Question

A Carnot refrigerator with a COP of 5.0 cools to 5.0°C. What is the high temperature, Th, needed to operate this refrigerator?

A) 30° C
B) 1395° C
C) 6° C
D) 61° C

Answer 1

The high temperature needed to operate the Carnot refrigerator is 6°C.

Step-by-step explanation:

The Carnot refrigerator equation is given by:

COP = Qc/W = Th/(Th - Tc)

where COP is the coefficient of performance, Qc is the heat extracted from the cold reservoir, W is the work done on the refrigerator, Th is the high temperature, and Tc is the low temperature.

From the given information, the COP is 5.0 and the low temperature is 5.0°C. Plugging in these values into the equation, we can solve for Th:

5.0 = Th / (Th - 5.0)

5.0(Th - 5.0) = Th

5.0Th - 25.0 = Th

25.0 = 4.0Th

Th = 6°C

Therefore, the high temperature needed to operate this refrigerator is 6°C, which corresponds to option C.