A Carnot engine whose sink is at 300K has an efficiency of 40%. By how much should the temperature source be increased so as to increase its efficiency by 50% of original efficiency?

A Carnot engine whose sink is at 300K has an efficiency of 40%. By how much should the temperature source be increased so as to increase its efficiency by 50% of original efficiency?

Explanation

Initial efficiency (η) = 40% = 0.4

Sink temperature (Tc) = 300 K

Initial source temperature (Th) = 300 / (1 - 0.4) = 500 K

New efficiency (η_new) = 0.4 + 0.5(0.4) = 0.6

New source temperature (Th_new) = 300 / (1 - 0.6) = 750 K

Increase in temperature = Th_new - Th = 750 - 500 = 250 K