4 PROCEEDINGS OP THE AMERICAN ACADEMT. 



therefore, 1"' expressed as the difference between two quantities, one 

 representing what maj be called the total free energy of the initial Btal 

 the other, the total free energy <>t the final Btate. Representing th( 

 quantities !■;• .1 and .,1. . we have, 



.1 = X -3,. 



Similarly, if we represent by ?.![ the total internal energy of the system 

 in the initial State, ami It)' £l._, the same in the final st:* 



equation (1) may he w ritten, 



d% , d% , . 



— -— and , " be mil taken at constant, volume. 

 d T d 1 ° 



This equation may be separated into two equations, 



%i=T^ + *L l + M % (2 



and 



<&=T^ + & a + M l (-2 in 



where M is an undeterminable quantity which can have only arbitrary 

 physical significance, since we are in practice only concerned with chai 



of tree energy at constant temperature, and in such changes J/alw 

 disappears. 



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

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

 simple form, 



A=?iIiT\n ' 



'l 



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

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

 '•, and r.j respectively, the initial and final molecular volumes. Al- 

 though ibe above expression gives a complete statement for the change 

 in free energy only in the tWO special cases mentioned, .-till 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 

 offered by the tact that the above term is present in the general equations 



of equilibrium which have found experimental verification in the most 



