Mechanical Theory of Heat to the Stea?n Engine. 197 



Low much of this work is really useful, and how much on the 

 other hand again is consumed in the machine in overcoming. the 

 friction and in moving the pumps, which are necessary for the 

 working of the machine, beside that indicated in the figure. 

 This part of the work may also be subsequently determined, and 

 subtracted, as will be shown farther on. 



It is moreover to be remarked with respect to the friction of 

 the piston in the cylinder, that the work consumed in overcoming 

 it is not to be considered as entirely lost, for by this friction heat 

 is generated, and thereby the interior of the cylinder kept warmer 

 than it otherwise would be, and consequently the force of the 

 steam is increased. 



Finally, as it is advantageous to learn in the first place the 

 action of the most complete machine possible before we study 

 the influence of the particular imperfections which naturally 

 occur, we shall add to this preliminary consideration two suppo- 

 sitions which at a future time will be again given up. Namely, 

 in the first place, that the conducting pipe from the boiler to the 

 cylinder, and the waste-pipe from the cylinder to the condenser 

 or to the atmosphere is so wide, or that the motion of the 

 steam engine is so slow, that the pressure in that part of the 

 cylinder which is in connexion with the boiler, is equal to that 

 in the boiler itself, and in like manner, that the pressure on the 

 other side of the piston is equal to the pressure in the condenser, 

 or to the pressure of the atmosphere, and secondly, that no inju- 

 rious space is present. 



20. Under these circumstances, the quantities of work done 

 during a circular process, may be expressed without further cal- 

 culation, with the help of the results obtained above, and give a 

 simple expression as the sum. Let the whole mass which passes 

 during the ascent of the piston from the boiler into the cylinder, 

 be called M, and let the part m , be in the form of vapor, and 

 the part if— m, liquid. The space which this mass occupies is, 

 if m , signifies the value of u belonging to T l , 



The piston is accordingly lifted as high as this space underneath 

 it becomes free, and as this happens under the action of the pres- 

 sure belonging to T J f the work done during this first process, 

 which we may call W 1 , is 



(18) W x ==m l u 1 p l +M(jp l . 



Let the expansion which now follows be so far continued, 

 until the temperature of the mass enclosed in the cylinder has 

 sunk from the value T x to a second given value, T 2 . The work 

 which is done hereby, which we may call W 2 , is found immedi- 

 ately from equation (ix), if T 2 is assumed in it, as the final tem- 

 perature, and also if the corresponding values are substituted for 

 the other quantities occurring in the equation, namely : 



