What is the heat supplied to a Carnot engine that produces 100 kW of useful work at an efficiency of 35%?
285.7 kW
A Carnot engine is the ideal, fully reversible heat engine operating between two fixed-temperature reservoirs. It sets the maximum possible efficiency any engine can reach between those temperatures. Its thermal efficiency is defined as the fraction of the heat drawn from the hot reservoir that is converted into useful work:
- η = W / QH, where W is the net work output and QH is the heat supplied from the hot reservoir.
We are given the work output W = 100 kW and the efficiency η = 35% = 0.35. Rearranging the definition to solve for the heat supplied:
- QH = W / η
- QH = 100 / 0.35 = 285.7 kW
So the engine must be supplied with about 285.7 kW of heat to deliver 100 kW of work; the remaining QH − W = 285.7 − 100 = 185.7 kW is rejected to the cold reservoir, consistent with the energy balance.
The other figures come from misapplying the relation. Multiplying instead of dividing (100 × 3 ≈ 300 kW) or taking simple fractions such as 200 kW or 150 kW does not satisfy η = W/QH; only 285.7 kW gives 100/285.7 ≈ 0.35. Hence the heat supplied is 285.7 kW.
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