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

Answer

C

Explanation

Since, `eta=1-(T_2)/(T_1)`
`eta_A=(T_1-T_2)/(T_1)=(W_A)/(Q_1)` and `eta_B=(T_2-T_3)/(T_2)=(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)` [as `W_A= W_B`]
`:. T_2=(T_1+T_3)/(2)=(800+300)/(2) = 550 K`.