First slide

Heat engine

Question

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

Moderate

A

275 K
B

325 K
C

250 K
D

380 K

Solution

$η = 1 - \frac{T_{2}}{T_{1}} \Rightarrow 1 - \frac{300}{T_{1}} = 0.4 \Rightarrow T_{1} = 500 K Now η' = 0.4 + 0.4 \times \frac{50}{100} = 0.6 Therefore 0.6 = 1 - \frac{300}{500 + ∆ T} \Rightarrow ∆ T = 250 K$

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