EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 157 



The values of c, a, E, and H will then be constant and m will denote 

 the total quantity of gas. As the equation will thus be reduced to 

 the form of (260), it is evident that an ideal gas-mixture, as defined 

 by (273) or (279), when the proportion of its components remains 

 unchanged, will have all the properties which we have assumed for 

 an ideal gas of invariable composition. The relations between the 

 specific heats of the gas mixture at constant volume and at constant 

 pressure and the specific heats of its components are expressed by 



the equations m r 



c = 2^, (280) 



m 



and . c+a=2 1 m '< c ' +ffi i>. (281) 



m 



We have already seen that the values of t, v, m 1} fa in a gas- 

 mixture are such as are possible for the component Q- t (to which ^ 

 and //! relate) existing separately. If we denote by p lt ij ly \fr lt e lt \i, & 

 the connected values of the several quantities which the letters 

 indicate determined for the gas G 1 as thus existing separately, and 

 extend this notation to the other components, we shall have by (273), 

 (274), and (279) 



P = 2 1 p 19 9 = 2^1, ^ = 2^; (282) 



whence by (87), (89), and (91) 



* = 2i*i> X = 2 lXl , f=2ifr (283) 



The quantities p, rj, \[s, e, %> f relating to the gas-mixture may 

 therefore be regarded as consisting of parts which may be attributed 

 to the several components in such a manner that between the parts 

 of these quantities which are assigned to any component, the quantity 

 of that component, the potential for that component, the temperature 

 and the volume, the same relations shall subsist as if that component 

 existed separately. It is in this sense that we should understand the 

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



It is to be remarked that these relations are consistent and possible 

 for a mixture of gases which are not ideal gases, and indeed without 

 any limitation in regard to the thermodynamic properties of the 

 individual gases. They are all consequences of the law that the 

 pressure in a mixture of different gases is equal to the sum of 

 the pressures of the different gases as existing each by itself at the 

 same temperature and with the same value of its potential. For let 

 Pi) n\y i> "0"!' Xi> fi Pz> e ^ c - 5 e ^ c - b e defined as relating to the different 

 gases existing each by itself with the same volume, temperature, and 

 potential as in the gas-mixture ; if 



then 



