Page:Scientific Memoirs, Vol. 1 (1837).djvu/362

will be represented geometrically by the area comprised between the axis of the abscisses, the two coordinates $C\;B$, $D\;E$, and the portion of a hyperbola $C\;E$.

Fig. 1

(Improve this image)

Supposing, again, that the body $A$ is removed and that the dilatation of the gas continues in an inclosure impermeable to heat; then a part of its sensible caloric becoming latent, its temperature will diminish and its pressure will continue to decrease in a more rapid manner and according to an unknown law, which law might be represented geometrically by a curve $E\;F$, the abscissæ of which would be the volumes of the gas, and the ordinates the corresponding pressures: we will suppose that the dilatation of the gas has continued until the successive reductions which its sensible caloric experiences have reduced the temperature $T$ of the body $A$ to the temperature $t$ of the body $B$; its volume will then be $A\;G$, and the corresponding pressure $F\;G$. It will also be evident from the same reasoning, that the gas during this second part of its dilatation will develop a quantity of mechanical action represented by the area of the mixtilinear trapezium $D\;E\;F\;G$.

Now that the gas is brought to the temperature $t$ of the body $B$, let us bring them together: if we compress the gas in an inclosure impermeable to heat, but in contact with the body $B$, the temperature of the gas will tend to rise by the evolution of latent heat rendered sensible by compression, but will be absorbed in proportion by the body $B$, so that the temperature of the gas will remain equal to $t$. The pressure will increase according to the law of Mariotte: it will be represented geometrically by the ordinates of a hyperbola $K\;F$, and the corresponding abscisses will represent the corresponding volumes. Suppose the compression to be increased until the heat disengaged and absorbed by the body $B$ is precisely equal to the heat communicated to the gas by the