198 R. Clausius on the Application of the 



(19.) W 2 = m 2 u 2 p. 2 ^m 1 u 1 p 1 +^[m 1 r 1 -m 2 r 2 ^Mc(T 1 -T 2 )]. 



In the forcing down of the piston, which now begins, the mass 

 which at the end of the expansion occnpied the space 



m 2 u 2 -f- Mcf 



is driven from the cylinder into the condenser, whereby the con- 

 stant counter pressure p 0 is to be overcome. The negative work 

 which is thereby done by this pressure is : 



(20.) W 3 = -m 2 u 2 p 0 -M(rp Q . 



While now the piston of the small pump rises so high that the 

 space Ma becomes free under it, the pressure p Q which takes 

 place in the condenser acts in its favor, and does the work 



(21.) W t =Afop,. 



Finally, at the descent of this piston, the pressure p , which 

 takes place in the boiler must be overcome, and does therefore 

 the negative work : 



(22.) W s = -M<r Px . 



By the addition of these five quantities, we obtain for the whole 

 work done during the circular process, by the pressure of the 

 steam, or as we may also say, by the heat, which we may call 

 W, the expression 



(x) W = ^[m 1 r 1 -m 2 r 2 +Mc (T ± - T 2 )] + m 2 u 2 (p 2 -p 0 ). 



From this equation, the quantity m 2 must be eliminated. This 

 quantity, if we substitute for u 2 the value deduced from (vi), 



occurs only in the combination m 2 r 2 , and for this product equa- 

 tion (vn) gives the expression 



T T 

 m 2 r 2 ~ m % r , -^f - M c T 2 log . 



By substituting this expression we obtain an equation in which 

 only known quantities occur on the right side, since the masses 

 m, and if and the temperatures T,, T 2 and T 0 are assumed as 



immediately given, and the quantities r, p and are supposed 



to be known as functions of the temperature. 



21. If in equation (x) we put T 2 equal to T n we obtain the 

 work for the case in which the machine works without expan- 

 sion, namely: 



(23) W=m l u l (jo 1 ~p„) 



