A Carnot engine whose efficiency is 40%, receives heat at 500 K. If the efficiency is to be 50%, the source temperature for the same exhaust temperature is

A Carnot engine whose efficiency is 40%, receives heat at 500 K. If th

1.	A Carnot engine whose efficiency is 40%, receives heat at 500 K. If the efficiency is to be 50%, the source temperature for the same exhaust temperature is
Answer» 900 K 600 K 700 K 800 K Solution :Efficiency of CARNOT engine, `ETA = 1 - (T_(2))/(T_(1))` where `T_(1)` and `T_(2)` are the temperature of SOURCE and sink RESPECTIVELY. `:. (T_(2))/(T_(1)) = 1 - eta = 1 - (40)/(100) = (60)/(100) = (3)/(5) (because eta = 40%)` or `T_(2) = (3)/(2)T_(1) = (3)/(5) xx 500 K = 300 K` ...(i) LET `T._(1)` be the temperature of the source for the same sink temperature. `:. (T_(2))/(T._(1)) = 1 - eta. = 1 - (50)/(100) = (1)/(2) "" (because eta. = 50%)` or `T._(1) = 2T_(2) = 2 xx 300 K = 600 K` (Using (i))