A frictionless piston of mass m = 3.0 kg is a precise fit in the narrow vertical cylindrical neck of a large container of volume V = 1000 litres and can move frictionless. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A = 1.00 x 10-4 m2. a) Assuming that the pressure and volume of the gas change slowly and isothermally, determine the differential equation of motion for small displacements of the piston about its equilibrium position and hence calculate the angular frequency of oscillation. [Hint: find an equilibrium pressure and consider how small displacement of the piston from the equilibrium position changes the volume and pressure in the vessel]. b) Without calculation, consider whether the frequency will increase or decrease if the pressure and volume of the gas were to change adiabatically. Explain your reasoning.

A frictionless piston of mass m = 3.0 kg is a precise fit in the narrow vertical cylindrical neck of a large container of volume V = 1000 litres and can move frictionless. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A = 1.00 x 10-4 m2. a) Assuming that the pressure and volume of the gas change slowly and isothermally, determine the differential equation of motion for small displacements of the piston about its equilibrium position and hence calculate the angular frequency of oscillation. [Hint: find an equilibrium pressure and consider how small displacement of the piston from the equilibrium position changes the volume and pressure in the vessel]. b) Without calculation, consider whether the frequency will increase or decrease if the pressure and volume of the gas were to change adiabatically. Explain your reasoning.