A Carnot's engine operates with an efficiency of40% with its sink at 270C. By what amount should the temperature of the source be increased with an aim to increase the efficiency by 10%?

Let T1 be the initial temperature of the source, then, using η = 1-T2T1We have, 40100= 1-(273+27 K)T1or T1 = 500 K For the efficiency to be 10% more i.e., 50%, let T1' be the new temperature of the sink,then, 50100 = 1-(273+27 K)T'1or T'1 = 600 KThe required increase in the temperature of the source  T'1-T = 600 K -500 K = 100 K