An ideal Carnot refrigerator with a performance coefficient (COP)of 5.0 cools items inside of it to $5.0 ^ { \circ } \mathrm { C } \text {. }$ 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 performance coefficient (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 $T_c = 5.0 ^ { \circ } \mathrm { C } \text {. }$ Solving for $T_h$, we get:$$T_h = T_c + \frac{T_c}{COP} = 5.0 ^ { \circ } \mathrm { C } + \frac{5.0 ^ { \circ } \mathrm { C } }{5.0} = 61 ^ { \circ } \mathrm { C }$$Therefore, the high temperature needed to operate this refrigerator is 61° C.

An Ideal Carnot Refrigerator with a Performance Coefficient (COP)of 5 5.0∘C. 5.0 ^ { \circ } \mathrm { C } \text {. }5.0∘C.

An Ideal Carnot Refrigerator with a Performance Coefficient (COP)of 5 $5.0 ^ { \circ } \mathrm { C } \text {. }$