Question

Considering an ideal refrigerator, heat from its inside at a temperature of $277\text{K}$ is transferred to a room at temperature of $300\text{K}$. Find the amount of heat extracted for each Joule of electrical energy consumed by refrigerator.

• A. $1\text{J}$
• B. $1.3\text{J}$
• C. $12\text{J}$
• D. $15\text{J}$

Answer 1

The correct option is C $12\text{J}$

From the definition of coefficient of performance for a Carnot refrigerator (ideal refrigerator),
$\beta =\frac{Q_2}{W}=\frac{T_2}{T_1-T_2}$
$\Rightarrow Q_2=W\left(\frac{T_2}{T_1-T_2}\right)...\left(i\right)$
$T_2=277\text{K},T_1=300\text{K}$
$W=\text{Electrical work consumed by refrigerator}$
$W=1\text{J}$
From Eq.$\left(i\right)$ we get,
$Q_2=1\times \frac{277}{300-277}=12\text{J}$
Hence amount of heat extracted by the refrigerator will be $12\text{J}$