Answer
$10.8$ kW
Work Step by Step
The exit stagnation temperature of air $T_{02}$ is determined from $$
T_{02}=T_{01}\left(\frac{P_{02}}{P_{01}}\right)^{(k-1) / k}=(308.2 \mathrm{~K})\left(\frac{900}{100}\right)^{(1.4-1) / 1.4}=577.4 \mathrm{~K}
$$ From the energy balance on the compressor,
$$
\dot{W}_{\text {in }}=\dot{m}\left(h_{20}-h_{01}\right)
$$ or, $$
\dot{W}_{\text {in }}=\dot{m} c_p\left(T_{02}-T_{01}\right)=(0.04 \mathrm{~kg} / \mathrm{s})(1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K})(577.4-308.2) \mathrm{K}=\mathbf{1 0 . 8 k W}
$$
