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

The temperatures T_(1) and T(2) of two heat reservoirs in an ideal car

1.	The temperatures T_(1) and T(2) of two heat reservoirs in an ideal carnot engine are 1500^(@)C and 500^(@)C. Which of these (a) increasing T_(1) by 100^(@)C or (b) decreasing T_(2) by 100^(@)C would result in greater improvement of the efficiency of the engine?
Answer» SOLUTION :`eta=1-T_2/T_1 ` (i) `T_1` is INCREASED from `1500^@C" to " 1600^@C` `T_1 =1873k` `T_2` REMAIN constant `T_2 = 773k` `eta_1=(1873-773)/(1873)=58.73%` (ii) `T_1` remain constant `=1500^@C` `T_1 = 1500+273=1773k` `T_2` is decreased by 100 i.e., `400^@C` `T_2=400+273=673k` `eta_2=(1773-673)/1773=(1100)/1773=62.04%` `eta_2 gt eta_1`