200 



R. Clausius on the Application of the 



we have 



To 



T x -T 0 z 



and we therefore obtain 

 T T 



— — — I — U U etc. 



i.? T 2.3 T a.4 T 



Equation (25) or (xi) thus becomes 



(27) W— m,r, *+Mc(T,-T n )^.(— + — -\-— t + etc) 

 K J 11 A K 1 °M \1.2 T 2.3 T 3.4 T / 



The value of the infinite series enclosed in the brackets which 

 distinguishes the factor of the quantity of heat Mc(T l — T 0 ) 

 from that of the quantity of heat m 1 r„ varies, as one may 

 easily see, between -J and 1 while z increases from 0 to 1. 



23. We may also obtain the expression for the work very 

 easily in another way, for this last considered case in which the 

 steam cools by expansion to the temperature of the condenser, 

 without following singly the different processes of which the 

 circular process consists. In this case, namely, the circular pro- 

 cess is invertible in all its parts — we may imagine that the evap- 

 oration takes place in the condenser at the temperature T 01 and 

 that the mass if, of which the part m 0 is vapor, and the part 

 (if— m 0 ) is liquid, passes into the cylinder, and lifts the piston; 

 that then during the descent of the piston, the steam is first 

 compressed until its temperature has risen to and is there- 

 upon forced into the boiler, and that finally by means of the 

 small pump, the mass M is again forced as a liquid from the 

 boiler into the condenser, and cools to the initial temperature 

 T 0 . The substance passes here through the same states as for- 

 merly, only in inverse order. The additions or subtractions of 

 heat take place in a contrary direction, but in the same quantity 

 and with the same temperature as the mass, and all the quanti- 

 ties of work have contrary signs but the same numerical values. 



Hence it follows that in this case no uncompensated trans- 

 formation occurs in the circular process. We must therefore in 

 equation (2) put iV=0, and thereby obtain the equation already 

 cited in (3) in which only for the sake of correspondence, W is 

 to be written in place of W. 



z 



\~zlz z 2 z z \ 



