Question

A refrigerator has a coefficient of performance of 5. If the temperature inside the freezer is $-20^{\circ}C$, the temperature of the surroundings to which it rejects heat is:

• A. $31^{\circ}C$
• B. $41^{\circ}C$
• C. $21^{\circ}C$
• D. $11^{\circ}C$

Hint:

Always convert Celsius to Kelvin before using thermodynamic formulas!

Answer 1

The Correct Option is A

Step 1: Concept
The Coefficient of Performance (COP) of a refrigerator is given by $\beta = \frac{T_{L}}{T_{H} - T_{L}}$, where temperatures are in Kelvin.

Step 2: Meaning
Given $\beta = 5$ and $T_{L} = -20^{\circ}C = 253$ K. We need to find $T_{H}$.

Step 3: Analysis
$5 = \frac{253}{T_{H} - 253}$
$5(T_{H} - 253) = 253$
$T_{H} - 253 = 50.6$
$T_{H} = 303.6$ K.

Step 4: Conclusion
Converting back to Celsius: $303.6 - 273 = 30.6^{\circ}C$, which rounds to $31^{\circ}C$. Final Answer: (A)