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The Coefficient of Performance (COP) is a measure of the efficiency of a refrigerator or a heat pump. It tells us how well a refrigerator performs by comparing the amount of heat it moves with the amount of work it requires to do so. You can think of COP as a 'bang for your buck' measure in terms of energy.

The formula to calculate the coefficient of performance for a refrigerator is:
\[\text{COP} = \frac{Q_c}{W}\]where

• \( Q_c \) is the heat removed from the refrigerator's cold compartment
• \( W \) is the work input required

For instance, in our problem, the refrigerator removes \( 560 \mathrm{~J} \) of heat with an energy input of \( 150 \mathrm{~J} \) of work. By substituting these values into the COP formula, we can calculate:
\[\text{COP} = \frac{560}{150} = 3.73\]This means the refrigerator is quite efficient as it manages to remove 3.73 times the energy it consumes as work.

The refrigerator cycle is the process through which a refrigerator removes heat from its interior to maintain a cool environment. This cycle relies on the principles of thermodynamics and energy transfer.

In this cycle, refrigerant absorbs heat from the internal compartment, thereby cooling it. This absorbed heat, along with the heat generated by work done by the motor, is then expelled to the outside environment, often into the kitchen.

Steps in the Refrigerator Cycle

• **Evaporation:** The refrigerant absorbs heat as it evaporates inside the refrigerator, cooling the interior.
• **Compression:** The gaseous refrigerant is compressed, which increases its temperature.
• **Condensation:** The heat is released to the surroundings as the refrigerant condenses back to a liquid state.
• **Expansion:** The refrigerant is expanded, cooling it further, and the cycle repeats.

Energy conservation is a fundamental principle in physics, stating that energy cannot be created or destroyed; it can only change forms. This principle is crucial in understanding the operation of a refrigerator.

For any refrigerator, the energy balance can be represented as:
\[ Q_h = Q_c + W \]where

• \( Q_h \) is the heat exhausted to the environment
• \( Q_c \) is the heat extracted from the refrigerator's cold compartment
• \( W \) is the work input

Using energy conservation, the equation ensures that the energy entering the refrigerator is equal to the energy leaving it, after accounting for the work done. In the given exercise, the exhausted heat \( (Q_h) \) will be the sum of the heat removed \( (Q_c) \) and the work done \( (W) \). Calculating, we find:
\[Q_h = 560 + 150 = 710 \mathrm{~J} \]This confirms that the cycle maintains the energy equilibrium as expected.