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Air enters a compressor operating at steady state at $1\mathrm{.}05$ bar, $300$ K $,$ with a volumetric flow rate of $12\frac{m}{m}in$ and exits at $12$ bar, $400$

K$.$ Heat transfer occurs at a rate of $2$ kW from the compressor to its surroundings.

Assuming the ideal gas model for air and neglecting kinetic and potential energy effects, determine the power input, in kW$.$

$W_{cv}^{}=$

kW