Page:Scientific Memoirs, Vol. 1 (1837).djvu/374

362 of the liquid corresponding to the temperature $$t$$ of the body $$A$$, and $$f\,g$$ that which corresponds to the temperature $$t - d\,t$$ of the body $$B$$; $$b\,h$$ the increase of volume due to the vapour formed in contact with the body $$A$$, $$h\,k$$ that which is due to the vapour formed after the body $$A$$ has been removed, the formation of which has reduced the temperature by the quantity $$d\,t$$; we have seen, I say, that the quantity of action developed by the transmission of the latent caloric furnished by the body $$A$$, [and transmitted] from that body to the body $$B$$, is measured by the quadrilateral figure $$c\,d\,e\,f$$. Now this surface is equal, if we neglect the infinitely small quantities of the second order, to the product of the volume $$c\,d$$ by the differential of the pressure $$d\,h - e\,k$$. Naming $$p$$ the pressure of the vapour of the liquid corresponding to the temperature $$t$$, $$p$$ will be a function of $$t$$, and we shall have $$d\,h - e\,k = \fracd\,t$$.

$$c\,d$$ will be equal to the increase of volume produced in water when it passes from the liquid into the gaseous state, under the pressure $$p$$, at a corresponding temperature. If we call $$\rho$$ the density of the liquid, $$\delta$$ that of the vapour, and $$v$$ the volume of the vapour formed, $$\delta v$$ will be its weight, and $$\frac$$ will be the volume of the liquid evaporated. The increase of volume owing to the formation of a volume $$v$$ of vapour will therefore be

The effect produced will therefore be

The heat, by means of which this quantity of action has been produced, is the latent caloric of the volume $$v$$ of vapour formed; let $$k$$ be a function of $$t$$ representing the latent caloric contained in the unity of volume of the vapour furnished by the liquid subjected to experiment, at a temperature $$t$$, and under a corresponding pressure, the latent caloric of the volume $$v$$ will be $$k v$$, and the ratio of the effect produced to the heat expended will be expressed by

We have demonstrated that it is the greatest which can possibly be obtained; that it is independent of the nature of the liquid employed, and the same as that obtained by the employment of the permanent gases: now we have seen that this is expressed by $$\frac$$, $$C$$ being a function of $$t$$ independent of the nature of the gases; we shall therefore also have