APPENDIX 371 



the gain of entropy of the colder body is - . The 



J- 1 



nett change of entropy of the system is - 



L l - 2 



Since T 2 is greater than TI, ^ is less than ^ c . There- 



fore the expression - - is positive, that is, the 



J- 1 -* 2 



entropy of the system, as a whole, has increased. 

 When heat flows from a hotter to a colder body 

 the nett entropy of the two bodies, therefore, in- 

 creases. 



But we can also cause heat to flow from a colder to 

 a hotter body by effecting a compensatory energy-trans- 

 formation. Such a compensation would not occur by 

 itself in any system capable of effecting an energy- 

 transformation, if it is to be effected some external 

 agency must act on the transforming system. We 

 can suppose it to happen in a perfectly reversible 

 imaginary mechanism. Suppose a Carnot engine works 

 in the positive direction, taking heat from a reservoir 

 at temperature TV, and giving up part of this heat to 

 a refrigerator at 7Y, and doing a certain amount of 

 work W. Suppose that this work is stored up, so to 

 speak, say by raising a heavy weight, which can then 

 fall and actuate the same Carnot engine in the opposite 

 (negative) direction. The engine then exactly reverses 

 its former series of operations. The work it did is 

 reconverted into heat, and as much of this heat flows 

 from the refrigerator into the source, that is, from a 

 colder to a hotter bod}^, in the negative operations, as 

 flowed from the source to the refrigerator in the 

 positive operations. In this primary energy-transfor- 

 mation, combined with a compensatory energy-trans- 

 formation, there is no change of entropy. The 



