Mechanical Theory of Heat to the Steam Engine. 187 



(2) jr=i(§,-r o y d -®-T 0 .N). 



o 



If we assume specially that the whole circular process is inverta- 

 ble, according to the above iV=0, and the foregoing equation 

 becomes 



o 



This expression is only distinguished from the previous one by 

 T 



the term ~ . N. Since N can only be positive this term can 



only be negative, and we see from this, which is also easily de- 

 duced from a direct consideration, that we obtain the greatest 

 possible amount of work under the conditions above determined, 

 when the whole circular process is invertable, and that the quan- 

 tity of work is diminished by every circumstance which causes 

 one of the special processes occurring in the circular process to 

 be uninvertable. 



Equation (2) leads accordingly to the sought value of the work 

 in a manner which is directly opposed to the usual one, inasmuch 

 as we do not, as formerly, determine singly the quantities of 

 work performed during the different processes and then add them 

 together, but set out from the maximum work, and subtract from 

 it the losses of heat which have arisen from the single incom- 

 plete parts of the process. 



If we make the limiting condition with respect to the commu- 

 nication of the heat that the whole quantity of heat Q l is com- 

 municated to the body at a determined temperature T l , the 

 portion of the integration embracing this quantity of heat may 

 be at once executed, and gives 



Qt 



by which equation (3), which holds good for the maximum of 

 the work, takes the following form, 



(4 '-Sfsra- 



In this special form the equation was already deduced by W. 

 Thomson and Rankine from the combination of Carnot's theo- 

 rem, modified by me, with the theorem of the equivalence of 

 heat and work.* 



10. Before we can pass from these considerations, which hold 

 good for all thermodynamic machines, to the treatment of the 

 steam engine, some remarks with respect to the behavior of va- 

 pors at a maximum density must first be brought forward. 



* Phil. Mag., July, 1851. 



