654 



The whole of the given cyclic process 

 ma.y be broken up into pairs of correspond- 

 ing parts like a and b, so that the entire 

 heat taken in and given out by the fluid 

 during the given process consists of parts 

 M'hieh correspond in pairs like dH^ and 

 dH.,, and each pair of heat parts satisfies 

 an equation like (iii). Therefore, the sum 

 of all quotients obtained by dividing the 

 heat taken in by a fluid at each step of any 

 reversible cyclic process by the absolute 

 temperature of the fluid at the step is 

 equal to zero. That is 



■ y 



(5) 



for any reversible cyclic process. 



Fig. 2. 



Consider two states of thermal equilib- 

 rium of a fluid represented by the points 

 A and B, Fig. 2. Let the lines a and b 

 represent any two different reversible pro- 

 cesses leading from A to B. Then process 

 a together with process b reversed consti- 

 tute a cyclic process starting from A and 

 returning to A. Therefore the sura 

 I dH/T is equal to zero when it is extended 

 over process a and over process b reversed. 



[N. S. Vol. XVIII. No. 464. 



this into symbolic form we have: 





(iv) 



in which the subscript a indicates that the 

 first summation is extended over process a, 

 and the subscript — b indicates that the 

 second summation is extended over process 

 b reversed. 

 But 



-i T ~ t T' 



(v) 



That is, the summation I dH/T extended 

 over the process b reversed is equal but 

 opposite in sign to the value of this sum- 

 mation IdH/T extended over the process 

 b not reversed, that is, when process b leads 

 from state A to state B. 



Substituting the value of IdH/T from 

 equation (v) in equation (iv) we have 



.dH 

 T 





(6) 



That is, the sum (zdE/T) has the same 

 value for any two, and therefore, for all 

 reversible processes which lead from one 

 given state of thermal equilibrium A to 

 another given state of thermal eqiiilibrium 

 B. 



If the state B is one which can be 

 reached from state A by a sweeping pro- 

 cess, then the sum {IS dH/T) extended over 

 a reversible process leading from A to 5 

 is positive in value. Therefore the value 

 of the sum {SdH/T) extended over any 

 reversible process leading from state A to 

 state i? of a substance may be used as a 

 measure of the thermodynamic degenera- 

 tion which is associated with the change of 

 the substance from state A to state B. This 

 Slim is called the increase of entropy of the 

 substance. When the sum ( I dH/T) is 

 negative it measures a thermodynamic re- 

 generaticn and is called a decrease of 

 entropy. 



