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.

Two Carnot engines A and B are operated in series. The engine A receiv

1.	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.
Answer» `(T_(1) - T_(2))/(2)` `T_(1)T_(2)` `SQRT(T_(1)T_(2))` `(T_(1) + T_(2))/(2)` Solution :Efficiency of a carnot engine, `ETA = 1 - (T_(2))/(T_(1))` where `T_(1)` is the TEMPERATURE of source and `T_(2)` is the temperature of sink respectively. For engine A, `eta_(A) = 1 - (T)/(T_(1))` For engine B, `eta_(B) = 1 - (T_(2))/(T)` As per question, `eta_(A) = eta_(B)` As per question, `eta_(A) = eta_(B)` `:. 1 - (T)/(T_(1)) = 1 - (T_(2))/(T)` or `(T)/(T_(1)) = (T_(2))/(T)` or `T^(2) = T_(1)T_(2)` or `T = sqrt(T_(1)T_(2))`