To determine the coefficient of performance (COP) of the refrigerator, we need to understand how the COP is defined in the context of refrigeration cycles. The COP is a measure of the efficiency of a refrigerator, calculated as the ratio of the heat removed from the cold reservoir (the freezer compartment) to the work input required to operate the refrigerator. The formula for COP can be expressed as:
Understanding the Coefficient of Performance
The formula for the coefficient of performance (COP) is given by:
COP = Q_c / W
Where:
- Q_c = Heat removed from the cold space (freezer compartment)
- W = Work input to the refrigerator
Given Data
From the problem, we have the following information:
- Heat transfer from the freezer compartment, Q_c = 8000 kJ/h
- Power input to the refrigerator, W = 3200 kJ/h
Calculating the COP
Now, we can substitute the values into the COP formula:
COP = Q_c / W
Substituting the known values:
COP = 8000 kJ/h / 3200 kJ/h
When we perform the division:
COP = 2.5
Interpreting the Result
A COP of 2.5 indicates that for every unit of work input (in this case, 1 kJ of energy), the refrigerator removes 2.5 kJ of heat from the freezer compartment. This is a good indicator of efficiency, as a higher COP means the refrigerator is effectively transferring more heat for less energy input.
Real-World Implications
In practical terms, a refrigerator with a COP of 2.5 is performing well. It means that the system is designed efficiently, allowing it to maintain the desired temperature in the freezer while minimizing energy consumption. This efficiency is crucial not only for reducing electricity bills but also for environmental considerations, as lower energy consumption translates to reduced greenhouse gas emissions.
In summary, the coefficient of performance for the refrigerator in this scenario is 2.5, showcasing its effectiveness in transferring heat from the cold space to the surroundings while requiring a reasonable amount of work input. This understanding of COP helps in evaluating and comparing the performance of different refrigeration systems.
