[UPSC CSE 2022] Thermodynamics (Q29, 15M)

A thermally insulated cylinder, closed at both ends, is fitted with a frictionless heat-conducting piston which divides the cylinder in two parts. Initially, the piston is clamped in the centre, with one litre of air at 200\ \mathrm{K} and 2\ \mathrm{atm} pressure on one side and one litre of air at 300\ \mathrm{K} and 1\ \mathrm{atm} pressure on the other side. The piston is released and the system reaches equilibrium in pressure and temperature, with the piston at a new position. Compute the final pressure and temperature.