$5.(25$ points$)$

Steam enters the turbine in a Rankine steam power cycle at a pressure of $5$ MPa and leaves as a saturated vapor at $5$ kPa $.$ Heat is transferred to the boiler at a rate of $\backslash (50,000\backslash$mathrm$\{$KW$\}\backslash ).$ Steam is condensed by cooling water at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

NOTE: When using the steam tables you may opt to not use interpolation and just pick the closest value in the table for your calculations. There will be no penalty for this.

a$)(5$ points$)$ sketch a TS diagram of the cycle and for each process indicate the direction of heat or work flow

b$)$ determine the turbine inlet temperature

c$)$ determine the net power output

d$)$ determine the thermal efficiency

e$)$ find the mass flow rate of cooling water required $($hint: find change in enthalpy of cooling water from $20$C to saturation temperature at $5$ kPa in $\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}\backslash )$ then find the enthalpy change for saturated water from vapor phase to fluid phase at $5$ kPa in $\backslash (\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$kg$\}\backslash ))$