218 (./. W. (jribhs — Equilibrkiiu of Heterogeneous Suhstances. 



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

 (278) or (279), when the proportion of its components remains un- 

 changed, will have all the properties which we have assumed for an 

 ideal o-as 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 



c = ^'^-\ (280) 



m 



and 



,;^_«=^' !!hj£i+^. (281) 



We have already seen that the values of t, v, m^, /.i^ in a gas- 

 mixture are such as are possible for the component G^ (to which 

 /«j and /<j relate) existing separately. If we denote by jOj, j/^, //'j, 

 £,, ^'j, Cj the connected values of the several quantities which the 

 letters indicate determined for the gas 6^j as thus existing sepa- 

 rately, and extend this notation to the other components, we shall 

 have by (273), (274), and (279) 



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



The quantities p, //, '/', €, j, ? relating to the gas-mixture may 

 therefore be regarded as consisting of parts which may be attrib- 

 uted 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 pos- 

 sible for a mixture of gases which are not ideal gases, and indeed 

 without any limitation in regard to the thei'modynamic properties of 

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

 pressure in a mixtuz-e of dilFerent gases is equal to the sum of the 

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

 tempei'ature and with the same value of its potential. For let 

 Pii V\i ^n '/'i' /I'l' ^1 ' P2-> etc.; etc. be defined as relating to the 

 different gases existing each by itself with the same volume, tem- 

 perature, and potential as in the gas-mixture ; if 



