$(30$ pts$.)$ Air is compressed by an adiabatic compressor from $100$ kPa and $20$C to $1\mathrm{.}8$ MPa

and $400$C$.$ Air enters the compressor through a $0\mathrm{.}15$ m $2$ opening with a velocity of $30$ m$/$s$.$

It exits through a $0\mathrm{.}08-$m$2$ opening. Use cp $=1\mathrm{.}026$ kJ$/$kg$-$K and R $=0\mathrm{.}287$ kPa$-$m$3/$kg$-$K$.$

a$.(4$ pts$.)$ Calculate the specific volume at State $1($the inlet, in m $3/$kg$)$

ANS: $0\mathrm{.}84$ m$^3/$kg

b$.(4$ pts$.)$ Calculate the mass flowrate $($kg$/$s$)$

ANS: $5\mathrm{.}3$ kg$/$s

c$.(4$ pts$.)$ Calculate the specific volume at State $2($the outlet, in m $3/$kg$)$

ANS: $1\mathrm{.}073$ m$^3/$kg

d$.(4$ pts$.)$ Calculate the velocity at State $2($m$/$s$)$

ANS: $7\mathrm{.}149$ m$/$s

e$.(4$ pts$.)$ Calculate the change in kinetic energy $($kW$)$

f$.(10$ pts$.)$ Calculate the require power input $($kW$)$