$(52$ points$)$ Open vs Closed Rankine Cycle

In a Rankine cycle, steam leaves the boiler at $400C$ and $5$ MPa $.$ The condenser pressure is $0\mathrm{.}01$ MPa $.$ The water entering the pump is saturated. Assume isentropic turbine and pump.

$($a$)(6$ points$)$ Plot the cycle in the $T-$s coordinates and indicate its direction with arrows. Label each state of the cycle starting with state $1$ entering the pump, state $2$ entering the boiler, $q,$ Note that $1$MPa$=\frac{10}{b}ar.($b$)(6$ points$)$ Write down the energy balance equation for each component of the system. State all simplifying assumptions.

$($c$)(12$ points$)$ Determine the thermal efficiency of the cycle. You may use the following table to organize your work.

$\backslash$table$[[$State$,p(MPa),T(C),h(k\frac{J}{k}g),s(k\frac{J}{k}g-K)$