$1.)(10$ points$)$ A power plant using a Rankine power generation cycle and steam operates with a condenser output temperature of $81\mathrm{.}25C,$ a pressure of $5$ MPa in the boiler and a boiler output temp of $775C.$ The cycle runs through an adiabatic and reversible compressor, an isobaric boiler, an adiabatic and reversible turbine, and an isobaric condenser. The cycle operates at steady state with a mass flow rate of $2\mathrm{.}5k\frac{g}{s}.$ Use the steam tables in the appendix of Sandler $($p$.917$ to $925).$

a$.)$ Draw out the cycle, calculate the work required for the pump, the work output by the turbine, the heat into the boiler, and the heat out of the condenser.

b$.)$ What is the efficiency of this power plant?

c$.)$ If the turbine was only $89\%$ efficient but still adiabatic $($only generates $89\%$ of the calculated work from part b$),$ what is the overall efficiency of the cycle?

d$.)$ For the reduced $89\%$ efficient turbine, what is the temperature of the steam leaving the turbine? $($hint: