[UPSC CSE 2023] Thermodynamics (Q21, 20M)

A piston-cylinder device initially contains air at 150\text{ kPa} and 27^\circ\text{C}. At this state, the piston is resting on a pair of stops, as shown in the figure, and the enclosed volume is 400\text{ L}. The mass of the piston is such that a 350\text{ kPa} pressure is required to move it. The air is now heated until the volume is doubled. Determine : (i) the final temperature, (ii) the work done by the air, and (iii) the total heat transferred to air. Given : U_{300\text{ K}} = 214\text{ kJ/kg} and U_{\text{final}} = 1113\text{ kJ/kg} Gas constant of air, R = 0\cdot287\text{ kPa.m}^3/\text{kg.K}