LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 61 



The influence of temperature is expressed for two states simultane- 

 ously in equation (1G), which conforms to equation (18) except for the 

 minus sign. This slight difference might be explained away, but a much 

 weightier difficulty confronts us when we attempt to split equation (1G) 

 into two equations, each expressing the influence of temperature upon 

 the fugacity for a single phase, in the form, 



( 9R Tlnif, \ 



v 9 T / 



= -& 



This equation is in general not true, notwithstanding the fact that we 

 may choose arbitrarily the zero of entropy. If for each temperature 

 this zero could be chosen arbitrarily it could be so chosen that the equa- 

 tion would be true, but as a matter of fact the entropy is in all cases a 

 determinate function of the temperature, and the zero chosen for one tem- 

 perature must be retained for all. We must conclude, therefore, either 

 that the general equation (19) is false, or that entropy is not the capacity 

 dimension of heat. To make the latter conclusion would appear too 

 arbitrary were it not that other considerations lead also to the suspicion 

 that entropy has been too hastily chosen as the capacity in question. In 

 fact, the equation, d Q = TdS, for the heat absorbed in a reversible 

 process, corresponding to the general equation for change of energy, 

 dE — Id H, is the only argument for the consideration of entropy as 

 the capacity dimension of heat. This argument would apply equally 

 well to any other quantity, h, such that d Q = ± Td h ; in other words, 

 such that dh = ± d S. It is interesting, therefore, to determine whether 

 there is, in fact, a quantity which fulfils this condition and also the 

 condition 



If a simple function can be found which satisfies these two require- 

 ments it may, I think, be accepted, at least provisionally, as the true 

 capacity of heat energy. 



The entropy of every body is a very complex function of its other 

 variables, and even the entropy of a perfect gas is represented by the 

 complicated equation,* 



S=S f- G P \n^-R\n^. 



* See Clausius, Warmetheorie, I. p. 214, third edition. 



