The temperatures T_(1)and T_(2)of two heat reservoirs in the ideal Carnot engine are 1500^(@)C and500^(@)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?

The temperatures T_(1)and T_(2)of two heat reservoirs in the ideal Car

1.	The temperatures T_(1)and T_(2)of two heat reservoirs in the ideal Carnot engine are 1500^(@)C and500^(@)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?
Answer» Solution :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.