248 Prof. Clausius on the Application of the Mechanical 



was imparted or, if negative, abstracted. The sums of all the 

 known and unknown quantities of heat shall be represented by 

 Qi and Q^ respectively. 



1" Divide the integral in equation (II) into two parts, of which 

 the one shall extend over the known quantity of heat Q^ and 

 the other over the unknown quantity Qq. In the latter part, T 

 having a constant value Tq, the integration may be immediately 

 effected, and as result we have 



Qo 



To' 

 Tlie equation (II) thus becomes 



whence results 



Jo T +To- '^' 

 Qo=-To.f'^-T, 



N. 





Further, seeing that in our case 



Q=Q, + Qo, 



we have from equation (I), 



>r»fT?Ls flip i Oilt fo mo'iOfj/lj ofit bna ,?ra ^o baf 



Substituting the above-found value of Q^ in this equation, it 

 becomes 



= r(«^-^or^-To.N). . . (2) 



AX5^ If, a4 a 'fip?^eial (^s6, the whole circtdar process is reversible, 

 then 



-■91' i4; N = 0, 



'^^ the above equation becomes 



" '■■"*'i(«.-.rT)- • ■ ■ o 



■This expression differs from the preceding one only in the absence 

 V' q' 



of the term — -^ N. Now as N can only be positive, this term 



'must necessarily be negative; and thus we see, that, under the 

 above conditions with respect to the communication of heat, the 

 greatest possible amount of work is obtained when the whole 

 process is reversible ; and that every circumstance which renders 

 one of the operations in the circular process not reversible, dimi- 



