Question

Define the coefficient of performance of a refrigerator in words. Can it be greater than unity?

Short answer

Answer: Yes, the coefficient of performance (COP) of a refrigerator can be greater than unity. A COP greater than 1 indicates that the refrigerator can transfer more heat from the cold environment than the amount of work input provided by the compressor, making it more efficient and utilizing less energy to achieve the same cooling effect compared to a refrigerator with a lower COP.

Step-by-step solution

Understanding the Refrigerator's Purpose

The main objective of a refrigerator is to move heat from a colder environment (inside the refrigerator) to a warmer environment (outside the refrigerator). This process is accomplished using a refrigeration cycle, which utilizes a working fluid, compressor, condenser, expansion valve, and evaporator.

Coefficient of Performance (COP) Definition

The coefficient of performance (COP) is defined as the ratio of the desired result (the amount of heat removed from the colder environment) to the amount of work required to achieve it (the work done by the compressor). In other words, COP is an indicator of the efficiency of a refrigerator, as it describes how much cooling effect is achieved per unit of work input. Mathematically, COP can be expressed as: COP = \frac{Q_c}{W} where Q_c is the amount of heat removed from the colder environment and W is the work done by the compressor.

Can the Coefficient of Performance be Greater than Unity?

Yes, the coefficient of performance (COP) of a refrigerator can be greater than unity. Since the COP is the ratio of the amount of heat removed from the cold environment to the work input, a COP greater than 1 indicates that the refrigerator can transfer more heat from the cold environment than the amount of work input provided by the compressor. A refrigerator with a COP greater than 1 is more efficient and utilizes less energy to achieve the same cooling effect compared to a refrigerator with a lower COP.