Consider an ideal gas refrigeration cycle using air as the working fluid which is used to maintain a cold space at \(-15^{\circ} \mathrm{C}\) while discarding the heat to the environment at \(30^{\circ} \mathrm{C}\). The pressure ratio of the compressor is 4 . Take \(C_{P}=1.007 \mathrm{~kJ} / \mathrm{kg}\) and \(\gamma=1.4\). Determine

(a) The coefficient of performance

(b) The cooling rate for a mass flow rate of \(0.06 \mathrm{~kg} / \mathrm{s}\).