67 



i.e. the sum of the quantities of heat absorbed by the working 

 substance in a reversible Garnot cycle, each divided by the 

 absolute temperature at which it takes place, is zero. In 1854, 

 Kelvin and Clausius independently showed that this result 

 may be extended to any reversible cyclic process whatever, 

 since any reversible cyclic process whatever may be resolved 

 into a number of simple Carnot cycles. Thus, we may write: 



where dQ is the element of heat absorbed at the temperature t 

 in any reversible cycle, and the integration is extended round 

 the cycle. 



Let us now designate by A and B two reversible paths by 

 which a body or system of bodies may be brought from a state 

 (/) to a state (//) . We may take the system through a reversible 

 cycle by changing it from state (7) to state (77) by path A and 

 returning it to its original state (7) by path B. Therefore, 



= 



B 



or, by changing the direction of the second term, 



/•(") dQ 

 Jin t 



1 =^T^• 



J A Jm t Jb 



