Question

The inside of your refrigerator is approximately 2 ∘C. Heat from the inside of your refrigerator is deposited into the air in your kitchen, which has a temperature of approximately 24 ∘C. At these operating temperatures, what is the maximum possible coefficient of performance of your refrigerator?

Answer 1

The maximum possible coefficient of performance for the refrigerator operating at 2°C inside and 24°C outside is approximately 12.51.

Step-by-step explanation:

The maximum possible coefficient of performance (COP) for a refrigerator can be calculated using the temperatures of the inside of the refrigerator and the room temperature into which it dumps heat. The formula for the COP of a refrigerator is given by:

COP = T_cold / (T_hot - T_cold)

where T_cold is the temperature inside the refrigerator and T_hot is the temperature of the outside environment. Both temperatures must be in Kelvin. Converting the temperatures given in the question, we get:

T_cold = 2 + 273.15 = 275.15 K
T_hot = 24 + 273.15 = 297.15 K

Now, substituting these values into the formula, we get:

COP = 275.15 / (297.15 - 275.15) = 275.15 / 22 = 12.51

So, the maximum possible COP for the refrigerator operating under these conditions is approximately 12.51.