If the temperature of the sink of a Carnot engine having an efficiency `(1)/( 6)` is reduced by `62^(@)C`, then its efficiency is doubled. Find the temperature of the sink and source respectively.

Options

A. `124^(@), 62^(@)` C
B. `99^(@), 37^(@)` C
C. `37^(@), 99^(@)` C
D. `62^(@), 124^(@)` C

Answer

C

Explanation

`T_( c)` = Temperature of sink.
`T_H` = Temperature of source.
`1/6 = 1-T_( c)/T_(H)`
`T_( C)/T_(H) = 1- (T_( C) - 62)/T_(H) = 1- T_( c)/T_(H) + (62)/T_(H)`
`62/T_(H) = 1/6 T_(H) = 372 K`
`1/6 = 1- T_( C)/372`
`T_( C)/372 = 5/6`
`T_( c) = (5 xx 372)/6 = 310 K`