A carnot engine whose heat sink is at `27^(@)C` has an efficiency of `40%`. By how many degrees should the temperature of source be changed to increase the efficiency by `10%` of the original efficiency?

Explanation

Here `T_(2)=273+27=300K`
We know that `eta=1-(T_(2))/(T_(1))`
or `0.40=1-300/(T_(1))`
or `T_(1)=500K`
increase in efficiency of engine `=10%` or `40=4%`
Thus new efficiency of the engine becomes `=40+4=44%`
Let `T_(1)^(.)` is the new temperature of the source then
`0.44=1-(T_(2))/(T_(1))`
or `0.44=1-300/(T_(1)^(.))`
or `T_(1)(.)=535.7K`
Increase in temperature of the source
`=T_(1)^(.)-T_(1)=535.7-500`
`=35.7K`