$7\mathrm{.}1$ Steam at $30$ bar, $350C$ expands through a convergent$-$divergent nozzle. The exit plane pressure is $3$ bar. The flow rate is $0\mathrm{.}5k\frac{g}{s}$ and the nozzle efficiency is $0\mathrm{.}8.$ Assuming that the velocity at inlet is negligible, determine the throat and exit areas, steam velocity at the exit, and the quality of steam at the exit plane. The critical pressure ratio can be taken as $0\mathrm{.}546.$