356 



M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 



perature t of the body B is lower by the infinitely small quantity dt, 

 than the temperature t of the body A. We shall suppose in the first 

 instance that a gas serves for the transmission to the body B, of the ca- 

 loric of the body A. Let v^ be the volume of the gas under the pres- 

 sure Pq at a temperature of t,^ ; let p and v be the volume and the 

 pressure of the same weight of gas at the temperature t of the body A. 

 The law enunciated by Mariotte, combined with that of Gay-Lussac, 

 establishes between these different quantities the relation 



or, for simplicity, ^°J^'° _, = R: 

 2o7 + to 



JO « = R (267 + 0- 

 The body A is brought into contact with the gas. Let me = v, 

 ae = p (fig. 3.). If the gas be allowed to expand by the infinitely 

 small quantity dv = eg, the temperature will remain constant, in con- 

 sequence of the presence of the source of heat A ; the pressure will 

 diminish, and become equal to the ordinate bg. We now remove the 



Fig. 3. 



body A, and allow the gas to expand, in an inclosure impermeable to 

 heat, by the infinitely small quantity g h, until the heat becomes latent, 

 reduces the temperature of the gas by the infinitely small quantity dl, 

 and thus brings it to the temperature t — dt oi the body B. In con- 

 sequence of this reduction of temperature, the pressure will diminish 

 more rapidly than in the first part of the operation, and will become 

 ch. We now take the body B, and reduce the volume mh by the 

 infinitely small quantity fh, calculated in such a manner that during 

 this compression the gas may transmit to the body B all the heat 

 it has derived from the body A during the first part of the opera- 

 tion. Let/df be the corresponding pressure; that done, we remove 



