,1 



-v"dp -f i)"dt -H mi"dMi" + m^'dii<l' = O.J 



At equiUbrium d/x/ = diix' , dii-l = dix2" , whence, if m^'/mi = r' 



