A vertical cylinder contains v moles of an ideal gas and is closed offby a piston of mass M and area A. the acceleration due to gravity is g . the molar specific heat Cv (at constant volume) of the gas is a constant independent of temperature .the heat capacities of the piston and cylinder are negligibly small and any frictional forces between the piston and the cylinder walls can be neglected. The whole system is thermally insulated . Initially ,the piston is clamped in piston so that the gas has a volume V0 and a temperture T0.the piston is now released and, after some oscillations, comes to rest in a final equilibrium situation corresponding to a larger volume of the gas

a) Does the temperture of the gas increase ,decrease or remain the same?

b) Does the entropy of the gas increase, decrease or remain the same?

c) Calculate the final temperture of the gas in termof T0,V0 and the other parameters mentioned in the statement of the problem.