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Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T₁ and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T₂. For what value of T the efficiencies of the two engines are equal?

1. T₁ + T₂ / 2
2. T₁ - T₂ / 2
3. T₁T₂
4. √T₁T₂

Correct answer: √T₁T₂

Solution

The efficiency of a Carnot engine is given by η = 1 - (T_sink / T_source). For the efficiencies of both engines to be equal, we equate their expressions and solve for T. This results in T = √(T₁T₂).

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