Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
What is the maximum possible coefficient of performance for a refrigerator operating between 2.0°C (a typical refrigerator temperature) and 20°C (a typical kitchen temperature)?
A
0.89
B
1.6
C
4.5
D
11
E
13
F
15
Verified step by step guidance
1
First, understand that the coefficient of performance (COP) for a refrigerator is defined as the ratio of the heat removed from the cold reservoir (Q_c) to the work input (W). For an ideal refrigerator, this is given by the formula: COP = Q_c / W.
For a Carnot refrigerator, which is an idealized model, the COP is given by the formula: COP_Carnot = T_c / (T_h - T_c), where T_c is the absolute temperature of the cold reservoir and T_h is the absolute temperature of the hot reservoir.
Convert the given temperatures from Celsius to Kelvin by adding 273.15 to each. So, T_c = 2.0°C + 273.15 = 275.15 K and T_h = 20°C + 273.15 = 293.15 K.
Substitute the Kelvin temperatures into the Carnot COP formula: COP_Carnot = 275.15 / (293.15 - 275.15).
Simplify the expression to find the maximum possible coefficient of performance for the refrigerator operating between these temperatures.