A supply line carries a two$-$phase liquid$-$vapor mixture of steam at $300lb\frac{f}{i}n.{?}^2$A small fraction of the flow in the ne is diverted through a throttling calorimeter and exhausted to the atmosphere at $14\mathrm{.}7lb\frac{f}{i}n.{?}^2$ The temperature of e exhaust steam is measured as $250F.$ Determine the quality of the steam in the supply line.

hat$(h{)}_2=$hat$(h{)}_1=1168\mathrm{.}8$