Mr. W. J. M. Rankine on the Mechanical Action of Heat. 121 



1 



Li-Lo+Kl (T,-To)-/*"rfT. Ks 



M31) 



J 



If the vapour be such that it can be regarded as a perfect gas 



dV 

 without sensible error, the substitution of fe + P ^- for Ks, and 



of TT-TTT =feNT for PV, transforms the above to 



Lj-Lo+{Ki.-fe(l+N)}(ri-To) 1 



=-p,^.+Po.ot^ ^-p=-ypo ^p-^J 



In almost all cases which occur in practice, v is so small as 

 compared with V, that —jdP . v may be considered as sensibly 

 = 0; and therefore (sensibly) 



L,+Ki.(T,-To) = Lo + fe(l+N)(Ti-To). . . (33) 



Now this quantity is the total heat required to raise unity of 

 weight of liquid from Tq to Tj of absolute temperature, and to 

 evaporate it at the latter temperature. Therefore the total heat 

 of evajjoration, where the vapour may be treated as a peifect gas, 

 increases sensibly at an uniform rate with the temperature of eva- 

 poration ; and the coefficient of its increase with temperature is 

 equal to the apparent specific heat of the vapour at constant pres- 

 sure, h{l+l^). 



(20.) The experiments of M. Regnault prove that the total 

 heat of evaporation of water increases unifomily with the tem- 

 perature from 0° to 200° Centigrade. 

 The coefficient of increase is equal to 

 Kw X 0-305. 

 Its mechanical value is consequently . 



129-18 metres =422-83 feet per Centigrade degree, or i ' ^^'^'^ 

 235- i6 feet per degree of Fahrenheit. 

 Although the principle of the conservation of vis viva has thus 

 enabled us to ascertain the law of increase of the total heat of 

 evaporation, it does not enable us to calculate a priori the con- 

 stant Lq of the formula, being the latent heat of evaporation at 

 the fixed temperature from which the total heat is measured ; for 

 the changes of molecular arrangement which constitute evapora- 

 tion are imknown*. 



* Other investigations have showTi that the latent heat of evaporation is 

 connected with the increase of volume by the equation 



L=(r-«J^(V-v); 

 (It 

 but tlie exact values of V are yet unknown. 



Phil. May. S. 4. Vol. 7. No. 43. Feb. 1854. K 



