The temperatures `T_(1)` and `T_(2)` of two heat reservoirs in the ideal Carnot engine are `1500^(@)C` and `500^(@)C` respectively. Which of these, increasing `T_(1)` by `100^(@)C` or decreasing `T_(2)` by `100^(@)C`, would result in a greater improvement in the efficiency of the engine?

Explanation

As the efficiency of a heat engine is given by
`eta= 1-(T_(2))/(T_(1))= (T_(1)-T_(2))/(T_(1))`
so when `T_(1)` is increased by `100^(@)C`,
`eta_(1)=((1600-500))/((1600+273)) = (1100)/(1873)=59% ……(1)`
and when `T_(2)` is decreased by `100^(@)C`,
`eta_(2)=((1500-400))/((1500+273))=(1100)/(1773)=62%........(2)`
From Eqns. (1) and (2),
it is clear that decreasing `T_(2)` results in greater improvement in the efficiency.