A Carnot engine, having an efficiency of η=1/10 as a 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 a lower temperature is

Question

A Carnot engine, having an efficiency of η=1/10 as a 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 a lower temperature is (A) 99 J (B) 90 J (C) 1 J (D) 100 J

Tardigrade Admin · Accepted Answer

Relation between coefficient of performance and efficiency of refrigerator is

β = \frac{1 - η}{η}

∴ β = \frac{1 - \frac{1}{10}}{\frac{1}{10}} = 9

Coefficient of performance,

β = \frac{Heat absorbed ( Q _{2} )}{Work done ( W )}

\Rightarrow 9 = \frac{Q _{2}}{10}

Q_{2} = 90 J

Q. A Carnot engine, having an efficiency of $η = 1/10$ as a 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 a lower temperature is

$99 J$

$90 J$

$1 J$

$100 J$

Relation between coefficient of performance and efficiency of refrigerator is
$β = \frac{1 - η}{η}$
$∴ β = \frac{1 - \frac{1}{10}}{\frac{1}{10}} = 9$
Coefficient of performance, $β = \frac{Heat absorbed ( Q _{2} )}{Work done ( W )}$
$\Rightarrow 9 = \frac{Q _{2}}{10}$
$Q_{2} = 90 J$

Q. A Carnot engine, having an efficiency of η=1/10 as a heat engine, is used as a refrigerator. If the work done on the system is 10J , the amount of energy absorbed from the reservoir at a lower temperature is

99J

90J

1J

100J