A reversible engine converts one - sixth of the heat suplied into work . When the temperature of the sink is reduced by `62^@C`, the efficiency of the engine is doubled . The temperatures of the source and sink are

Options

A. `99^(@)C , 37^(@)C`
B. `80^(@)C , 37^(@)C`
C. `95^(@)C , 37^(@)C `
D. `90^(@)C ,37^(@)C`

Answer

A

Explanation

Efficiency of the heat engine, `eta = 1 - T_(2)/T_(1)`
`eta = (T_(1)-T_(2))/T_(1)`
`2eta= (T_(1)-(T_(2)-62))/T_(1)`
From equations (1) and (2),
`implies (1)/(2) = (T_(1)-T_(2))/(T_(1)-(T_(2)-62))`
`T_(1)-(T_(2)-62) = 2T_(1)-2T_(2)`
`therefore T_(1)-T_(2)=62`
verification : option (a) satisfies the above condition.