Page:Scientific Memoirs, Vol. 1 (1837).djvu/373

Rh We shall add that the equation gives the law of the specific calorics at a constant pressure and volume.

The expression of the first is of the second, equal to

The first may be obtained by differentiating $$Q$$ with relation to $$t$$, supposing $$p$$ constant; the second, by supposing $$v$$ constant. If we take equal volumes of different gases at the same temperature and under the same pressure, the quantity $$R$$ will be the same for all; and accordingly we see that the excess of specific caloric at a constant pressure, over the specific caloric of a constant volume, is the same for all, and equal to $$\frac C$$.

§ IV.

The same method of reasoning applied to vapours enables us to establish a new relation between their latent caloric, their volume, and their pressure.

We have shown in the second paragraph how a liquid passing into the state of vapour may serve to transmit the caloric from a body maintained at a temperature $$T$$, to a body maintained at a lower temperature $$t$$, and how this transmission develops the motive force.

Let us suppose that the temperature of the body $$B$$ is lower by the infinitely small quantity $$d\,t$$ than the temperature of the body $$A$$. We have seen that if $$c\,b $$ (fig. 4.) represents the pressure of the vapour Fig. 4.