LEWIS. — FREE ENERGY AND EQUILIBRIUM. 11 



\(pv v rT c Vl -c v \ 



in 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, 



/, 



t c — C 



11 •* dT-H=F, (1G) 



equation (14) differentiated with respect to temperature then becomes 



d\*K_ ir d \~~TJ *dU x U_ + dF\ 



dT ~ B\_ dT "TdT^T 2 dT_\' { } 



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, 



dF ZF ZF d\x\K. 



dT sr + ) 



T 5 



where 8 signifies a partial differential. Since 77 is independent of the 



temperature, and 



pT c — C 

 F =j T ' T x - dT-II, 



then, 



*F_ c Vi -c vt _ \au (orQ _ c ._dU 



Therefore, 



dF 1 dU ZF d\nK 



dT T dT ' 6luK dT ' 

 and equation (17) becomes 



tfln K 1 f V T ) ldU U \dU IF d\nK ~\ 



dT ' R\_ d~T~ TdT + ~T- TdT + BlnJC dT J' 



and by transposition 



dT \ BnnKj"Ri m d~T~~ + T 2 J { } 



