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

`eta_(A)=(T_(1)-T_(2))/(T_(1))=(W_(A))/(Q_(1)),eta_(B)=(T_(2)-T_(3))/(T_(3))=(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) `