 —— R. Clausius on the Application of the 
we have to do, namely, the — of the whole mass now pres- 
ich is in the form of steam, be rep- 
mn M,. 
To Sletermine this quantity, let us consider the mass M+, in 
any manner brought back to its initial condition, The vapor- 
ized portion m,, 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much heat be in any manner withdrawn from the mass, that its 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 7’, remains constant. Then the portion m, of the 
whole fluid mass is pressed back into the boiler where it again as- 
sumes the original temperature 7’,. 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, 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 7’, to 7; 
and at this temperature the portion «, is converted into steam, by 
which the piston moves so far that this steam can again assume 
its original space. 
34. The mass M+u, has consequently gone through a com- 
plete circular process, to which we may now apply the theorem 
t 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 MW is heated from the temper 
ature T, to 7,, and the portion m, must be converted into 
steam at the latter temperature : 
: m7, Me(T,- 7). 
2. During the condensation of the portion m, at the temper 
ature 7, : 
— Myo. : 
8. During the cooling of the portion « from 7’, to T,: 
— Be(T,-7,). 
ae eg the evaporation of the portion #,, at the tempera 
as Hg Fos ‘ 
