A Carnot engine having an efficiency of 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 [2017, 2015]

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Solution

Q.
A Carnot engine having an efficiency of 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 [2017, 2015]

1 90 J

2 99 J

3 100 J

4 1 J

Ans.
(1)

The relation between coefficient of performance and efficiency of Carnot engine is given as

$β = \frac{1 - η}{η} .$ Given $η = \frac{1}{10},$ $W = 10$ $J$

$β = \frac{1 - \frac{1}{10}}{\frac{1}{10}} = \frac{9}{10} . 10 = 9$

Since, $β = \frac{Q_{2}}{W}, where Q_{2} is the amount of energy absorbed from the reservoir$

$∴$ $Q_{2} = β W = 9 \times 10 = 90$ $J$

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