LEWIS. — FREE ENERGY AND EQUILIBRIUM. 



11 



A'=e 



1 (P V V PT 



'^C\',__ ^^''^dT-II 



T 



) 



(15) 



ill which e is the base of the natural system of logarithms. 



From this general equation of equilibrium may be easily deduced the 

 expression for the change of the conditions of equilibrium with change of 

 temperature. In equation (14) let, for convenience, 



L 



TC — C 



H=.F, 



(16) 



equation (14) differentiated with respect to tem2:)erature then becomes 



'PV 



) \ ^ TT TJ d f1 



(17) 



rfln K 



dT 



1 



rd 



dT 



_}^dU U dF 



] 



Now 7^ is a function of T and also of In K, which is itself a function of 

 T. According to the laws of partial derivatives, 



d_F_hF hF d\nK 



d2'~ IT^ Ih^<:~dV 



where 8 signifies a partial differential. Since // is independent of the 

 temperature, and 



PT (J — C 



then, 



SF^a^^C^^ldJT 

 8T T TdT' 



Therefore, 



for 0..-C., = ^. 



\ dU ^F d\uK 



^ + 



dT T dT^ hlnK dT ' 

 and equation (17) becomes 



d\uK _ 1 [ \ T J 1 



dT i?L dT 

 and by transposition 



dn U IdU 8F dl 

 Td T'^ T- Td T^ SluK d 



'T J' 



dT \ Ii8\nKj~Ji\_ TT^'^T^j 



(18) 



