368 M, CLAPEYRON ON THE MOTIVE POWER OF HEAT. 



dTdf U ^ = 1 

 dv dp dp dv 

 (See the note appended to this Memoir.) 



We shall now deduce various consequences from the general equation 

 at which we have arrived. 



We have previously seen that when we compress a body by the quan- 

 tity dv, the temperature remaining constant, the heat disengaged by 

 the condensation is equal to 



dQ = dv 



dQ _ dQ \dv ) 

 dv ~ dp {iJ\ 

 \dp}_ 



and as 



dQt_d^ dQ dT _^ 



dv dp dp dv 

 the preceding expression takes the form 



dQ = dv -ij— - = -dp ^ 



\dp) \dv) 



This last equation may be put under the form 



— is the differential coefficient of the volume with regard to the tem- 

 dT 



perature, the pressure remaining constant. 



We thus arrive at this general law, which is applicable to all the sub- 

 stances of nature, solid, liquid, or gaseous : If f he pressure supported by 

 different bodies, taken at the same temperature, be augmented by a small 

 quantity, quantities of lieat will be disengaged from it, which will be pro- 

 portional to their dilatability by heat. 



This result is the most general consequence deducible from this axiom : 

 that it is absurd to suppose that motive force or heat can be created 

 gratuitously and absolutely. 



§ VI. 

 The function of the temperature C is, as we see, of great importance 

 in consequence of the part it sustains in the theory of heat : it enters 

 into the expression of the latent caloric which is contained in all sub- 

 stances, and which is disengaged from them by pressure. Unfortu- 

 nately no experiments have been made from which we can determine 

 the values of this function, corresponding to all the values of the tem- 

 perature. To obtain < = we must proceed in the following manner. 



