# Coefficient of Performance

## Introduction

Coefficient of performance, or COP, is a number that indicates how efficient the heat pump, air conditioning system, or refrigerator is. Heat pumps (heating systems) are characterized by a coefficient of performance that is defined as a ratio between energy delivered to the hot reservoir and work input. As a result, it is known as a performance heating coefficient. The greater the value of a device's coefficient of performance, the greater its efficiency. The coefficient of performance is typically greater than one because, in the case of these appliances, work is not simply converted to heat, but additional heat is pumped to the region where it is needed.

## Coefficient of performance

The coefficient of performance (K or C. O. P.) can be defined as a number that represents the efficiency of refrigerators, heat pumps, and also air conditioners. The C.O.P. of a heating or cooling system is different from one another. For a heating system, the C.O.P. is given by the amount of energy delivered to the hot reservoir divided by work input. This is called the heating C.O.P. In contrast, in the case of a cooling system like a refrigerator, the C O P is the amount of energy removed from the cold reservoir divided by work input. Therefore, it is known as a cooling C. O. P. A heat pump, when turned off, behaves like a refrigerator. The cooling C.O.P of a heat pump operating in reverse can be described by the term energy efficiency ratio (EER). The performance coefficient for both heating and cooling is comparable to the thermal efficiency of heat engines.

The ratio of heat dissipation to electrical power intake is used to calculate the C. O. P. It is the criterion used to assess the performance of an air conditioning unit. It demonstrates the efficiency of heating and cooling systems. The following points demonstrate the characteristics of COP.

## Properties

• It is the proportion of compressor power to refrigeration output.

• When the C. O. P. increases, the cooling output increases proportionally to the power input.

• Increased C.O.P. equals higher efficiency.

• It means that as COP increases, efficiency increases, and as COP decreases, efficiency decreases.

• It is the ratio of the evaporator cooling output to the work input of the air conditioner or refrigerator.

• When the C.O.P. increases, so does the power consumption and the operating costs.

The C. O. P. is represented with a number and usually denotes how effective the heat pump, air conditioning system or the refrigerator is. The COP is given by the ratio of the amount of cooling or heating generated to the amount of electrical power intake and is generally denoted by the variable K. Since the coefficient of performance is a ratio, it has no unit. The higher is the value of the coefficient of performance of any device, the higher will be its efficiency. This in turn means it will have a lower energy consumption and the cost of operating will also be lower. The coefficient of performance is generally of two types −

• In case of a heat pump the C.O.P. is the ratio of the amount of heat that is delivered to the system from the environment to the power intake and it is written as Kheating.

• In case of a refrigerator or an air conditioner, the C.O.P. is the ratio of the amount of heat removed to the power intake. It is written as Kcooling.

The coefficient of performance usually has a value greater than 1 as in case of these appliances, the work is not just converted to heat, but additional heat is pumped to the region where it is required. Though the value of COP is greater than 1, it doesn’t mean the value of efficiency is more than 100% as it is not possible for any kind of heat engine to have a value of efficiency which is greater than 100%.

The equation for the coefficient of performance is given by

$$\mathrm{K =\frac{\lvert Q\rvert}{W}}$$

Here the |Q| denoted the amount of heat that is supplied or removed from the system and W is the amount of power intake.

In the case of a refrigerator or an air conditioning system, the coefficient of performance,

$$\mathrm{K_{cooling}=\frac{\lvert Q_{cooling}\rvert}{W}}$$

In case of a heat pump, the coefficient of performance,

$$\mathrm{K_{cooling}=\frac{\lvert Q_{heating}\rvert}{W}=\frac{\lvert Q_{cooling}\rvert +W}{W}=K_{cooling}+ 1}$$

The value of the coefficient of performance of any system can be improved by decreasing the temperature gap between the two reservoirs. In the case of a heat pump this can be done by any one of two processes: By decreasing the output temperature or by increasing the input temperature.

## Conclusion

The C. O. P. is a number that depicts the efficiency of a heat pump, air conditioning system, or refrigerator. Heat pumps (heating systems) are characterized by a coefficient of performance that is defined as a ratio between energy delivered to the hot reservoir and work input. The higher the value of a device's coefficient of performance, the more efficient it is. Because work is not simply converted to heat in the case of these appliances, but additional heat is pumped to the region where it is needed, the C.O.P. is typically greater than one.

## FAQs

Q1. What is the purpose of the coefficient of performance?

Ans. The coefficient of performance (K or C.O.P.) can be defined as a number that represents the efficiency of refrigerators, heat pumps, and also air conditioners. The C.O.P. of a heating or cooling system is different from one another. Higher C.O.P.s imply greater efficiency, lower energy (power) consumption, and, as a result, lower operating costs.

Q2. Is the coefficient of performance always greater than one?

Ans. The refrigeration coefficient of performance (C.O.P.) is always greater than one. The C.O.P. is the ratio of heat obtained from the refrigerator to refrigerant work done. Theoretical coefficient of performance is another name for it.

Q3. Is efficiency the same as performance coefficient?

Ans. It is the ratio of the evaporator cooling output to the work input of the air conditioner or refrigerator. The more effective the system, the greater the Performance Coefficient.

Q4. How does the coefficient of performance (C.O.P.) change with temperature?

Ans. C.O.P. can be affected by both the inlet and outlet temperatures of a heat pump. As the inlet temperature rises from the ground, the C.O.P. will increase.

Q5. What is the connection between the C.O.P.s of heating and cooling?

Ans. C.O.P. describes a heat pump's ability to draw out cooling or heat in relation to the power supplied to the compressor. As an example: The COP of a given heat pump used for air cooling is 2.

Updated on: 28-Apr-2023

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