370 



R. Clausius on the Application of the 



shall be called as before p , , T 1 , the mass flowing from the boiler 

 into the cylinder J/j and the part of it which is in the form of 

 steam m r It is not necessary, as already mentioned, that the 

 pressure exerted upon the piston during the influx, be constant. 

 "We will call this pressure the mean pressure, and will denote it 

 by p\ , by which the space described by the surface of the piston 

 during the period of the influx must be multiplied, in order to 

 obtain the same work which is done by the variable pressure. 

 Let the pressure which actually takes place in the cylinder at the 

 moment of the cut-off, be denoted by p 2 and the temperature by 

 T 2 , and let finally the quantity, with the determination of whiph 

 we. have to do, namely, the portion of the whole mass now pres- 

 ent in the cylinder M+p, which is in the form of steam, be rep- 

 resented by m 2 . 



To determine this quantity, let us consider the mass Mjr in 

 any manner brought back to its initial condition. The vapor- 

 ized portion m 2 , is condensed in the cylinder by the downward 

 pressure of the piston, whereby it is supposed that the piston can 

 also penetrate into the injurious space. Let at the same time so 

 much heat be in any manner withdrawn from the mass, that its 

 temperature T 2 remains constant. Then the portion m l of the 

 whole fluid mass is pressed back into the boiler where it again as- 

 sumes the original temperature T x . The same condition is thereby 

 restored in the boiler as before the influx, inasmuch as it is of no 

 importance whether exactly the same mass, m T which was pre- 

 viously in the form of steam, is so now again, or whether an 

 equally large other mass has taken its place. The remaining por- 

 tion |W is first cooled down, in the fluid condition from T 2 to T Q1 

 and at this temperature the portion ^ 0 is converted into steam, by 

 which the piston moves so far that this steam can again assume 

 its original space. 



34. The mass M+p, has consequently gone through a com- 

 plete circular process, to which we may now apply the theorem 

 that the sum of all the quantities of heat taken up by the mass, 

 during a circular process, must be equivalent to the whole exter- 

 nal work performed in it. The following quantities of heat are 

 taken up, one after another. 



1. In the boiler, where the mass if is heated from the temper- 

 ature T 2 to T J} and the portion m, must be converted into 

 steam at the latter temperature : 



ro 1 r 1 +ilfc(Z T 1 -Z T 2 ). 



2. During the condensation of the portion m 3 at the temper- 

 ature T a : 



3. During the cooling of the portion ^ from T 2 to T 0 : 



4. During the evaporation of the portion at the tempera- 

 ture : 



