Page:Reflections on the Motive Power of Heat.djvu/209

Rh corresponding to the temperature t, is known. For, by § 30, equation (6), we have

where dq is the quantity of heat absorbed, when the volume is allowed to increase from v to v + dv; or the quantity evolved by the reverse operation. Hence we deduce

Now, $$\tfrac{E p_{_0} v_{_0}}{\mu}$$ is constant, since the temperature remains unchanged; and therefore we may at once integrate the second number. By taking it between the limits V'  and V, we thus find

where Q denotes the required amount of heat evolved by the compression from V to P'. This expression may be modified by employing the equations PV = P'V' = p0 v0 (1 + Et); and we thus obtain