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) 61° C
B) 1395° C
C) 6° C
D) 30° C

Question

Quizplus · Accepted Answer

The COP of a Carnot refrigerator is given by:$$COP = \frac{T_c}{T_h - T_c}$$where $T_c$ is the low temperature and $T_h$ is the high temperature.We are given that $COP = 5.0$ and $T_c = 5.0 ^ { \circ } \mathrm { C }$. Substituting these values into the equation, we get:$$5.0 = \frac{278.15 \mathrm { K }}{T_h - 278.15 \mathrm { K }}$$Solving for $T_h$, we get:$$T_h = 61.0 ^ { \circ } \mathrm { C }$$Therefore, the high temperature needed to operate this refrigerator is 61° C.

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