A Carnot engine operating between temperature `T_1 and T_2` has efficiency 1/6. When `T_2` is lowered by 62K its efficiency increase to 1/3. Then `T_1 and T_2` are, respectively:

Options

A. `372K` and `310K`
B. `372` and `300K`
C. `330K` and `268K`
D. `310K` and `248K`

Answer

A

Explanation

`eta = 1 - (T_(2))/(T_(1)) = (1)/(6) rArr (T_(2))/(T_(1)) = 1 - (1)/(6) = (5)/(6)`
`(1)/(3) =1 - ((T_(2)-62))/(T_(1)) rArr (T_(2)-62)/(T_(1)) = (2)/(3)`
`(5(T_(2)-62))/(6T_(2)) = (2)/(3)`
`5T_(2) - 310 = 4T_(2)`
`T_(2) = 310` and `T = (6 xx 310)/(5)`
`T_(1) = 372 K`