M. CLAPEYRON ON THE MOTIVE POWER OS HEAT. 



367 



dQ 

 dp 



dQ 



dv 



dQ. 



dv 



dQ\d_vJ 



dp /dT\ 



\dp). 



such is the quantity of heat consumed in the production of the effect 

 that we have just calculated. The effect produced by a quantity of heat 

 equal to unity will therefore be 



JT 



dQ d^_d_Q dT 



d V dp dp d V 



It will be shown, as in the case of the gases, that this effect produced, 

 is the largest which it is possible to realize ; and as all the substances of 

 nature may be employed, in tlie manner that has just been indicated, 

 to produce this maximum effect, it is necessarily the same for all. 



When this theory has been applied specially to the gases, we have 



called -— the coefficient of d T in the expression of this maximum quan- 

 tity of action ; the equation therefore of all the substances of nature, solid, 

 liquid, or gaseous, will be 



dQ dj: dQ dT 

 dv dp dp dv 



in which C is a function of the temperature which is the same for all. 



For the gases we have 



T:=-261 + ±pv.. 



R^ 



whence we deduce 



dT 



dT 



__ ^ H — ^ 



dp ~ R dv ~ K 



The preceding equation applied to the gases talces therefore the 

 form 



dQ dQ 



dv P dp 



= nC = F(p,v): 



it is the equation at which we have already arrived, and of which the 

 integral is 



Q= R(B- Clog/)); 

 that of the general equation 



dQ dT dQ dT 



dv dp dp dv 

 IS of the form 



Q = F(T)-Ci>(p,v); 

 F (T) is an arbitrary function of the temperature, and <j> (p, v) a parti- 

 cular function satisfying the equation 



= C 



