As shown in the figure, five Carnot engines, each with efficiency η and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider Q₀ to be the amount of heat absorbed per cycle by the first engine and W as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be η(net) = W/Q₀ = 211/243. The value of η is:

Question

G1 Physics · Accepted Answer

Each engine passes a fraction (1 − η) of its input heat to the next engine. After five engines, Q(out) = Q₀(1 − η)⁵. Thus η(net) = 1 − (1 − η)⁵ = 211/243. Hence (1 − η)⁵ = 32/243 = (2/3)⁵, so 1 − η = 2/3 and η = 1/3 ≈ 0.33.