Consider a steam power plant that operates on a regenerative Rankine cycle with one closed feedwater

heater and a trap, as shown in the schematic below. Steam enters the turbine at $3$MPa and $350C$

and exits to the condenser at $20$kPa. Steam to the feedwater heater exits the turbine at $1$MPa. The

water that leaves the closed feedwater heater and enters the trap is a saturated liquid, and the

temperature of the water going to the boiler from the feedwater heater is $20C$ higher than the water

that enters the trap. The water leaving the condenser is cooled to a temperature that is $10C$ degrees

lower than the saturation temperature of the water in the condenser $($this is called $"10$ degrees of

subcooling"$).$ The mass flow rate of steam through the boiler is $20k\frac{g}{s}.$ The isentropic efficiency of

the pump is $60\%,$ and the isentropic efficiency of the turbine $($all stages$)$ is $90\%.$

a$.$ Determine the work input to the pump $($and the pump outlet enthalpy$),$ in $k\frac{J}{k}g.$

b$.$ Determine the work output of each turbine section, in $k\frac{J}{k}g.$

c$.$ Determine the fraction of the flow extracted from the turbine going to the closed feedwater heater.

d$.$ Determine the heat addition in the boiler, in $k\frac{J}{k}g.$

e$.$ Determine the mass flow rate at each of the turbine exits and through the pump, in $k\frac{g}{s}.$

f$.$ Determine the heat rejected in the condenser, in $kW.$

g$.$ Sketch the cycle on a T$-$s diagram, including the saturation lines $($dome$)$ and the locations of states

$5$ and $6.$

h$.$ Determine the pump work, the net turbine work, and the net work for the cycle, all in $kW.$

i$.$ Calculate the thermal efficiency.

j$.$ Determine the net power output of the power plant, in MW$.$

k$.$ Determine the heat rate for the power plant.

Summarize and clearly label your answers.