$8\mathrm{.}8$ WP A nuclear power plant based on the Rankine cycle operates with a boiling$-$water reactor to develop net cycle power of $3$ MW $.$ Steam exits the reactor core at $\frac{100}{b}ar,520C$ and expands through the turbine to the condenser pressure of $1$ bar. Saturated liquid exits the condenser and is pumped to the reactor pressure of $100$ bar $.$ Isentropic efficiencies of the turbine and pump are $81\%$ and $78\%,$ respectively. Cooling water enters the condenser at $15C$ with a mass flow rate of $114\mathrm{.}79k\frac{g}{s}.$ Determine

a$.$ the thermal efficiency.

b$.$ the temperature of the cooling water exiting the condenser. in $C.$