1.

An engine has an efficiency of `1/6`. When the temperature of sink is reduced by `62^(@)C`, its efficiency is doubled. Temperature of the source isA. `127^(@)C`B. `37^(@)C`C. `62^(@)C`D. `99^(@)C`

Answer» Correct Answer - D
Effeciency of engine is given by , `eta = 1-(T_2)/(T_1)`
`:. (T_2)/(T_1) = 1-eta=1-1/6=5/6` ..(i)
In other case
`(T_(2)-62)/(T_1) = 1-eta=1-2/6=2/3` ..(ii)
Using eq(i)
`T_(2)-62=2/3T_(1)=2/3xx6/5 T_(2) or 1/5 T_(2)=62`
`T_(2) = 310K = 310-273^@C=37^@C`
Hence, `T_(1) = 6/5 T_(2)=6/5xx310=372K`
Temperature at `.^(@)C=372-273=99^(@)C`
Hence, temperature of sourve is `99^(@)C`.


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