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

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{He a t ab sor b e d ( Q _{2} )}{W or k d o n e ( W )}

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

or Q_{2} = 90 J

Q. A Carnot engine, having an efficiency of a heat engine ( $η = 1/10$ ), 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

$99 J$

$90 J$

$1 J$

$100 J$

Q. A Carnot engine, having an efficiency of a heat engine ( η=1/10 ), 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

Relation between coefficient of performance and efficiency of refrigerator is β=η1−η​ ∴β=101​1−101​​=9 Coefficient of performance, β=Workdone(W)Heatabsorbed(Q2​)​ ⇒9=10Q2​​ orQ2​=90J

Q. A Carnot engine, having an efficiency of a heat engine ( $η = 1/10$ ), 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

$99 J$

$90 J$

$1 J$

$100 J$