A heat engine does 30 j of work per cycle while exhausting 50 j of waste heat. what is the engine's thermal efficiency?

The maximum possible efficiency, i. e the efficiency of a Carnot engine, is give by the ratio of the absolute temperatures of hot and cold reservoir.

η_max = 1 - (T_c/T_h)

For this engine:

η_max = 1 - [ (20 + 273) K / (600 + 273) K ] = 0.66 = 66%

The actual efficiency of the engine is 30%, i. e.

η = 0.3 ∙ 0.664 = 0.20 = 20 %

On the other hand thermal efficiency is defined as the ratio of work done to the amount of heat absorbed from hot reservoir:

η = W/Q_h

So the heat required from hot reservoir is:

Q_h = W/η = 1000J / 0.20 = 5000J