4 ' PROCEEDINGS OF THE AMERICAN ACADEMY. 



therefore, be expressed as the difference between two quantities, one 

 representing wliat may be called the total free energy of the initial state; 

 the other, the total free energy of the final state. Representing these 

 quantities by Sli and ^2 ? ^e have, 



Similarly, if we represent by ^1 the total internal energy of the system 

 in the initial state, and by Wi« the same in the final state, 



equation (1) may be written, 



dT dT 



a^ =T^ - T^ + 51, _ ^2 , 



beino; taken at constant volume. 







This equation may be separated into two equations, 



^1= 2'^ + m, + il/, (2 a) 



and 



d^ 

 ^,^ T^, + Wi, + M, (2b) 



where 31 is an undeterminable quantity which can have only arbitrary 

 j)hysical significance, since we are in practice only concerned with changes 

 of free energy at constant temperature, and in such changes J/ always 

 disappears. 



In two special cases, viz. the ideal gas and the dilute solution, the 

 expression for the change in free energy has been found to assume a very 

 simple form, 



A = nET\n'^, 



where n denotes the number of gram-molecules of the gas or solute ; R, 

 the gas constant ; T, the absolute temperature ; In, a natural logarithm; 

 Vy and Vn respectively, the initial and final molecular volumes. Al- 

 though the above expression gives a complete statement for the change 

 in free energy only in the two special cases mentioned, still we are led 

 by many considerations to believe that it forms an important factor in 

 many other, if not all, free energy changes. Evidence on this point is 

 ofi^ired by tlie fact that the above term is present in the general equations 

 of equilibrium which have found experimental verification in the most 



