# Understanding the Coefficient of Performance (COP) of a Refrigerator The Coefficient of Performance (COP) is a measure of a refrigerator's efficiency. It indicates how much heat is removed from the food compartment per unit of work input. --- ## Step 1: Understand the given data - Heat extracted from the food compartment, \( Q_{in} = 150\, \text{kJ} \) - Work input, \( W = 50\, \text{kJ} \) **Note:** The heat extracted from the food compartment is the amount of heat removed to keep the food cool. --- ## Step 2: Recall the formula for COP of a refrigerator \[ \boxed{ \text{COP}_{\text{refrigerator}} = \frac{Q_{in}}{W} } \] Where: - \( Q_{in} \) = heat removed from the cold space (food compartment) - \( W \) = work input needed for the process --- ## Step 3: Substitute the known values \[ \text{COP} = \frac{150\, \text{kJ}}{50\, \text{kJ}} \] --- ## Step 4: Calculate the COP \[ \text{COP} = 3 \] --- ## **Final Answer:** **The Coefficient of Performance (COP) of the refrigerator is \(\boxed{3}\).** --- ## Theoretical Explanation: **Why is COP important?** - It measures the effectiveness of a refrigerator. - A higher COP indicates a more efficient refrigerator, meaning it removes more heat per unit of work. **How does it relate to thermodynamics?** - The refrigerator operates between two thermal reservoirs: the cold space (food compartment) and the surroundings. - It uses work to transfer heat from the cold to the hot reservoir. - The ideal behavior is based on the second law of thermodynamics, which prevents a refrigerator from having a COP greater than that of a Carnot cycle operating between the same two temperatures. --- ## Summary: - The COP of a refrigerator shows how well it performs. - Given data: heat removed \( Q_{in} = 150\, \text{kJ} \), work input \( W = 50\, \text{kJ} \). - Calculation: \( \text{COP} = 150/50 = 3 \). This indicates that for every 1 unit of work, the refrigerator removes 3 units of heat from the food compartment.