Page:Scientific Memoirs, Vol. 1 (1837).djvu/363

Rh source $$A$$ during its dilatation in contact with it in the first part of the process. Let then the volume of gas be $$A\; H$$, and the corresponding pressure $$H\; K$$: the gas in this state contains the same absolute quantity of heat that it did at the moment of commencing the process, when it occupied the volume $$A\; B$$ under the pressure $$C\; B$$. If therefore we remove the body $$B$$ and continue to compress the gas in an inclosure impermeable to heat, until the volume $$A\; H$$ is reduced to the volume $$A\; B$$, its temperature will successively increase by the evolution of the latent caloric, which the compression converts into sensible caloric. The pressure will increase in a corresponding ratio; and when the volume shall be reduced to $$A\; B$$, the temperature will become $$T$$, and the pressure $$B\; C$$. In fact, the successive states which the same weight of gas experiences are characterized by the volume, the pressure, the temperature, and the absolute quantity of caloric which it contains: two of these four quantities being known, the other two become known as consequences of the former; thus in the case in question the absolute quantity of heat and the volume having become what they were at the beginning of the process, we may be certain that the temperature and pressure will also be the same as before. Consequently, the unknown law according to which the pressure will vary when the volume of gas is reduced in its inclosure impermeable to heat, will be represented by a curve $$K\; C$$, which will pass through the point $$C$$, and in which the abscisses always represent the volumes, and the ordinates the pressures.

However, the reduction of the gaseous volume from $$A\; G$$ to $$A\; B$$ will have consumed a quantity of mechanical action which, for the reasons we have stated above, will be represented by the two mixtilinear trapeziums $$F\; G\; H\; K$$ and $$K\; H\; B\; C$$. If we subtract from these two trapeziums the two first, $$C\; B\; D\; E$$ and $$E\; D\; G\; F$$, which represent the quantity of action during the dilatation of the gas, the difference, which will be equal to the sort of curvilinear parallelogram $$C\; E\; F\; K$$, will represent the quantity of action developed in the circle of operations which we have just described, and after the completion of which the gas will be precisely in the same state in which it was originally. Still, however, the entire quantity of heat furnished by the body $$A$$ to the gas during its dilatation by contact with it, passes into the body $$B$$ during the condensation of the gas, which takes place by contact with it.

Here, then, we have mechanical force developed by the passage of caloric from a hot to a cold body, and this transfer is effected without the contact of bodies of different temperatures.

The inverse operation is equally possible: thus, we take the same volume of gas $$A\; B$$ at the temperature $$T$$ and under the pressure $$B\; C$$, inclose it in an envelope impermeable to heat, and dilate it until its temperature, gradually diminishing, becomes equal to $$t$$; we continue the