Question

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

• A. $99J$
• B. $90J$
• C. $1J$
• D. $100J$

Answer 1

The correct option is B

$90J$

Step 1. Given data

Efficiency of Carnot engine, $\eta =\frac{1}{10}$

Work done, $W=10J$

Step 2. Finding the amount of heat added to the system, $Q_H$

By using the formula of Efficiency,

$\eta =\frac{W}{Q_H}$

$\frac{1}{10}=\frac{10}{Q_H}$

$Q_H=100J$

Step 3. Finding the amount of heat absorbed, $Q_C$

By using the formula, $Q_C=Q_H-W$

$Q_C=100-10$

$Q_C=90J$

Therefore, the heat added to the system is $90J$

Hence, the correct option is $\left(B\right)$