Page:Scientific Memoirs, Vol. 1 (1837).djvu/366

354 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 continue 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 commencement of the operation: its temperature and its pressure ought, therefore, 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 quantity 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 mixtilinear 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 between bodies of the same temperature.

It might be proved in the same manner as for the gases, that by repeating 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 quantities 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 velocity, 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 by causing the quantity of heat $$C$$ of the body $$A$$ to