$8\mathrm{.}21$ Figure P$8.21$ provides steady$-$state operating data for a vapor power plant using water as the working fluid. The mass flow rate of water is $15k\frac{g}{s}.$ The turbine and pump operate adiabatically but not reversibly. Determine

$($a$)$ the thermal efficiency.

$($b$)$ the rates of heat transfer $Q_{in}^{}$ and $Q_{\text{o}\text{u}\text{t}}^{},$ each in kW $.$