Page:Reflections on the Motive Power of Heat.djvu/105

The elevation of temperature ought, evidently, to be still more considerable if the capacity of the air for heat becomes less as its volume diminishes. Now this is probable, and it also seems to follow from the experiments of MM. Delaroche and Bérard on the specific heat of air taken at different densities. (See the Mémoire in the Annales de Chimie, t. lxxxv. pp. 72, 224.)

The two theorems explained on pp. 72 and 81 suffice for the comparison of the quantities of heat absorbed or set free in the changes of volume of elastic fluids, whatever may be the density and the chemical nature of these fluids, provided always

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to $({\tfrac {115}{116}})^{2}$, and the temperature should rise another degree. After x similar reductions the volume becomes $({\tfrac {115}{116}})^{x}$ and the temperature should be raised x degrees. If we suppose $({\tfrac {115}{116}})^{x}={\tfrac {1}{14}}$, and if we take the logarithms of both, we find

   x = about 300°.

If we suppose $({\tfrac {115}{116}})^{x}={\tfrac {1}{2}}$, we find

   x = 80°;

which shows that air compressed one half rises 80°.

All this is subject to the hypothesis that the specific heat of air does not change, although the volume diminishes. But if, for the reasons hereafter given (pp. 86, 89), we regard the specific heat of air compressed one half as reduced in the relation of 700 to 616, the number 80° must be multiplied by ${\tfrac {700}{616}}$, which raises it to 90°.