Page:Scientific Memoirs, Vol. 1 (1837).djvu/376

364 deducible from them; if then we take two of them, $$p$$ and $$v$$ for example, as independent variables, the two others $$T$$ and $$Q$$ may be considered as functions of the former two.

In what manner the quantities $$T$$, $$p$$, and $$v$$, vary with respect to each other may be ascertained by direct experiments upon the elasticity and dilatability of bodies; it is thus that Mariotte's law relative to the elasticity of the gases, and Gay Lussac's relative to their dilatability, lead to the equation all that remains is to determine $$Q$$ in functions of $$p$$ and $$v$$.

A relation exists between the functions $$T$$ and $$Q$$, which may be deduced from principles analogous to those which we have just established. Let us increase the temperature of the body by the infinitely small quantity $$d\,T$$, and at the same time prevent the increase of the volume; the pressure will then be augmented; if we represent the volume $$v$$ by the absciss $$a\, b$$ (fig. 5), and the primitive pressure by the ordinate $$b\, d$$, this Fig. 5.

augmentation of pressure may be represented by the quantity $$d\,f$$, which will be of the same order as the increase of temperature $$d\,T$$ to which it is owing, that is infinitely small.

Now we will take a source of heat $$A$$, maintained at the temperature $$T + d\,T$$, and allow the volume $$v$$ to increase by the quantity $$b\, c$$; the presence of the source $$A$$, maintained at the temperature $$T + d\,T$$, prevents the reduction of the temperature. During this contact, the quantity $$Q$$ of heat that the body possesses will increase by the quantity $$d\,Q$$, which will be derived from the source $$A$$. We will afterwards remove the source $$A$$, and the given body will become cool by the quantity $$d\, T$$, at the same time retaining the volume $$a\, c$$. The pressure will then diminish by the infinitely small quantity $$g\, e$$.

The temperature of the body being thus reduced to $$T$$, which is that of the source of heat $$B$$, we will take $$B$$, and reduce the volume of the