Two Carnot engines are operated in succession. The first engine receives heat from a source at `T=800K` and rejects to sink at `T_(2)K`. The second engine receives heat rejected by the first engine and rejects to another sink at `T_(3)= 300K`. If work outputs of the two engines are equal, then find the value of `T_(2)`.

Options

A. `100 K`
B. `300 K`
C. `550 K`
D. `700 K`

Answer

C

Explanation

`eta_(A)=(T_1-T_2)/(T_1)=(W_A)/(Q_1) implies eta_(B)=(T_2-T_3)/(T_1)=(W_B)/(Q_2)`
`(Q_1)/(Q_2) = (T_1)/(T_2) xx (T_(2)-T_(3))/(T_(1)-T_(2)) = (T_1)/(T_2) :. W_A = W_B`
`:. T_(2) = (T_(1)+T_(3))/(2) = (800+300)/(2) = 550K`