Consider an ideal Helium gas at a pressure  $P_0$  and volume  $V_0$  placed in a vertical cylindrical container as shown in figure. A moveable frictionless horizontal piston of mass m and cross section A compresses the gas leaving the upper section of the container void. There is a vertical spring attached to the piston and the upper wall of the cotainer. Disregard any gas leakage through their surface contact, and neglect the specific thermal capacities of the contianer, piston and spring. Initially the system is in equilibrium and the spring is unstreched. Neglect the spring’s mass.
Let the spring constant  $k=mgA/V_0$ . All the processes in gas are adiabatic. Acceleration due to gravity is g. For mono-atomic gas (Helium) use Laplace constant  $\gamma =5/3$ .