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 22 ∘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 a refrigerator with an inside temperature of 2°C and an external temperature of 22°C is 13.7575, calculated by converting temperatures to Kelvin and using the COP formula for refrigerators.

Step-by-step explanation:

The maximum possible coefficient of performance (COP) of a refrigerator can be calculated using the temperatures of the inside of the refrigerator and the temperature of the surroundings into which it is depositing heat. The COP is defined as the heat removed from the cold reservoir (Qc) divided by the work done (W) to remove that heat.

Calculating the Coefficient of Performance

For an ideal refrigerator, the formula for calculating the COP for a refrigerator is:

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

Where Tc is the cold reservoir temperature and Th is the warm reservoir temperature, both in Kelvin. To convert Celsius to Kelvin, add 273.15.
So for this question:

• Inside of refrigerator temperature: 2 °C = 275.15 K
• Kitchen air temperature: 22 °C = 295.15 K

Now, we can compute the COP as follows:

COP = 275.15 / (295.15 - 275.15) = 275.15 / 20 = 13.7575

The maximum possible coefficient of performance of the refrigerator operating between these temperatures is 13.7575.