For a heat pump that operates on a Carnot cycle, calculate (a) the coefficient of performance of cooling when the pump is used to cool a house to \(72{ }^{\circ} \mathrm{F}\) on a day when the outside air is at \(105^{\circ} \mathrm{F}\) and \((b)\) the coefficient of performance of heating when the pump is used to heat a house to \(72^{\circ} \mathrm{F}\) on a day when the outside air is at \(-15^{\circ} \mathrm{F}\).