Page:Reflections on the Motive Power of Heat.djvu/270

246 If, to abridge, we call N the quantity $$\frac{P}{267}$$, the equation would become

whence we deduce, according to equation (1),

Regarding t as constant, and taking the integral of the two numbers, we shall have

If we suppose r = 0 when v = 1, we shall have C = 0; whence

This is the motive power produced by the expansion of the air which, under the temperature t, has passed from the volume 1 to the volume v. If instead of working at the temperature t we work in precisely the same manner at the temperature t + dt, the power developed will be

Subtracting equation (2), we have

Let e be the quantity of heat employed to maintain the temperature of the gas constant during its