AND OF THE SECOND LAW 93 



the former case this process is an irreversible one, in the latter 

 case a reversible one. 



" Equality of entropy in the two states therefore constitutes 

 a sufficient and at the same time a necessary condition for the 

 complete reversibility of the passage from one state to the other, 

 provided no changes are to remain behind in other bodies." 



(8) "This proposition has a very considerable range of validity; 

 for there was expressly no limiting assumption made concerning 

 the way in which the gas system reached its final condition; the 

 proposition is therefore valid not only for slowly and simply 

 changing processes but also for any physical and chemical proc- 

 esses provided at the end no changes remained in any body out- 

 side of the gas system. Nor need we believe that entropy of a 

 gas has significance only for states of equilibrium, provided we can 

 suppose the gas mass (moving in any way) to consist of sufficiently 

 small parts each so homogeneous that it possesses entropy." l 



Then the summation must extend over all these gas parts. 

 " The velocity has no influence on the entropy, just as little as the 

 height of the heavy gas parts above a particular horizontal plane." 



(9) "The laws thus far deduced for ideal gases can in the 

 same way be transferred to any other bodies, the main difference 

 in general being that the expression for the entropy of any body 

 cannot be written in finite magnitudes because the equation of 

 condition is not generally known. But it can always be shown 

 and this is the decisive point that for any other body there 

 really exists a function possessing the characteristic properties 

 of entropy." 



Now let us assume any physically " homogeneous body, by 

 which is meant that the smallest visible space parts of the system 

 are completely alike. Here it does not matter whether or no 

 the substance is chemically homogeneous, i.e., whether it consists 



1 If the motion of the gas is so turbulent that temperature and density cannot 

 be denned, then we must have recourse to BOLTZMANN'S broader definition of 

 entropy. 



