$(20$ 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 neglected. The temperature and pressure of the reference atmosphere $(=$dead state$)$ are $25C$ and $1$ atm $,$ respectively. Determine $($a$)$ the exit temperature of the steam and $($b$)$ the rate of availability destruction.