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PROCEEDINGS OP THE AMERICAN ACADEMY. 



which osmotic work is eliminated by the balancing of nearly equal pressures. 

 In the uext place, as has been stated, the sign and magnitude of the dif- 

 ference between the free and total energy changes is dependent upon the 

 sign and magnitude of the change of the heat capacity of the system. 



These inferences are of very great interest, for according to the well- 



known equation of Helraholtz, neQ-rr — U = n € T -^r-^ , we know that 



d 1 



the temperature-coefficient of the free energy change is a simple function 

 of the difference between the free and the total energy change. More- 

 over, the effect of the change of heat capacity of the system on the total 

 energy change was pointed out long ago by Kirchhoff in the well-known 

 A U 



equation — A A' 



A 2 



7 , where A represents a finite change. 



Hence we may draw the further inference : The change of the available 

 or free energy of a reaction with the temperature must have some fundamen- 

 tal connection with the change of the total energy with the temperature. 



This fundamental connection becomes manifest on comparing the actual 



values of ^r-^, with those of ^^, the former quantity being given accord- 

 ing to the equation of Kirchhoff by the change in the heat capacities, and 

 the latter being calculated from the difference between the total and free 

 energy changes by the equation of Helmholtz. 

 The following table contains the comparison : — 



* In this equation ?i represents the number of equivalents, eq represents 96,580 

 coulombs, IT the potential, 6^ the total heat of action, and T the absolute temperature. 



