A heat engine that operates on a Carnot cycle is used to pump water out of a well that is \(45.0 \mathrm{~m}\) deep. The hightemperature reservoir for the heat engine is at \(215^{\circ} \mathrm{C}\), and the low-temperature reservoir is at \(-10^{\circ} \mathrm{C}\). The engine must move water from the bottom of the well to the surface at a rate of \(6600 \mathrm{~L} / \mathrm{min}\), and the speed of the water when it reaches the surface is negligible. At what rate must thermal energy be supplied to the engine?