Air enters a convergent-divergent nozzle at \(20 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) and \(40^{\circ} \mathrm{C}\). The receiver pressure is \(2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\) and the nozzle throat area is \(10 \mathrm{~cm}^{2}\).

(a) What should the exit area be for the design conditions above (i.e., to operate at third critical?)

(b) With the nozzle area fixed at the value determined in part

(a) and the inlet pressure held at \(20 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\), what receiver pressure would cause a shock to stand at the exit?

(c) What receiver pressure would place the shock at the throat?