A compressor is to be designed to provide a compression ratio of 4 . The inlet temperature is \(27^{\circ} \mathrm{C}\). The \(C_{p}\) may be assumed to be a constant, \(38.9 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\), and \(\gamma=1.3\).

Find the power needed per unit mass, the temperature at the exit, the cooling needed, and the amount cooling water needed.

The volumetric flow rate is \(360 \mathrm{~m}^{3} / \mathrm{h}\).