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

350 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

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