What are (a) the heat extracted from the cold reservoir and (b) the coefficient of performance for the refrigerator shown in FIGURE EX21.21?

Verified step by step guidance

1. Identify the relevant information from FIGURE EX21.21, such as the heat Q_H released to the hot reservoir, the work W done by the refrigerator, and any other given parameters like temperatures of the reservoirs.
2. Calculate the heat extracted from the cold reservoir, Q_C, using the first law of thermodynamics for the refrigerator, which states that the net heat transfer is equal to the net work done on the system: Q_C = Q_H - W.
3. Understand the concept of the coefficient of performance (COP) for a refrigerator, which is defined as the ratio of the heat removed from the cold reservoir to the work done by the refrigerator: COP = Q_C / W.
4. Substitute the values of Q_C and W into the COP formula to find the coefficient of performance of the refrigerator.
5. Review the calculations to ensure all units are consistent and the principles of thermodynamics are correctly applied.

Key Concepts

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or system to another due to a temperature difference. In the context of refrigeration, heat is extracted from the cold reservoir, which is the area being cooled, and transferred to the hot reservoir, typically the surrounding environment. Understanding the principles of heat transfer is essential for analyzing the efficiency and operation of refrigeration systems.

Refrigerator Coefficient of Performance (COP)

The Coefficient of Performance (COP) of a refrigerator is a measure of its efficiency, defined as the ratio of the heat removed from the cold reservoir to the work input required to remove that heat. A higher COP indicates a more efficient refrigerator, as it means more heat is extracted for each unit of work done. This concept is crucial for evaluating the performance of refrigeration systems and optimizing their design.

Thermodynamic Cycles

Thermodynamic cycles describe the series of processes that a refrigerant undergoes in a refrigeration system, including compression, condensation, expansion, and evaporation. These cycles are fundamental to understanding how refrigerators operate, as they illustrate how energy is transferred and transformed within the system. Familiarity with these cycles helps in analyzing the performance and efficiency of refrigeration systems.