RICHARDS. — CHANGING HEAT CAPACITY. 307 



some basis for separating the change of free energy into two components, 

 one representing the sum of all the attracting energies, and the other a 

 resisting tendency which is connected with the restriction of the heat 

 capacity. It seems to me that further light upon the question of atomic 

 energy is to be had only by means of some such analysis of those com- 

 posite effects which thermodynamics is content to leave superposed. 



The results of this section may be summed up once more in the fol- 

 lowing sentences : — 



When the heat capacity of a system does not change daring a reaction, 

 and concentration influences are balanced, the free-energy and total-energy 

 changes of the reaction are equal and unchangeable with the temperature, 

 and each may be supposed to represent the total " attracting energy" — • a 

 term which covers gravitational and electrical attraction as xoell as purely 

 chemical attraction. 



Wlten, on the other hand, in such a system the heat capacity of the 

 system changes, it seems reasonable to suppose that the " attracting energy " 

 lies between the free-energy and the total-energy change, one being too 

 small and the other too large. 



II. Systems involving Appreciable Concentration Effect. 



Allusion has been made more than once to the osmotic or gas-pressure 

 work which results from differences of concentration. Even in the most 

 favorable cases given above, this modifying influence must have had a 

 slight although negligible effect. 



The present chapter will show how slight this effect may be supposed 



to have been, as well as indicate the manner of its action in other cases. 



It is well known, according to the work of Helmholtz, Nernst, and 



others, that in dilute solutions the potential due to difference of concen- 



RT c 

 tration is approximately represented by the equation tt = In — * if 



it €q C 



the reaction takes place in a constant volume and migration velocities are 

 eliminated. When the solutions are so dilute that there is no heat of 

 reaction, this equation represents quite closely the actual potential. 



The effect of this osmotic work on tlie electrical potential of cells 

 where heat-producing affinity is also at work is, according to the preced- 

 ing analysis, best seen in those cells which exhibit no change of heat 

 capacity under their operation. Such cells are those which involve 

 simply the dilution of amalgams, which thus assume great theoretical 



* c = initial concentration, c = final concentration. 



