Question

A refrigerator whose coefficient of performance is $5$, extracts heat from the cooling compartment at the rate of $250\text{J/cycle}$. Find the amount of heat discharged per cycle to the room.

• A. $50\text{J}$
• B. $250\text{J}$
• C. $300\text{J}$
• D. $200\text{J}$

Answer 1

The correct option is C $300\text{J}$

Coefficient of performance of refrigerator is, $\beta =5;Q_2=250\text{J/cycle}$
where $Q_2$ is the heat removed per cycle by the refrigerator.
$Q_1=$ heat rejected to the source by refrigerator, i.e amount of heat discharged to room.
$\Rightarrow \beta =\frac{Q_2}{W}$
Or, $5=\frac{Q_2}{W}$
$\therefore W=\frac{250}{5}=50\text{J/cycle}$
from energy conservation on refrigerator,
$Q_2+W=Q_1$
$\therefore Q_1=(250+50)\text{J}=300\text{J}$