Current Attempt in Progress $\backslash$table$[[$ES$5$It$,,05,8],[0,6,$SSIT,,$000\text{'}$s$,/\_],[,$S$65,86,,000\backslash$deg $$I$,9],[,860\backslash$tau $,$SESE,,$000\backslash$deg ZI$,],[0,60$T$,,,05,$AA$],[980,8899,,,05,\backslash$epsi $],[,8899,$I$$E$,,000\text{'}5,],[,8899,9058,095,000\text{'}$ZI$,\backslash$tau $]]\backslash$table$[[$State$,$p$($kPa$),$T$(\backslash$deg C$),$h$($kJ$/$kg$),$s$($kJ$/$kg$*$K$),$x$],[1,12,000,560,3506,6\mathrm{.}683,],[2,5,000,,3221,6\mathrm{.}683,],[3,50,2323,6\mathrm{.}683,0\mathrm{.}86,],[4,50,3412,1\mathrm{.}093,0,],[5,12,000,353\mathrm{.}5,1\mathrm{.}093,,],[6,12,000,982\mathrm{.}4,2\mathrm{.}595,,],[7,5\mathrm{.}000,1155,2\mathrm{.}921,0,],[8,50,1155,3\mathrm{.}387,0\mathrm{.}353,]]$

As indicated in the figure below, a power plant operates on a regenerative vapor power cycle with one closed

feedwater heater. Steam enters the first turbine stage at state $1$ where pressure is p$1=12$ MPa and temperature is

$560\backslash$deg C$.$ Steam expands to state $2$ where pressure is p$2=5$ MPa and some of the steam is extracted and diverted to the closed feedwater heater. Condensate exits the feedwater heater at state $7$ as saturated liquid at a pressure of

p$7=5$ MPa, undergoes a throttling process through a trap to a pressure of pg $=50$ kPa at state $8,$ and then enters

the condenser. The remaining steam expands through the second turbine stage to a pressure of p$3=50$ kPa at state

$3$ and then enters the coldenser. Saturated liquid feedwater exiting the condenser at state $4$ at a pressure of pa

$=50$ kPa enters a pump and exits the pump at a pressure of p$5=12$ MPa. The feedwater then flows through the

closed feedwater heater, exiting at state $6$ with a pressure of p$6=12$ MPa. The net power output for the cycle is

$330$ MW$.$

For isentropic processes in each turbine stage and the pump, determine:

$($a$)$ the percent 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 feedwater heater, in kW$/$K$.$

$($d$)$ the rate of entropy production in the steam trap, in kW$/$K$.$