Two heat engines X and Y of same efficiency are connected in series in such a way that the sink of X works as source of Y. X receives heat at 900 K and rejects some heat to its sink at TK and in turn Y rejects heat to its sink at 400 K, then the temperature T is

Options

A. 550 K
B. 600 K
C. 650 K
D. 700 K

Answer

B

Explanation

According to the question, a series combination of two heat engines are shown in the figure below,

Given, temperature of X heat engine, `T_(1) = 900 K` and temperature of Y heat engine, `T_(2) = 400 K`
So, efficiency of x heat engine,
`eta_(x) = 1 - (T)/(T_(1)) = 1 - (T)/(900)`
Similarly `eta_(y) = 1 - (T_(2))/(T) = 1 - (400)/(T)`
`because` Given, `eta_(x) = eta_(y)`
`1 - (T)/(900) = 1 - (400)/(T)`
`T^(2) = 900 xx 400`
`T = 600 K`
Hence, the correct option is (b).