260 Prof. Clausius on the Application of the Mechanical 



Tp the work performed during this first operation is 



W,=miWijt?i + Moy, (18) 



The expansion which now follows is continued until the tem- 

 perature of the mass enclosed in the cylinder sinks from T^ to a 

 second given value Tg. The work thus done, which shall be W^, 

 is given immediately by equation (IX), if Tg be taken therein as 

 the final temperature, and for the other magnitudes involved in 

 the equation the corresponding values be substituted, thus 



Wg=m2Wa;?2— 7WiWijt?i+ -^\rnir^ — m^^ + ^ci^^—T^'], (19) 



By the descent of the piston, which now commences, the mass, 

 which at the close of the expansion occupied the volume 



TWgWg H- Mo-, 



is driven from the cylinder into the condenser, and has to over- 

 come the constant pressure Pq, The negative work hereby done 

 by this pressure is 



W3=-7W2M2;^0-M(7po (20) 



Whilst the piston of the small pump now ascends, so as to 

 leave the free space M<r under it, the pressure Pq in the con- 

 denser acts favourably and does the work, 



W4=M(7ji?o. ..*.... (21) 

 Lastly, during the descent of this piston, the pressure />i in 

 the boiler must be overcome, and therefore it does the negative 

 w^ork 



W5=:-M(7J0, (22) 



By adding these five magnitudes together we obtain the fol- 

 lowing expression for the work done by the vapour pressure, or, 

 as we may say, by heat, during a circular process : 



W'=l[m,r,-m^, + Mc(T,-T,)]+mA(j»,-;,„). . (X) 



n 



,.> With respect to the magnitude m^ which must be eliminated 

 firom this equation, it will be observed that, if for Wg we substi- 

 tute the value 



.T.( 





as given in (VI), it only occurs in the combination m.^r^, and for 

 this product we have from equation (VII) the expression 



T T 



OT3ra=m,ri^ -McTg log^ 



