An ideal Carnot refrigerator with a performance coefficient (COP) of $5.0$ cools items inside of it to $5.0 ^ { \circ } \mathrm { C }$. What is the high temperature needed to operate this refrigerator?
A) $1395 ^ { \circ } \mathrm { C }$
B) $30 ^ { \circ } \mathrm { C }$
C) $61 ^ { \circ } \mathrm { C }$
D) $6 ^ { \circ } \mathrm { C }$

Question

Quizplus · Accepted Answer

The COP of a Carnot refrigerator is given by $ \text{COP} = \frac{T_C}{T_H - T_C} $. Given $ \text{COP} = 5.0 $ and $ T_C = 5 + 273 = 278 \, \text{K} $, solve for $ T_H $: $ 5 = \frac{278}{T_H - 278} $, leading to $ T_H = 334 \, \text{K} $ or $ 61 \, ^{\circ} \mathrm{C} $.

An Ideal Carnot Refrigerator with a Performance Coefficient (COP) Of 5.0