Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature `T_1` 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 `T_(2)`. For what value of T the efficiencies of the two engines are equal?

Options

A. `(T_(1) + T_(2))/2`
B. `(T_(1)-T_(2))/2`
C. `T_(1)T_(2)`
D. `sqrt(T_(1)T_(2))`

Answer

D

Explanation

Efficiency of engine A, `eta_(1) =1 -T/T_(2)`,
Efficiency of engine B, `eta_(2)=1-T_(2)/T`
Here, `eta_(1)=eta_(2), therefore T/T_(1)= T_(2)/T rArr T = sqrt(T_(1)T_(2))`