372 THE PHILOSOPHY OF BIOLOGY 



mechanism is an ideal one — the limit to an irreversible 

 mechanism. 



But— and now we appeal to experience and cease to 

 work with ideal mechanisms — the actual engine which 

 we can design and work is one in w^hich there will be 

 friction, in which some parts will conduct heat im- 

 perfectly, and other parts will insulate heat imperfectly. 

 Let the friction generate q units of heat, and let the 

 quantity of heat which is " wasted " by imperfect 

 conduction and insulation be q^^. This heat will flow 

 into the refrigerator, or will be radiated or conducted 

 to the surrounding medium, which we suppose to 

 be at the same temperature as the refrigerator. If, 

 then, we divide this total quantity of heat by the 



temperature T°, we get -^j^=Si as the quantity 



of entropy which is generated as the result of 

 the imperfections of the engine, in addition to the 

 quantity of entropy, S, which would be generated 

 if the engine were a perfect one. Both S and S. 

 are positive. 



Also in the working of the engine in the negative 

 direction a certain quantity of entropy. Si, is generated 

 for reasons similar to those mentioned above. 



The entropy generated when the engine works in 

 the positive direction is therefore S+5i, and when it 

 works negatively the quantity generated is also Si. 

 The entropy destroyed when the engine works negatively 

 is S. The total change of entropy is therefore 2S1+S 

 - S, that is, 2S1. In an actual energy-transformation 

 combined with a compensatory energy-transformation 

 there is therefore an increase of entropy. 



We can generalise these statements so that they 

 will apply not only to a heat-engine but to all mechan- 

 isms which effect energy-transformations. In all such 



