Pressure of an Ideal Gas on a Moving Piston

The pressure exerted by an ideal gas on the face of a moving piston is calculated for constant piston speeds that are small compared to the average speed of the gas molecules, and is found to be proportional to the expression, $1 − (8/π)α + (8/π)α2$⁠, where $α$ is the ratio of piston speed to the average molecular speed, or, better, is the ratio of the piston speed, corrected for the motion of the gas in the direction of piston motion, to the average molecular speed. The drift speed of the gas is investigated and found to be proportional to the displacement of the piston and the difference between piston speed and molecular speed. Work done in isothermal and adiabatic processes is calculated. Possible experimental verification is considered.