344 Prof. Clausius on tlie Application of the Mechanical 



We must now consider the following problem : — Given, first, 

 the initial condition of the whole mass undsr consider atiouy viz, 

 that which ivas previously in the vicious space, as well as that more 

 recently arrived from the boiler ; secondly, tJie magnitude of the 

 work done by the pressure acting upon the piston during the entrance 

 of the vapour ; and thirdly, t/ie pressure in the cylinder at the 

 moment of cutting off the same from the boiler : to determine how 

 much of tlie mass in the cylinder at this moment is vaporous. 



33. Let /Lt be the whole mass in the vicious space before the 

 entrance of the fresh vapour, and, for the sake of generality, let 

 us suppose that the part fju^ of it is vaporous and the rest liquid. 

 For the present let Pq and Tq represent respectively the pressure 

 of this vapour and its corresponding absolute temperature, with- 

 out implying, however, that these ai-e exactly the same values as 

 those which refer to the condenser. As before, p^ and Tj shall 

 be the pressure and temperature in the boiler, M the mass 

 issuing from the boiler into the cylinder, and m^ the vaporous 

 part of the latter. As we have already remarked, the pressure 

 iipon the piston during the entrance of the vapour need not be 

 constant. The mean pressure p\ may be defined as that by which 

 the space described by the surface of the piston, during the en- 

 trance of the vapour, must be multiplied in order to obtain the 

 same work as is actually done with the variable pressure. Further, 

 let jWg and Tg be the pressure and corresponding temperature in 

 the cylinder at the moment of cutting it oiff from the boiler ; 

 and lastly, mg the magnitude to be determined, that is to say, 

 the vaporous part of the whole mass M + /x- now in the cylinder. 



To determine this magnitude, let us conceive the mass M + //, 

 reduced in any manner to its original condition. For instance, 

 thus : let the vaporous part m^ be condensed in the cylinder by 

 depressing the piston, whereby we shall suppose that the latter 

 can also enter the vicious space. At the same time let heat be 

 constantly withdrawn from the mass in such a manner that the 

 temperature T^ may remain constant. Then of the whole liquid 

 mass, let the part M be forced back into the boiler, where it may 

 assume its original temperature T,. By this means the condition 

 of the mass within the boiler is the same as it originally was, for 

 of course it is of no importance whether precisely the same mass 

 wi„ which was before vaporous, is again so now, or whether an- 

 other equally great mass has taken its place. With respect to 

 the remaining part /t, let it be at first cooled in the liquid state 

 from Tg to Tq, and at this temperature let the part ^q become 

 vaporous, to do which the piston must recede so that this vapour 

 can again occupy its original volume. ''7^ 



34. In this manner the mass M + /a has gone through a com- 

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



