A heat engine that operates on a Carnot cycle is used to pump crude oil at a rate of 25,000 barrels/day from a well that is \(1.70 \mathrm{~km}\) deep. The mass density of the oil is \(850 \mathrm{~kg} / \mathrm{m}^{3}\), the oil is under minimal pressure and so has no initial speed, and it has negligible speed as it reaches the surface. The engine operates between \(50^{\circ} \mathrm{F}\) and \(250^{\circ} \mathrm{F}\), and each barrel has a volume of \(0.159 \mathrm{~m}^{3}\). At what rate must thermal energy be supplied to this heat engine?