Intelligence and Miscellaneous Articles. 237 



equivalent of the work; the heat expended on internal work is 

 Q— Att(u' — u). 



(2) The body M' is reduced to saturated vapour. The heat con- 

 sumed by external work is Ap'(v'—u); that consumed by internal 

 work is L'— Ap'(v' — u). 



(3) The temperature being kept constant, the volume of the 

 vapour formed is changed so that the pressure becomes equal to^>; 

 the internal work consumes the quantity q of heat. 



(4) We condense the vapour under the constant pressure p ; 

 the body returns to the initial state M. The heat disengaged is 

 L, of which the portion corresponding to the internal work is 

 L— Ap(v — u). 



The cycle is closed ; the change of internal heat is nil : 



Q— Air(u'— u)+L'— Ap'(v'—u')+q— [L— Ap(v— w)]=0; 

 Q=L— L'-f AttO'— u) + Ap'{v'— u')— Ap(y— u) — q. . . (1) 



If we neglect the volumes u and u', if we assume that the internal 

 work hi the transformation of the vapour during the second opera- 

 tion is insensible, and, further, that the vapour follows Mariotte's 

 law 



pv=p'v', . (2) 



we obtain the relation, in general sufficiently approximate, 



Q=L-L' (3) 



The heat of transformation is equal to the difference of the heats of 

 evaporation. 



According to Carnot's theorem, if T denotes the absolute tempe- 

 rature of the body, 



L=AT(»-«)* L'=AT(v'-»')*'. . . . (4) 



Taking into consideration relation (2), and neglecting u and u in 

 comparison with v and v', we get another expression — 



Q=ATi r -Jlog(J) ) ...... (5) 



where log denotes a Napierian logarithm. 



Let us apply these relations to a few examples. 



Solution. — Let us consider a kilogramme of water and a sufficient 

 weight of salt to give a saturated solution at the temperature T. 

 Pure water has a vapour-tension p ; that of the saturated solution 

 is p'. The quantity of heat absorbed by the solution of the salt in 

 the water is given by the preceding relations. Eelation (5) was 

 first pointed out by Kirchhoif *. 



Fusion. — "We owe to M. Eegnault a series of " Eesearches under- 

 taken for the purpose of deciding if the solid or liquid state of 



* Journal de Physique theorique et appliquee, vol. i. p. 30. 



