Problem #$2(50$ point$)$:

Air enters a compressor operating at steady state at a pressure of $1$ bar, a temperature of $17C,$ and a velocity of $12\frac{m}{s}$ through an inlet with an area of $0\mathrm{.}15m^2.$ At the exit, the pressure is $9$ bar, the temperature is $207C,$ and the velocity is $2\frac{m}{s}.$ Heat transfer from the compressor to the surroundings occurs at a rate of $360k\frac{J}{m}in.$ Employing the ideal gas model, calculate:

a$)$ the mass flow rate of air,

b$)$ the power input to the compressor, in kW $.$

Given: For Air, $,R=0\mathrm{.}287k\frac{J}{k}g.K,$

at $17C,h_1=290\mathrm{.}16k\frac{J}{k}g,$ and at $207C,h_2=482\mathrm{.}49k\frac{J}{k}g$

Draw sketch and show all calculations.