$6.[10$ Pts$]$ A steam plant has a pump and a boiler that turns saturated liquid water at $\backslash (25\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ into superheated steam at $\backslash (500\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $5$ MPa $.$ The pump consumes $\backslash (5\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )(5$ kJ consumed for every kg of water flowing$).$ Initially the pump adiabatically increases the pressure, and the boiler isobarically turns the compressed liquid into superheated steam. The steam from the boiler enters an adiabatic turbine and leaves as saturated steam at $120\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ Ignore kinetic and potential energy for this question.

$($a$)$ What is the efficiency of the turbine? $[4$ Pts$]$

$($b$)$ Draw this in T$-$s diagram and indicate the area corresponds to lost work in the turbine $[4$ Pts$]$

$($c$)$ Can you reverse the turbine in this process with an adiabatic compressor? $($i$.$e$.$ use an adiabatic compressor to go from saturated steam at $\backslash (120\mathrm{.}23^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to superheated steam at $\backslash (500\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $5$ MPa $[2$ Pts$$