Problem $1.$ A simple Rankine cycle uses water as the working fluid. The boiler operates at $6$MPa

and the condenser at $50$ kPa $.$ At the entrance of the turbine, the temperature is $450C.$ The

isentropic efficiencies of the pump and turbine are $100\%.$ The water enters the pump as a saturated

liquid. The boiler is sized for a mass flow rate of $20k\frac{g}{s}.$ Determine $1)$ the rate at which heat is

added in the boiler, $2)$ the power required to operate the pump, $3)$ the net power produced by the

cycle, and $4)$ the thermal efficiency.

Please show all steps. Thanks.