402 M. B,. Clausius on the Deportment of Vapour 



change of temperature may be so much the more neglected, in- 

 asmuch as the entire volume of the water is scarcely deserving 

 of notice. This expression introduced into (2.) gives 



Q.= / " h + X{s-a)^-^dt + Ap,[s,-a)(l-i'^^.{^.) 



The sum h + A{s — cr)-^ is, according to equation (HI.) of my 



dr 

 former memoir*, = — -f c ; and this sum again, according to 



the determinations of Regnault, is nearly a constant quantity, 

 viz. 0'305. Equation (3.) thus passes into 



Q,= -0-S05{t,-t,)+Ap,{s-a)(l + P-f). . (4.) 



V Pi/ 



The only unknown quantity here is A/>j(6, — cr), and this can be 

 expressed as a function of the temperature at the commencement 

 by means of equation (26.) of my former memoirf ; so that for 

 every commencing pressure and the corresponding commencing 

 temperature the value of Qg may be calculated. Supposing, for 

 example, the pressure at the commencement, as in the former 

 case, to be five or ten atmospheres, we obtain 



Q2 = 19-5 or =17-0 units of heat. . . (II.) 



As Qg is a positive quantity, it follows that in this case also heat 

 must not be withdrawn, but on the contrary communicated, to 

 preserve the vapour from partial precipitation, which, however, 

 would take place not only at the orifice, but also within the 

 vessel. The quantity of vapour thus precipitated would be 

 smaller than in the former case, inasmuch as Qg is less than Q^ 



It may appear singular that the equation (II.) gives for a 

 commencing pressure of five atmospheres a greater quantity of 

 heat than for ten atmospheres. This is explained by the fact, 

 that under a pressure of five atmospheres the volume of the 

 vapour is already so small, and under ten atmospheres is only 

 reduced to one-half the volume, that the increase of work thus 

 rendered necessary during the issue of the vapour is more than 

 compensated by the excess of the sensible heat in the one state 

 over that in the other, the vapour being heated in one case to 

 180°-3, and in the other case to 152°-2. 



This second case which we have just considered can be applied 

 Avith some degree of approximation to the case of vapour issuing 

 without expansion from the cylinder of a high-pressure engine 



* L. c. p. 389. t L. c. p. 544. 



