The temperatures T_1 and T_2of 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 ?

The temperatures T_1 and T_2of two heat reservoirs in the ideal Carnot

1.	The temperatures T_1 and T_2of 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 ?
Answer» SOLUTION :As the EFFICIENCY of a heat engine is given by ` eta=11- (T_L )/( T_H)= (T_H - T_L)/( T_H)` so when `T_n`is INCREASED by `100^@ C,eta _1= ((1600 - 500))/(( 1600 +273)) = (1100 )/( 1873 ) = 59 % ` and when `T_L` is DECREASED by `100^@ C,eta_2 = ((1500- 400 ))/( 1500+ 273 ) = (1100)/( 1773 )= 62 % ` From Egns. (1) and (2), it is CLEAR that decreasing `T_L` results in greater improvement in the efficiency.