THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 



III. THE RELATION OF CHANGING HEAT CAPACITY TO CHANGE 

 OF FREE ENERGY, HEAT OF REACTION, CHANGE OF VOL- 

 UME, AND CHEMICAL AFFINITY. 



By Theodore William Richards. 



Received June 16, 1902. 



I. Systems Involving a Minimum of Concentration Effect. 



Julius Robert Mayer showed, sixty years ago, that when a gas is 

 compressed, the work of compression reappears almost exactly as heat. 

 One of the circumstances which permitted the discovery of this relation- 

 ship is the fact that the heat capacity of a gas at constant volume is ap- 

 proximately independent of the volume. If the heat capacity of the gas 

 were diminished by the compression while the other influences remained 

 unchanged, it is clear that some of the heat energy already in the system 

 would be displaced by the compression, and hence that the apparent evo- 

 lution of heat would be made up of two added quantities, one due to 

 the work put into the system from the outside, and the other due to the 

 lessened heat capacity of the system. Thus the total evolution of heat 

 would be greater than the heat corresponding to the work which had 

 been done upon the system, unless the diminution of heat capacity in- 

 volved the storing of energy in potential change. In order to develop 

 the reasoning, step by step, this latter possibility will be waived for the 

 present, and taken up again after the facts have been studied. 



If $1 is used to represent the unknown total heat energy necessary to 

 raise the original system from the absolute zero to the reaction tempera- 

 tures, W that necessary to raise the final system through the same in- 

 terval, IF the outside work done upon the system, and £7 the heat actually 

 evolved, we may represent the possible relationship as follows : — 



U= W+ Wi-W 



Unfortunately 2E and $£' are not definitely known, hence the exact 

 solution of the equation is not possible at present. Nevertheless, a 

 qualitative study of the situation in the light of the facts leads to inter- 



