Air flows through a pipe of diameter $0\mathrm{.}15m$ at a rate of $0\mathrm{.}3\frac{m^3}{s}$ at $100$kPa and

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$02000$CHT$202052101$

$300K$ before entering a compressor. A cooler removes heat from the compressed gas at a rate of $75\mathrm{.}0k\frac{J}{s}.$ The stream leaves the compressor at $315K$ and $550$kPa through a pipe of diameter $0\mathrm{.}03m.$ Calculate the power input to the compressor. Assume air to be an ideal gas with molar heat capacity $C_P=30k\frac{J}{k}$molK.