One mole of methane in a piston-cylinder assembly undergoes an adiabatic compression from an initial state (P1 = 0.5 bar, v1 = 0.05 m3/mol) to a fi nal state (P2 = 10 bar, v2 = 3 * 10²³ m3/mol) .

Use the van der Waals equation of state for nonideal gas behavior.

(a) How much work is done on the system?

(b) Do you expect the magnitude of work to be larger or smaller than what would be needed if methane behaved like an ideal gas? Explain based on molecular potential energy.