To increase the efficiency of a carnot engine, will you prefer to (i) increase the temp. of source by`10K` or (ii) decrease the temp. of sink by `10K`?

Explanation

We know, `eta= 1 - (T_(2))/(T_(1))`
When temp. of source is increased by `10K`,
`eta_(1)= (1-(T_(2))/(T_(1)+10))`
When temp. of sink is decreased by `10K`, then
`eta_(2)= (1-(T_(2)-10)/(T_(1)))`
we find that `(n_(2)-n_(1))`
`=(1- (T_(2))/(T_(1)+10))-(1-(T_(2)-10)/(T_(1)))= (T_(2)-10)/(T_(1))-(T_(2))/(T_(1)+10)`
`(eta_(2)-eta_(1)) gt 0 or eta_(2)gt eta_(1)`
Hence efficiency of carnot engine can be increased by a greater amount by increasing the temp. of source by `10 K`.