Question

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, T₁ and T₂. The temperature of the hot reservoir of the first engine is T₁ and the temperature of the cold reservoir of the second engine is T₂. T is temperature of the sink of first engine which is also the source for the second engine. How is T related to T₁ and T₂, if both the engines perform equal amount of work ?

Answer 1

Answer is (3) T = (T₁ + T₂)/2

Answer 2

Answer is (3) T = (T₁ + T₂)/2

Q_H : Heat input to 1^st engine

Q_L : Heat rejected from 1^st engine

Q_L' : Heat rejected from 2^nd engine

Work done by 1^st engine = work done by 2^nd engine

Q_H – Q_L = Q_L – Q_L'

2Q_L = Q_H + Q_L'