A heat pump that operates on a Carnot cycle cools a house in a very hot climate. During the hottest part of the day, the outside temperature is \(45^{\circ} \mathrm{C}\), and you want to keep the inside temperature at \(20^{\circ} \mathrm{C}\). The heat pump operates on electricity.

(a) What is the coefficient of performance of cooling during the hottest part of the day?

(b) At what maximum rate does the pump use electrical energy if it removes thermal energy from the house at a rate of \(1.50 \mathrm{~kW}\) ?