Two carnot engine A and B are operated in series.The first one A receives hat at 800K and rejects to a reservoir at TK. The second engine B receives the heat rejected by the first engine and in turn rejects to a heat reservoir at 300K.Calculate the value of T ,when outputs of the two engines are equal.

Let the output of both engines be W

Let the 1^st engine take Q₁ heat as input at temperature T₁ = 800K and gives out heat Q₂ at temperature T the second engine receive Q₂ as input and give out Q₃ at temperature T₃ = 300k to the sink.

Work done by first engine W =  Q₁ – Q₂

Work done by 2nd engine W = Q₂ – Q₃

Thus,

 Q₁ – Q₂ = Q₂ – Q₃

Dividing both sides by Q₁

1 – Q₂/Q₁  = Q₂/Q₁ – Q₃/Q₁

=> 1-T/T₁ = Q₂/ Q₁(1- Q₃/ Q₂)

=> 1-T/T₁ = Q₂/ Q₁(1- T₃/ T)

=>  1-T/T₁ = T/T₁ (1- T₃/ T)

=> T₁/T – 1 = 1 - T₃/ T

=> T₁/T + T₃/ T = 2

=> 1/T (T₁ + T₃) = 2

=>T = (T₁ + T₃)/2

=> T = (800+300)/2 = 550 K