A cylinder fitted with a piston contains \(2 \mathrm{~kg}\) steam at \(500 \mathrm{kPa}, 400^{\circ} \mathrm{C}\). Find the entropy change and the work done when the steam expands to a final pressure of \(200 \mathrm{kPa}(a)\) adiabatically and reversibly, and \((b)\) adiabatically and irreversibly to an equilibrium temperature of \(300^{\circ} \mathrm{C}\).