A Carnot engine whose hot-reservoir temperature is 420 ∘C has a thermal efficiency of 40 % .
By how many degrees should the temperature of the cold reservoir be decreased to raise the engine's efficiency to 61 % ?
Express your answer to two significant figures and include the appropriate units.
Hot reservoir temperature = Th = 420 oC = 693 K
Initial cold reservoir temperature = Tc1
Initial thermal efficiency = 1 = 40% = 0.4
Tc1 = 415.8 K
Tc1 = 142.8 oC
New cold reservoir temperature = Tc1
New thermal efficiency = 2 = 61% = 0.61
Tc2 = 270.27 K
Tc2 = -2.73 oC
Decrease in the cold reservoir temperature = Tc
Tc = Tc1 - Tc2
Tc = 142.8 - (-2.73)
Tc = 145.53 oC
Rounding off to two significant figures,
Tc = 1.5 x 102oC
Decrease in temperature of the cold reservoir to increase efficiency to 61% = 1.5 x 102oC
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