III. Problem Solving: Actual Rankine Cycle $($Application$,$ Analysis, and Synthesis$)(50$ points$)$

A simple Rankine cycle uses water as a working fluid. The boiler operates at $6$ MPa and the condenser at $0\mathrm{.}4$ bar. At

the entrance to the turbine, the temperature is $550C.$ The isentropic efficiency of the turbine is $88\%,$ pressure and

pump losses are negligible, and the water leaving the condenser is sub$-$cooled by $6\mathrm{.}3C.$ The boiler is sized for a

mass flow rate of $20k\frac{g}{s}.$ Determine the following;

a$.$ Rate at which heat is added to the boiler,

b$.$ Power required to operate the pumps,

c$.$ Net power produced by the cycle, and

d$.$ Thermal efficiency.

Note: $T_3=T_{\text{s}\text{a}\text{t}}$@$t40$kPa$-6\mathrm{.}3=75\mathrm{.}86-6\mathrm{.}3=69\mathrm{.}56C($use $70C)$

e$.$ Draw a T$-$s Diagram and a Schematic Diagram of the problem and plot all the given data. $(20$ points$)$

Good Luck $!!!$