First slide

Heat engine

Question

A Carnot engine operates between 327 $^{0} C$ and 27 $^{0} C$ . How much heat (in joules) does it take from the 327 $^{0} C$ reservoir for every 100 J of work done?

Moderate

A

100 J
B

200 J
C

300 J
D

400 J

Solution

W = $Q_{1} - Q_{2}$
As $η = \frac{Q_{1} - Q_{2}}{Q_{1}} = \frac{T_{1} - T_{2}}{T_{1}}$
$∴ Q_{1} = (\frac{T_{1}}{T_{1} - T_{2}}) W = \frac{600}{600 - 300} \times 100$
= 200 J

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