A frictionless piston of mass m is a precise fit in the vertical cylindrical neck of a large container of volume V. the container is filled with a gas and there is a vacuum above the piston. The cross-sectional area of the neck is A
(a) Calculate the pressure of the gas in the container when the piston is in equilibrium.
(b) Assuming that the pressure and volume of the gas are related by Bole’s law, calculate the restoring force on the piston when it is displaced by a small distance x.
(c) Assuming that the motion of the piston is slow enough for Boyle’s law to be valid, obtain the differential equation for small displacements of the piston about its equilibrium position.
(d) Show that the angular frequency of oscillation ω is independent of m.
(e) Calculate ω for V = 2000 liters and A = 1.0 × 10–4 m2.