Problem: $(60$ points$)$

Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at $P=8\mathrm{.}0$MPa and saturated

liquid exits the condenser at a pressure of $P3=8$kPa. The net power output of the cycle is $Wby=90MW.$

Determine for the cycle:

$($a$)$ the thermal efficiency

$($b$)$ the mass flow rate of the steam in $k\frac{g}{h}r,$

$($c$)$ the rate of heat transfer into the working fluid as it passes through the boiler, in MW$,$ and

$($d$)$ the mass flow rate of the condenser cooling water in $k\frac{g}{h}r,$ if cooling water enters the condenser at $Tc1=15C$

and exits at $Tc2=35C.$