A reversible engine converts one-sixth of the heat input 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

`eta _(1) =1-(T_(L))/(T_(H))=(W)/(Q_(1))=(1)/(6)`
or `5T_(H)-6T_(L) = 0`
` eta _(2) =1-(T_(L)-62 )/T_(H)=2eta _(1) =(1)/(3)`
or `2T_(H) -3T_(L)=- 186`
`therefore T_(H) = 372 K=99^(@)C`
`T_(L)=(5)/(6)T_(H)=(5)/(6)xx372 K=310 K =37^(@)C`