A Carnot's engine operates with an efficiency of 40% with its sink at 27oC. By what amount should the temperature of the source be increased with an aim to increase the efficiency by 10%?

Let T be the initial temperature of the source, then, using η=1−T2T1, We have, 40100=1−(273+27K)T1 or  T1=500KFor the efficiency to be 10% more, i.e., 50% , let T1' be the new temperature of the sink ? then 50100=1−(273+27K)T1′ or  T1′=600KThe required increase in the temperature of the source T1′−T=600K−500K=100K