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. Steaming 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 flow fraction 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.