Question

A Carnot engine, having an efficiency of a heat engine ( $\eta=1/10$ ), 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. $100J$

Answer 1

Answer: (B)

Relation between coefficient of performance and efficiency of refrigerator is
$\beta =\frac{1 - \eta}{\eta}$
$\therefore \, \beta =\frac{1 - \frac{1}{10}}{\frac{1}{10}}=9$
Coefficient of performance, $\beta =\frac{H e a t \, a b s o r b e d \left(\right. Q_{2} \left.\right)}{W o r k \, d o n e \, \left(\right. W \left.\right)}$
$\Rightarrow \, \, 9=\frac{Q_{2}}{10}$
$or \, \, \, Q_{2}=90 \, J$