Problem $(20$ points$).$ Water is the working fluid in a Rankine cycle modified to include one closed feedwater heater and one open feedwater heater. Superheated vapor enters the turbine at $16$ MPa $,560$ C $,$ and the condenser pressure is $8$ kPa $.$ The mass flow rate of steam entering the first$-$stage turbine is $120k\frac{g}{s}.$ The closed feedwater heater uses extracted steam at $4$ MPa $,$ and the open feedwater heater uses extracted steam at $0\mathrm{.}3$ MPa $.$ Saturated liquid condensate drains from the closed feedwater heater at $4$ MPa and is trapped into the open feedwater heater. The feedwater leaves the closed heater at $16$ MPa and a temperature equal to the saturation temperature at $4$ MPa $.$ Saturated liquid leaves the open heater at $0\mathrm{.}3$ MPa $.$ The isentropic efficiencies of the turbine stages and pumps are $85\%.$ Determine

$($a$)$ the net power developed, in kW$.$

$($b$)$ the rate of heat transfer to the steam passing through the steam generator, in kW$.$

$($c$)$ the thermal efficiency. $($outcome $1).$

$($d$)$ the mass flow rate of condenser cooling water, in $k\frac{g}{s},$ if the cooling water undergoes a temperature increase of $18$ C with negligible pressure change in passing through the condenser.