A Carnot engine operating between temperatures `T_(1)` and `T_(2)` has efficiency `(1)/(6)`. When `T_(2)` is lowered by `62K`, its efficiency increases to `(1)/(3)`. Then `T_(1)` and `T_(2)` are, respectively:

Options

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

Answer

C

Explanation

`1-(T_(2))/(T_(1)) = (1)/(6) implies (T_(2))/(T_(1)) = (5)/(6)` `" "` …..`(1)` and `1-(T_(2)-62)/(T_(1)) = (1)/(3) implies (T_(2) - 62)/(T_(1)) = (2)/(3)` `" "` ….`(2)`
By solving equation (1) and (2) `T_(1) = 372K "and" T_(2) = 310K`