# Possibilities Of Carnot Cycle For Refrigeration And Its Performance

## Application of the Carnot cycle for refrigeration

In 1824, Sadi Carnot proposed a cycle that could convert heat into work in the most efficient way possible. This cycle is called the reversible Carnot cycle and it has the highest possible efficiency. Since it is reversible, the Carnot cycle for refrigeration is possible.

By reversing the operation of a reversible Carnot heat engine, it can be used as a refrigerating machine. In a reversed Carnot cycle, work is added to produce a cooling effect. A reversible refrigeration cycle also has the maximum efficiency or COP.

COP of the reversed Carnot cycle helps to determine the maximum possible COP of a refrigerating machine operating between two temperatures – the temperature at which heat is rejected and the temperature at which cooling is needed.

## Different Processes of the reversed Carnot cycle for refrigeration

Reversed Carnot cycle consists of Two isothermals and two isentropic processes as follows

## P-V and T-S diagram of a reversed Carnot cycle for refrigeration

With reference to the P-V and T-S Diagram

• Process 1-2 isentropic compression, s1=s2
•  Process 2-3 Isothermal heat rejection to the hot reservoir at Tk=Constant
• Process 3-4 Isentropic expansion Process s3=s4
• Process 4-1 isothermal heat absorption from the cold reservoir at To=Constant,
• Q1 = Heat removed form the cold body
• Q2= Heat rejected to the hot body
• Work added to the Refrigerating machine

The areas on the T-s diagram, representing the heat transfers and work done in the cycle as follows:

• Heat absorbed from a cold body, Qo = area 1-4-5-6
• Heat rejected to hot body Qk = area 2-3-5-6
• Work done = area 1-2-3-4

## Efficiency or COP of the reversed carnot cycle for refrigeration

### COP When Gas is used as a refrigerant in a Carnot Cycle

here, Tk>To, r = compression ratio

To know more about the carnot cycle efficiency in producing work then click/tap here

## Effect of Operating Temperatures on COP of the Reversed Carnot cycle for refrigeration

The Carnot coefficient of performance (COP) relies solely on the operating temperatures of the system, and not on the working substance (specific refrigerant) used.

When it comes to cooling, the refrigeration temperature (To) and the temperature at which heat is rejected to the surroundings (Tk) determine the COP.

The minimum achievable refrigeration temperature is absolute zero, at which the COP is zero

On the other hand, the maximum possible refrigeration temperature occurs when To = Tk, resulting in an infinite COP

Therefore, the range of COP values for cooling using the reversed Carnot cycle varies from zero to infinity.

## Strategies to achieve maximum COP of the reversed carnot cycle for refrigeration in any Application

To obtain the maximum possible COP in any application using reversed carnot cycle

1. the cold body temperature “To” should be as high as possible, and
2. the hot body temperature “Tk” should be as low as possible

## Selection of Operating Temperatures for reversed Carnot cycle for refrigeration

The selection of temperature “To” depends on the particular application of refrigeration e.g. air conditioning in summer, Cold storage, domestic refrigerators etc.

And “Tk” depends on the surrounding medium used for heat rejection viz. Air, water and ground.

## Limitation of a reversible Carnot cycle for refrigeration

In the reversed Carnot cycle that uses vapour as a refrigerant, isothermal processes can be easily accomplished in practice. However, there may be some difficulties in achieving partial evaporation since it can be challenging to design an expander that can handle a mixture of mostly liquid and partly vapour during the 3-4 process.

Additionally, due to internal irreversibilities in both the compressor and the expander, the actual coefficient of performance (COP) of the cycle is significantly lower than the ideal cycle COP.

Hence reversed Carnot cycle for refrigeration is theoretically possible but in practice, this is not possible to use this cycle in the refrigerating machine due to the limitations of the Carnot cycle.

To know more about the limitations of a reversible Carnot cycle that uses pure substance or gas as a working substance then click/Tap here

## References

Refrigeration and Air Conditioning by C P Arora

Heat pump and refrigeration cycle – Wikipedia

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