Question $3(25$ points$)$

Steam enters a turbine operating at a steady state at $2\mathrm{.}8$MPa,$380C$ with a velocity of $100\frac{m}{s}.$ The saturated vapor exits at $0\mathrm{.}18$ MPa and a velocity of $58\frac{m}{s}.$ The elevation of the inlet is $3$ m higher than at the exit. The mass flow rate of steam is $18k\frac{g}{s},$ and the power developed is $7$ MW$.$ Let $g=9\mathrm{.}81\frac{m}{s^2}.$ Determine $($a$)$ the area at the inlet, in $m^2,$ and $($b$)$ the rate of heat transfer between the turbine and its surroundings, in kW $.$ USE THE NEAREST VALUE ON THE PROPERTY TABLE.