Air is heated as it flows through a \(10 \mathrm{~cm} \times 10 \mathrm{~cm}\) square duct with negligible friction. At the inlet, air is at \(T_{1}=\) \(400 \mathrm{~K}, P_{1}=550 \mathrm{kPa}\), and \(V_{1}=80 \mathrm{~m} / \mathrm{s}\). Determine the rate at which heat must be transferred to the air to choke the flow at the duct exit, and the entropy change of air during this process.