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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?

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$\sqrt{T_{1} T_{2}}$

$\frac{T_{1} + T_{2}}{2}$

$\frac{T_{1} - T_{2}}{2}$

$T_{1} T_{2}$

answer is D.

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Detailed Solution

$η_{1} = 1 - \frac{T}{T_{1}} & η_{2} = 1 - \frac{T_{2}}{T} \Rightarrow 1 - \frac{T}{T_{1}} = 1 - \frac{T_{2}}{T} \Rightarrow T = \sqrt{T_{1} T_{2}}$

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