Question $3(25$ points$)$

Steam enters a turbine operating at a steady state at $2\mathrm{.}3$MPa,$330C$ with a velocity of $100\frac{m}{s}.$ The saturated vapor exits at $0\mathrm{.}13$ MPa and a velocity of $53\frac{m}{s}.$ The elevation of the inlet is $3$ m higher than at the exit. The mass flow rate of steam is $13k\frac{g}{s},$ 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 property tables should you need any property for your calculations.

Steam

$m^{}=13k\frac{g}{?}$

$T_1=330C$

$P_1=2\mathrm{.}3MP$

$V_1=130\frac{m}{?}$

ENGINEERING MODEL: $(1)$ The control volume shown on the sketch is at steady state. $(2)g=9\mathrm{.}81\frac{m}{s^2}$