188-192] Irreversibility 165 



Now T and , by definition, depend only on the heat-energy of the gas, 

 whereas jfc> depends also upon the density of the gas. Hence equation (396) 

 can only be satisfied by taking f(jb) equal to a constant, k, so that 



identifying the absolute thermodynamical scale with the Kinetic Theory 

 scale, except for a possible multiplicative constant. 



Entropy. 



191. The quantity > introduced by equation (393) is defined to be the 

 " Entropy " of the gas. It is, as we have seen, a function only of the quan- 

 tities which determine the state of the gas. Since 



(397), 



it is clear that ^ is the sum of two terms, of which the first depends only on 

 the motion of the molecules, and the second only on their positions. 



The importance of the function > is as follows : Let two systems, denoted 

 by suffixes 1 and 2, have initially entropies jbi and J^ 2 . and let a quantity 



of heat pass from the one to the other. The loss to j^i is -- , the gain 



to ^> 2 is - , so that 



(398). 



In nature, however, heat only passes from a hotter to a colder body, so that 

 T l must be greater that T 2 . Hence d (^ + 5& 2 ) must be positive. 



It follows, then, that any natural transfer of heat tends to increase the 

 entropy of the systems concerned, or, stated more concisely, the entropy tends 

 to its maximum value. 



Apparent Irreversibility. 



192. We seem here to have arrived again at an irreversible phenomenon, 

 although the equations of motion from which it ought to have been deduced 

 were strictly reversible. In Chapter II. we had an experience with the 

 function H which seems now to be repeated in the case of the function 5. 

 We apparently found in Chapter II. that dH/dt was always negative or zero, 

 although, as the whole calculation of dH/dt had rested solely upon rever- 

 sible equations of motion, it ought to have been found that dH/dt was as 

 likely to be positive as negative. In Chapters III. and IV. however, we 

 were able to trace this apparent fallacy to the imperfections of the statistical 

 method. We found that H had a minimum value ; if the initial value of H 



