First slide

Heat engine

Question

A carnot engine having an efficiency of $\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

Moderate

A

90 J
B

99 J
C

100 J
D

1 J

Solution

The relation between coefficient of performance and efficiency of carnot engine is given as
$β = \frac{1 - η}{η}$
$Given η = \frac{1}{10}, W = 10 J$
$β = \frac{1 - \frac{1}{10}}{\frac{1}{10}} = \frac{9}{10} \cdot 10 = 9$
$Since, β = \frac{Q_{2}}{W}, where Q_{2} is the amount of energy$ absorb from the reservor
$∴ Q_{2} = β W = 9 \times 10 = 90 J$

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