An electrical generating plant operates at a boiler temperature of 220$\degree$C and exhausts the unused heat into a nearby river at 19$\degree$C. If the generating plant has a power output of 800 megawatts (MW) and if the actual efficiency is 3/5 the theoretical efficiency, how much heat per second must be delivered to the boiler? (0$\degree$C = 273 K)

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Quizplus · Accepted Answer

The theoretical efficiency (Carnot efficiency) is calculated using the temperatures in Kelvin: η = 1 - (T_cold/T_hot). Convert the temperatures: T_hot = 220 + 273 = 493 K, T_cold = 19 + 273 = 292 K. η = 1 - (292/493) = 0.407. The actual efficiency is 3/5 of this: 0.407 * 3/5 = 0.2442. The power output is 800 MW, so the heat input Q_in = Power output / Efficiency = 800 MW / 0.2442 ≈ 3270 MW.

An Electrical Generating Plant Operates at a Boiler Temperature of 220