Page:Scientific Memoirs, Vol. 1 (1837).djvu/368

356 $$t$$ of the body $$B$$ is lower by the infinitely small quantity $$dt$$, than the temperature $$t$$ of the body $$A$$. We shall suppose in the first instance that a gas serves for the transmission to the body $$B$$, of the caloric of the body $$A$$. Let $$v_0$$ be the volume of the gas under the pressure $$p_0$$ at a temperature of $$t_0$$; let $$p$$ and $$v$$ be the volume and the pressure of the same weight of gas at the temperature $$t$$ of the body $$A$$. The law enunciated by Mariotte, combined with that of Gay-Lussac, establishes between these different quantities the relation or, for simplicity,

The body $$A$$ is brought into contact with the gas. Let $$me = v$$, $$ae = p$$ (fig. 3.). If the gas be allowed to expand by the infinitely small quantity $$dv = eg$$, the temperature will remain constant, in consequence of the presence of the source of heat $$A$$; the pressure will diminish, and become equal to the ordinate $$bg$$. We now remove the Fig. 3.

body $$A$$, and allow the gas to expand, in an inclosure impermeable to heat, by the infinitely small quantity $$gh$$, until the heat becomes latent, reduces the temperature of the gas by the infinitely small quantity $$dt$$, and thus brings it to the temperature $$t - dt$$ of the body $$B$$. In consequence of this reduction of temperature, the pressure will diminish more rapidly than in the first part of the operation, and will become $$ch$$. We now take the body $$B$$, and reduce the volume $$mh$$ by the infinitely small quantity $$fh$$, calculated in such a manner that during this compression the gas may transmit to the body $$B$$ all the heat it has derived from the body $$A$$ during the first part of the operation. Let $$fd$$ be the corresponding pressure; that done, we remove