X, ^, i', AND THE CRITERIA OF EQUILIBRIUM 231 



Since AQ > it follows that iji > 772. If ^ ^ ^2 throughout the 

 process, the integral is positive whether or not i is a single- 

 valued function of 77 during the process (i.e., whether or not the 

 system always has the same temperature at intermediate stages 

 at which the entropy takes the same value). Consequently 



A'W ^ AW. 



It follows that AW is the maximum amount of external work 

 that can be obtained by processes in which the temperature of 

 the system does not fall below (2. That is, the maximum work is 

 obtained when all the heat is given up reversibly at temperature 

 ti, and the amount of this work is 



AiA + vi ih - k), 



A^ being the decrease in the work-function. This extends the 

 physical significance of the work-function to processes of non- 

 constant temperature. 



The absolute value tji, of the entropy appears to occur in 

 this expression; but it must be remembered that the absolute 

 value of the entropy occurs also in the definition of \p. The 

 same constants used in fixing the entropy 77, must be employed 

 in the entropy-values used ia tracing the changes in \p. 



