$4.(\backslash (\backslash$mathbf$\{25\}\backslash )$ points$)$ Consider a water power cycle in which saturated liquid water, initially at $100$ kPa $,$ undergoes the following processes:

$\backslash (1\backslash$rightarrow $2\backslash )$ : adiabatic and reversible compression in a pump to $5$ MPa

$\backslash (2\backslash$rightarrow $3\backslash )$ : constant pressure evaporation$/$heating to $\backslash (700^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$

$\backslash (3\backslash$rightarrow $4\backslash )$ : adiabatic and reversible expansion in a turbine to the original pressure

$\backslash (4\backslash$rightarrow $1\backslash )$ : constant pressure condensation$/$cooling to the initial state

$($a$)(10$ points, $0\mathrm{.}5$ points each$)$ Determine the temperature, pressure, specific enthalpy, specific entropy and quality at each state in the cycle.. You may assume that enthalpy in the pump only varies with pressure, and that liquid water is incompressible. Fill the values out in the table below, or make a table similar to it$.$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline State & $\backslash (\backslash$mathrm$\{$T$\}\backslash$left$(\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash$right$)\backslash )$ & $\backslash (\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$kPa$\})\backslash )$ & $\backslash (\backslash$mathrm$\{$h$\}(\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\})\backslash )$ & $\backslash (\backslash$mathrm$\{$s$\}(\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}*\backslash$mathrm$\{$~K$\})\backslash )$ & x $\backslash \backslash$

$\backslash$hline $1$ & & & & & $\backslash \backslash$

$\backslash$hline $2$ & & & & & $\backslash \backslash$

$\backslash$hline $3$ & & & & & $\backslash \backslash$

$\backslash$hline $4$ & & & & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

$($b$)(5$ points$)$ If water exits the turbine as a mixture, determine the exit quality. Will this value be acceptable when considering wear on the turbine blades? Explain.

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

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