256 Prof. Clausius on the Application of the Mechanical 



the values of -, which would be obtained if the two assumptions 



formerly made in the theory of the steam-engine were correct ; 

 that, is to say, (1) that the vapour during expansion remains 

 without partial condensation at a maximum density ; (2) that it 

 follows Mariotte*s and Gay-Lussac's laws. According to these 

 hypotheses, we should have 



t. 



Pi 1 



P T, 



150° 



125*^ 



1-88 

 1-93 



100° 



3-90 

 416 



75° 



9-23 

 10-21 



50° I 25' 



257 



297 



J4i 



887 



17. We have still to determine the work done during the*^ 

 change of volume. In order to do so, we have the general* 

 equation ^^ 7~ j 



W = | Ddv (16) 



= j pdv. 



^70 Wv 



m, 



But, considering a constant, we have from equation (6), 



dv=d[mu)', 

 therefore 



pdv=pd[mu), 



for which we may also write 



pdv = d{mup) —mu ^ dT. 



dp . . . ^' 



In the place of mu -^ we might here substitute the expression;;. 



given in (VIII), and then integrate; but the result is at once - 

 obtained in a rather more convenient form by the following sub-*^ 

 stitution. According to (VI), y 



mu^dt^-'-dT' TaiifJ 



and through the application of equation (14), this becomes '»^ 



mu^d^= j^ [d{mr) + McdT] 



By,«ieans of this (17) becomes 



ap9 fiih f.i ^ 



iv. 



j^dv^d[mup) - j-[d{mr) + ^cdl^^,^^^;^ 

 Z .Oikil .V^O ST. .o/. XI .lu/ .^ .8 ^^' 



