366 M. CLAPEYRON ON THE MOTIVE POWER OF HEAT. 



from T to T + 6? T, we bring it successively into contact with the se- 

 cond, the third, and the (n + 1 )th of these sources, until it has ac- 

 quired tlie temperature of each of them. When, on the contrary, the 

 volume V of the body being increased by dv, we wish to give it the tem- 

 perature T, we bring it successively into contact with the n\h, the 

 (« — l)th, and the first of these sources, until it has acquired the tem- 

 perature of each of them. \A'e then return to these sources the heat 

 that has been borrowed from them in the first part of the operation ; for 

 it is not necessary to attend to the differences of an order of inferior mag- 

 nitude, arising from changes that may have been produced in the speci- 

 fic caloric of the bodjr, in conseqvience of the variations of v and Q. 



Nothing therefore will have been lost or gained by any of these 

 sources, excepting always the source of which the temperature is T+ rf T, 

 which will have lost the heat necessary to elevate the temperature of the 



body upon which we are operating from T + (^^ ~ 1)«T ^^ 'p + rfT, 



n 

 and the source maintained at the temperature T, which will have ac- 

 quired the heat necessary to reduce the temperature of the same body 



from T -)- . to T. If we suppose n to be infinitely great, these quan- 

 tities of heat may be neglected. 



We see, therefore, that when the body in question, (its temperature 

 being thus reduced to T,) is brought into contact with the source of 

 heat B, the heat commimicated to it from the source A will be all it 

 has gained from the commencement of tlie operation. In consequence 

 of tlie reduction of its volume in contact with the body B, it will be found 

 at its original volume and temperature; tlie quantities Q and P will 

 therefore have re-assumed their primitive value ; it is therefore certain 

 that all the heat borrowed from the source A, and nothing but that heat, 

 will have been given to the body B. 



Whence it results that the effect produced, 



dvd T 



dT 



dp 



is owing to the transmission of the heat absorbed by the body subjected 



to the experiment during its contact with the source A, and which has 



afterwards flowed into the source B. 



The temperature having remained constant during the contact with 

 the source A, it follows that the variations dp and dv oi the pressure 

 and the volume are connected by the relation 



d T J , d T J _ 

 — — dp+ ——dv = 

 dp dv 



These variations dp and dv occasion a variation in the absolute quan- 

 tity of heat Q, the expression of which is 



