A rocket engine combusts fuel at a temperature of 3,000°C. It is cooled by liquid hydrogen at a temperature of -250°C. The rocket lifts a payload of 5000 kg to an altitude of 100 km. How much heat energy is transferred to the engine by burning fuel if the engine is 50% as efficient as a Carnot engine? Assume that the specific heat capacity of the rocket exhaust gases is 1.0 kJ/(kg•K) and that the gravitational acceleration is 9.8 m/s².