$(30$ points$)$ Steam at $500C$ and $3$ MPa enters an adiabatic turbine at $450k\frac{g}{s}$ and leaves at $0\mathrm{.}6$ MPa $.$ The turbine produces work at a rate of $177\mathrm{.}7$ MW $.$ Potential energy and kinetic energy can be neglectod. The temperature and pressure of the reterence atmosphere $(-$dead state$)$ are $20C$ and $1$ atm $,$ respectively. Determine $($a$)$ the exit temperature of the steam, $($b$)$ the turbine isentropic efficiency, and $($c$)$ the rate of availability destruction.