One mole of methane in a piston-cylinder system undergoes an adiabatic compression from an initial state (P1 = 0.5 bar, V1 = 0.05 m3/mol) to a final state (P2 = 10 bar, V2 = 0.003 m3/mol). How much work is done on the system? You can use any equation of state you like but give justification. To receive full credit, draw a diagram of this process, the path taken to get from the initial state to the final state, and show all your work.