A solar electric engine operating between \(5^{\circ} \mathrm{C}\) and \(95^{\circ} \mathrm{C}\) has an efficiency equal to one-half the Carnot efficiency. This engine is to drive a \(4 \mathrm{~kW}\) pump. If the collector has an efficiency of \(50 \%\), calculate the area needed for operation in Egypt, where the insolation averages about \(2800 \mathrm{~kJ} / \mathrm{m}^{2} \mathrm{~h}\) during the day. State any additional assumptions.