Air at \(500 \mathrm{kPa}\) and \(573^{\circ} \mathrm{K}\) flows at \(0.1 \mathrm{~kg} / \mathrm{s}\) through a converging diverging nozzle whose exit is at \(100 \mathrm{kPa}\). Assume \(\gamma_{\text {air }}=1.4\), \(R_{\text {air }}=288 \mathrm{~J} / \mathrm{kgK}\), and that the flow is isentropic. Please find:

a. The exit Mach number

b. The exit area

c. The throat area