A piston-cylinder assembly contains \(3 \mathrm{~kg}\) of air at 15 bar and \(620 \mathrm{~K}\). The environment is at a pressure of 1 bar and \(300 \mathrm{~K}\). The air is expanded in a fully reversible adiabatic process to a pressure of 5.5 bar. Calculate the useful work which can be obtained from this process. Also calculate the maximum useful work which can be obtained from the gas in

(a) the initial state and

(b) the final state.

Assume that the specific heats for the gas are \(c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\) and \(c_{v}=0.718 \mathrm{~kJ} / \mathrm{kg} \mathrm{K}\). [295.5 kJ; \(509.6 \mathrm{~kJ} ; 214.1 \mathrm{~kJ}]\)