# Carnot Cycle for refrigeration

## 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 heat-engine cycle and it has the highest possible efficiency.

A reversible refrigeration cycle also has the maximum efficiency or COP. By reversing the operation of a reversible heat engine, it can be used as a refrigerating machine. So, a reversed Carnot cycle for refrigeration, which is a reversible heat-engine cycle, can be used as a reversible refrigeration cycle.

It 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.

Reversed carnot cycle consists of Two isothermals and two isentropic process

## 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,

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

## 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 Carnot cycle varies from zero to infinity.

## Strategies to achieve maximum Carnot COP in any Application

to obtain the maximum possible COP in any application

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

1. The reversed Carnot cycle that uses vapour as a refrigerant involves two isothermal processes: condensation and evaporation. These processes are internally reversible and 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 vapor 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, which represents the maximum possible efficiency.

2. The reversed Carnot cycle that employs gas as a refrigerant has two primary limitations. Firstly, it is impractical to achieve isothermal processes of heat absorption and rejection, 4-1 and 2-3, with gas as the working substance since these processes would take an infinite amount of time.

Secondly, the cycle’s p-v diagram is very narrow because the volume changes during both the reversible isothermal and adiabatic processes. The Carnot p-v diagram, drawn to scale, is much thinner than the diagram commonly illustrated. As a result, the stroke volume of the cylinder becomes quite large. The cycle’s actual coefficient of performance (COP) is therefore poor due to irreversibilities in both the compressor and the expander.

## Reference

Refrigeration and Air Conditioning by C P Arora

Heat pump and refrigeration cycle – Wikipedia

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