Question

# Problem 21.28 A Carnot engine whose hot-reservoir temperature is 420 ∘C has a thermal efficiency of...

Problem 21.28

A Carnot engine whose hot-reservoir temperature is 420 ∘C has a thermal efficiency of 40 % .

Part A

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.

ΔTcold =

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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