$(30$ points$)$ In a water power $($Rankine$)$ cycle, saturated liquid water $(0\mathrm{.}1k\frac{g}{s})$ initially at $100$ kPa undergoes the following processes:

$12$ : adiabatic compression in a pump to $4\mathrm{.}5$ MPa $({}_{\text{p}\text{u}\text{m}\text{p}}=0\mathrm{.}8)$

$23$ : constant pressure evaporation$/$heating to $600C$

$34$ : adiabatic expansion in a turbine to the original pressure $)=(0\mathrm{.}92$

$41$ : constant pressure condensation$/$cooling to the initial state

$($a$)(20$ points$)$ Determine the quality, temperature, pressure, enthalpy, and entropy at each state in the cycle. Remember, for the pump, use the equations shown in class to estimate temperature$/$entropy changes.

$($b$)(5$ points$)$ Calculate the cycle thermal efficiency.

$($c$)(5$ points$)$ Sketch the cycle on a T$-$s diagram.