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 temperature of the source and sink are

A reversible engine converts one-sixth of the heat input into work. Wh

1.	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 temperature of the source and sink are
Answer» `99^(@)C, 27^(@)C` `80^(@)C, 37^(@)C` `95^(@)C, 37^(@)C` `90^(@)C, 37^(@)C` Solution :`eta_(1) = 1 - (T_(2))/(T_(1)) = (W)/(Q_(1)) = (1)/(6)` R `5T_(1) - 6T_(2) = 0` ….(i) `eta_(2) = 1 - ((T_(2) - 62))/(T_(1)) = 2eta_(1) = (1)/(3)` or `2T_(1) - 3T_(2) = -186` …(II) Solving (i) and (ii), we get `T_(1) = 372 K = 99^(@)C` `T_(2) = (5)/(6)T_(1) = (5)/(6) xx 372 K = 310 K = 37^(@)C`