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?
Answer: 250K
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
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