Page:Scientific Memoirs, Vol. 1 (1837).djvu/361

Rh production of the mechanical force is attended by the passage of a part of the heat which is developed by combustion in the furnace, the temperature of which is very high, into the water in the condenser, the temperature of which is much lower.

Reciprocally, it is always possible to render the passage of caloric from a hot to a cold body useful for the production of a mechanical force: to obtain this it is sufficient to construct a machine resembling an ordinary steam-engine, in which the heated body serves to produce steam and the cold one to condense it. It results from this that there is a loss of vis viva, of mechanical force, or of quantity of action, whenever immediate contact takes place between two bodies of different temperatures, and heat passes from the one into the other without traversing an intermediate body; therefore in every machine intended to make efficient the motive force developed by heat, there is a loss of power whenever a direct communication of heat takes place between bodies of different temperatures, and consequently the maximum of the effect produced cannot be obtained but by means of a machine in which only bodies of equal temperature are brought into contact. Now the knowledge we possess of the theory of gases and vapours shows the possibility of attaining this object.

Let us, then, suppose two bodies retained, one at a temperature $$T$$, and another at an inferior temperature $$t$$; such, for example, as the sides of a steam-boiler, in which the heat developed by combustion constantly supplies the place of that which the steam produced carries away; and the condenser of the common atmospheric engine, in which a current of cold water removes, every moment, both the heat which the steam loses in condensing, and that which belongs to its proper temperature. For the sake of simplicity we will call the first body $$A$$ and the second $$B$$.

Let us now take any gas whatever, at the temperature $$T$$, and bring it into contact with the source of heat $$A$$, representing its volume $$V_0$$ by the absciss $$A\; B$$, and its pressure by the ordinate $$C\; B$$ (fig 1).

If the gas is inclosed in an extensible vessel, and which is allowed to extend in a void space in which it cannot lose heat either by radiation or by contact, the source of heat $$A$$ will supply it, from moment to moment, with the quantity of caloric which its increase of volume renders latent, and it will preserve the same temperature $$T$$. Its pressure, on the contrary, will diminish according to the law of Mariotte. The law of this variation may be represented by a curve $$C\; E$$, of which the volumes will be the abscisses, and the corresponding pressures the ordinates.

Supposing the dilatation of the gas to continue until the volume $$A\; B$$ has become $$A\; D$$, and that the pressure corresponding to this new volume is $$D\; E$$, the gas during its dilatation will have developed a quantity of mechanical action, which will have for its value the integral of the product of the pressure by the differential of the volume, and which