Problem #$1$: $(50$ pts$.)$

Sixteen $(16\frac{m^3}{m}in)$ of superheated steam enter a well$-$insulated turbine operating at steady state at $8\mathrm{.}0$ MPa and a Temperature of $500C($Celsius$).$ The steam expands to the turbine exit where the pressure is $100$ KPa $.$ If the Turbine has an adiabatic efficiency of $85\%,$ Determine:

a$)$ The ideal power developed by the turbine and the corresponding exit temperature.

b$)$ The real power developed by the turbine and the corresponding exit temperature.

c$)$ The entropy change, for the process when it is irreversible.

d$)$ Sketch the processes in a P$-$v and $T-s$ diagram.