354 M.CLAPEYRON ON THE MOTIVE POWER OF HEAT. 



at a temperature t, possesses the same absolute quantity of heat 

 that the liquid possessed at the commencement of the operation ; if, 

 therefore, we remove the body B, and contmue the condensation, in a 

 vessel impermeable to heat, until the volume again becomes equal to 

 A B, we shall have the same quantity of matter occupying the same 

 volume, and possessing the same quantity of heat as at the commence- 

 ment of the operation : its temperature and its pressure ought, there- 

 fore, also to be the same as at that epoch ; the temperature will thus 

 again become equal to T, and the pressure equal to C B. The law of 

 the pressures during this last part of the operation, will therefore be 

 given by a curve passing through the points K and C ; and the quan- 

 tity of action absorbed during the reduction of the volume from A F 

 to A B, will be represented by the rectangle F H K G and the mixti- 

 linear trapezium B C K H, If, then, we deduct from the quantity of 

 action developed during the dilatation, that which is absorbed during 

 the compression, we shall have for the difference the surface of the 

 mixtilinear parallelogram C E G K, which will represent the quantity of 

 action developed during the entire series of the operations that we 

 have described, and at the conclusion of which the liquid employed 

 will be found in its primitive state. 



But it is necessary to remark that all the caloric communicated by 

 the body A has passed to the body B, and that this transmission has 

 taken place without there having been any other contact than that be- 

 tween bodies of the same temperature. 



It might be proved in the same manner as for the gases, that by re- 

 peating the same operation in an inverse order, the heat of the body B 

 may be made to pass to the body A, but that this result will only be 

 obtained by the absorption of a quantity of mechanical action, equal 

 to that which has been developed in the passage of the same quantity 

 of caloric from the body A to the body B. 



From what precedes, it results that a quantity of mechanical action 

 and a quantity of heat passing from a hot to a cold body, are quan- 

 tities of the same nature, and that it is possible to substitute the one 

 for the other reciprocally ; in the same manner as in mechanics a body 

 falling from a certain height, and a mass endowed with a certain ve- 

 locity, are quantities of the same order, and can be transformed one 

 into the other by physical agents. 



Hence also it follows that the quantity of action F developed by the 

 passage of a certain quantity of heat C, from a body A maintained at 

 a temperature T, to a body B maintained at a temperature t, by one 

 of the processes that we have just indicated, is the same, whatever be 

 the gas or the liquid employed, and is the greatest that it is possible to 

 realize. 



Suppose that b/ causing the quantity of heat C of the body A to 



