Superheated steam at $40$ bar absolute and $500C$ flows at a rate of $250k\frac{g}{m}in$ to an adiabatuc $($no heat transfer$)$ turbine, where it expands to $\frac{5}{b}ar($steam$).$ The turbine develops $1500kW$ of work. The turbine inlet$)$ and outlet pipes have the same diameter of $0\mathrm{.}5m.$

$($a$)$ Neglecting kinetic energy changes, determine the outlet stream temperature using the energy balance and the steam tables.

$($b$)$ Taking the outlet temperature to be $310C,$ determine the change in kinetic energy. Show and comment on whether it is reasonable to neglect kinetic energy changes for this unit or not.

$($Data needed can be found in the steam tables $($Table B$\mathrm{.}7)$ attached.$)$

$D=0\mathrm{.}5m$