To tackle this problem, we need to apply the concept of the coefficient of performance (COP) of a refrigerator or freezer, which is a measure of its efficiency. The COP is defined as the ratio of the heat removed from the cold reservoir (the inside of the freezer) to the work input required to remove that heat. Let's break this down step by step.
Understanding the Coefficient of Performance
The formula for the coefficient of performance (COP) is given by:
COP = Q_c / W
Where:
- Q_c is the heat extracted from the cold reservoir (in this case, the freezer).
- W is the work done on the system (the freezer).
Part (a): Heat Delivered to the Room
When the freezer extracts heat from inside, it also delivers heat to the surrounding environment (the room). The total heat delivered to the room (Q_h) can be calculated using the relationship:
Q_h = Q_c + W
We know that:
- Q_c = 185 kJ (the heat extracted from the freezer).
- COP = 5.70
Calculating Work Done
First, we need to find the work done (W) using the COP formula:
W = Q_c / COP
Substituting the values:
W = 185 kJ / 5.70 ≈ 32.46 kJ
Finding Heat Delivered to the Room
Now that we have the work done, we can find the heat delivered to the room:
Q_h = Q_c + W
Q_h = 185 kJ + 32.46 kJ ≈ 217.46 kJ
Summary of Results
To summarize:
- (a) The heat delivered to the room is approximately 217.46 kJ.
- (b) The work required to run the freezer is approximately 32.46 kJ.
This example illustrates how the efficiency of a freezer can be quantified and how energy is transferred between different environments. Understanding these principles is crucial in thermodynamics and energy management.
