$.$ Water vapor enters a turbine at a pressure of $10$ bar and a temperature of $440$C with a speed of $80$ m$/$s$,$ the steam expands iso$-$entropically through the turbine until a saturation pressure of $0\mathrm{.}7$ bar, and a speed of $50$ m$/$s$.$ The mass flow of the steam is $50$ m$/$s$.$ Determine:

a$)$ The variation of kinetic energy in

$[$Kj$/$Kg$]$

b$)$ The variation of enthalpy in$.$

$[$Kj$/$Kg$]$

c$)$ The work carried out by the turbine. in

$[$Kj$/$Kg$]$

d$)$ The power developed by the turbine in

$[$Kj$/$Kg$]$

e$)$ The turbine outlet area in

$[$m$]$