LEWIS. — FREE ENERGY AND EQUILIBRIUM. 13 



Similarly, for any system in general in which the pressure is not very 

 FY 



great, cm ,., J will be negligible, and, for a very close approximation, 

 equation (18) becomes 



dlnK f }_JZ\ JL /on 



dT \ EBhxKJ ~ HI'*' { > 



Comparing equations (20) and (21), we see that the conditions under 

 which the above law of vau't IIolF holds true are practically the same 

 as those under which the equation '•isotherm" of the mass law, equation 

 (12), is true; namely, that F. and therefore C v [ — C v and H are, 

 at constant temperature, independent of the volume conditions of the 

 system. 



The various equations which have been here deduced from the general 

 equations of free energy and equilibrium can be best studied further by 

 their application to special cases of equilibrium, which we will proceed to 

 discuss somewhat systematically. 



II. Application to Mono-molecular Systems. 



(.1.) Homogeneous Systems. 



1. Gates. — The simplest conceivable case of physico-chemical equi- 

 librium is offered by a single molecular species in a single phase in 

 equilibrium with the external pressure. For this case the equation of 



condition has already been found, — equation (8), namely, 



RT r'\ dc d% dm 



p = - - + ' I r , d 1 — 1— — . 



v J TqJ- >' '" dv dv 



In the case of a perfect gas it has been shown that 



dc v n ''lb A dWi A . FT 



— ? = 0; p = 0; -j- = 0; and p = - - . (22) 



dv dv dv v 



The next case that deserves attention is that of a compressed gas. 

 Here, also, the specific heat at constant volume is independent of the 

 volume. This has been shown to be true up to pressures of several 

 thousand atmospheres.* A recent work has questioned the absolute 

 accuracy of this law. We will return to this point later. Meanwhile 



dc 



we mav consider , - = 0, and equation (8) then simplifies to 

 (I v 



* Mallard and Le Chatelier, Wied.-Beibl., XIV. 364. 



