As indicated in Fig. P$8\mathrm{.}52,$ a power plant similar to that inFig. $8\mathrm{.}11$ operates on a regenerative vapor power cycle withone closed feedwater heater. Steam enters the first turbine stage at state $1$ where pressure is $12$ MPa and temperature is $560$ C$.$ Steam expands to state $2$ where pressure is $1$ MPa andsome of the steam is extracted and diverted to the closedfeedwater heater. Condensate exits the feedwater heater atstate $7$ as saturated liquid at a pressure of $1$ MPa, undergoes a throttling process through a trap to a pressure of $6$ kPa atstate $8,$ and then enters the condenser. The remaining steam expands through the second turbine stage to a pressure of$6$ kPa at state $3$ and then enters the condenser. Saturated liquid feedwater exiting the condenser at state $4$ at a pressureof $6$ kPa enters a pump and exits the pump at a pressure of$12$ MPa. The feedwater then flows through the closedfeed water heater, exiting at state $6$ with a pressure of $12$ MPa.The net power output for the cycle is $330$ MW$.$ For isentropic Efficiencies of $83\%$ in each turbine stage and the pump, determine$($a$)$ the cycle thermal efficiency.$($b$)$ the mass flow rate into the first turbine stage, in kg$/$s$.($c$)$ the rate of entropy production in the closed feedwaterheater, in kW$/$K$.($d$)$ the rate of entropy production in the steam trap, in kW$/$K$.$