Air is stored in a tank where the pressure is \(40 \mathrm{psia}\) and the temperature is \(500{ }^{\circ} \mathrm{R}\). A converging-diverging nozzle with an exitto-throat area ratio of 2.5 attaches the tank to a duct where heat is exchanged with the air. The exit pressure is 15 psia and a normal shock stands at the exit of the nozzle. Determine the magnitude and direction of the heat exchange.