Page:Reflections on the Motive Power of Heat.djvu/96

74 to be V, the compression of $$\tfrac{1}{116}$$ reduces it to V − $$\tfrac{1}{116}$$V.

Direct heating under constant pressure should, according to the rule of M. Gay-Lussac, increase the volume of air $$\tfrac{1}{267}$$ above what it would be at 0°: so the air is, on the one hand, reduced to the volume V − $$\tfrac{1}{116}$$V; on the other, it is increased to V + $$\tfrac{1}{267}$$V.

The difference between the quantities of heat which the air possesses in both cases is evidently the quantity employed to raise it directly one degree; so then the quantity of heat that the air would absorb in passing from the volume V − $$\tfrac{1}{116}$$V to the volume V + $$\tfrac{1}{267}$$V is equal to that which is required to raise it one degree.

Let us suppose now that, instead of heating one degree the air subjected to a constant pressure and able to dilate freely, we inclose it within an invariable space, and that in this condition we cause it to rise one degree in temperature. The air thus heated one degree will differ from the air compressed $$\tfrac{1}{116}$$ only by its $$\tfrac{1}{116}$$ greater volume. So then the quantity of heat that the air would set free by a reduction of volume of $$\tfrac{1}{116}$$ is equal to that which would be required to raise it one degree Centigrade under constant volume. As the differences between the volumes V − $$\tfrac{1}{116}$$V, V, and