# Refrigeration Cycle Diagram Explained

The thermodynamic processes in the refrigeration cycle are complex. Calculation using formulae and tables requires a considerable amount of effort due to the three different states of the refrigerant from liquid, boiling and gaseous. Therefore, for reasons of simplify cation, the log p-h diagram was introduced.

## Refrigeration cycle concept

In general, a log p-h diagram shows the aggregate state of a substance, depending on pressure and heat. For refrigeration, the diagram is reduced to the relevant regions of liquid and gaseous as well as their mixed form.

The vertical axis shows the logarithmic pressure and the horizontal axis shows the specific c enthalpy with linear scaling. Accordingly, the isobars are horizontal and the isoenthalps are vertical. The logarithmic scaling makes it possible to represent processes with large pressure differences.

The saturated vapor curve and the boiling point curve meet at the critical point K.

• pressure p
• specific enthalpy h
• temperature T
• specific volume v
• specific entropy s
• gas content x

## Log p-h diagram

The distinctive feature of the refrigeration cycle is that it runs counter-clockwise, i.e. opposite to the joule or steam cycle. A change of state occurs when the refrigerant flows through one of the four main components of the refrigeration plant. The actual refrigeration cycle consists of the following changes of state:

• Green = compressor
• Red = condenser
• Yellow = expansion valve
• Blue = evaporator
• 1 – 2 polytropic compression to the condensing pressure (for comparison 1 – 2’ isentropic compression)
• 2 – 2’’ isobaric cooling, deheating of the superheated vapour
• 2’’ – 3’ isobaric condensation
• 3’ – 3 isobaric cooling, supercooling of the liquid
• 3 – 4 isenthalpic expansion to the evaporation pressure
• 4 – 1’ isobaric evaporation
• 1’ – 1 isobaric heating, superheating of the vapour

## Specific amounts of energy

The specific amounts of energy that can be absorbed and released to reach the state points are marked as lines in the log p-h diagram. The specific enthalpy h can be read for each separate state point directly from the log p-h diagram.

If the mass flow rate of the refrigerant is known, the associated thermal output can be calculated by means of the specific enthalpy at the respective state point.

• the line h1 – h4 = q0 corresponds to the cooling and results in the refrigeration capacity by multiplication with the the mass flow rate.
• the line h2 – h1 = pv corresponds to the technical work of the compressor, which is actually transferred to the refrigerant.
• the line h2 – h3 = qc corresponds to the emitted heat and results in the condenser capacity by multiplication with the the mass flow rate. It is the waste heat from a refrigeration plant.

## Limiting isobars

• p1 evaporation pressure
• p2 condensing pressure

## Compression process

• identifying the point of intersection of the isobars p1 with the temperature at the compressor inlet T1 gives the state point 1.
• identifying the point of intersection of the isobars p2 with the temperature at the condenser inlet T2 gives the state point 2.
• the connection between the two state points 1 and 2 describes the compression process

## Isenthalpic expansion

identifying the point of intersection of the isobars p2 with the temperature T3 at the condenser outlet gives the state point 3.

The expansion is an isenthalpic process. Therefore, the previously marked intersection point can be connected to the isobars p1 by a vertical line. This results in the last state point 4 with the evaporation temperature T4

## Reveal the specific enthalpy values

When calculating operating states of a refrigeration plant, it is necessary to determine the specific enthalpies of the individual changes of state. The procedure is as follows:

The specific enthalpy can be read off using a vertical connection of the state points and the x-axis.

• h1 spec. enthalpy after evaporator
• h2 spec. enthalpy after compressor
• h3 spec. enthalpy after condenser
• h4 spec. enthalpy after expansion valve

The specific refrigeration capacity q0 and the specific condensation capacity qc can be read directly from the log p-h diagram.

specific refrigeration capacity q0 = h1 – h4

specific condensation capacity qc = h2 – h3

What are the advantages of using a log p-h diagram in refrigeration cycle analysis?
The log p-h diagram simplifies the complex thermodynamic processes in the refrigeration cycle by providing a visual representation of the refrigerant’s state changes. It eliminates the need for tedious calculations using formulae and tables, allowing for faster and more accurate analysis of the refrigeration cycle. Additionally, the log p-h diagram enables engineers to quickly identify the different regions of the refrigerant’s state, including liquid, boiling, and gaseous, as well as their mixed forms.
How does the log p-h diagram show the aggregate state of a substance in a refrigeration cycle?

The log p-h diagram plots the logarithmic pressure (p) against the enthalpy (h) of the refrigerant, providing a comprehensive view of the refrigerant’s state changes during the refrigeration cycle. The diagram shows the relationships between pressure, temperature, and enthalpy, enabling engineers to visualize the refrigerant’s state changes and identify the different regions of the cycle, such as compression, condensation, expansion, and evaporation.

What are the key regions of the log p-h diagram in a refrigeration cycle?

The log p-h diagram in a refrigeration cycle typically shows three key regions: the liquid region, the boiling region, and the gaseous region. The liquid region represents the refrigerant’s state during the condensation process, while the boiling region represents the refrigerant’s state during the evaporation process. The gaseous region represents the refrigerant’s state during the compression process. The diagram may also show the mixed forms of these regions, such as the liquid-gas mixture during the expansion process.

How does the log p-h diagram help in identifying inefficiencies in a refrigeration cycle?

The log p-h diagram can help identify inefficiencies in a refrigeration cycle by revealing deviations from the ideal cycle. For example, if the diagram shows a larger than expected pressure drop during the expansion process, it may indicate an inefficient expansion valve. Similarly, if the diagram shows a higher than expected temperature during the condensation process, it may indicate an inefficient condenser. By analyzing the log p-h diagram, engineers can identify areas for improvement and optimize the refrigeration cycle for better performance and efficiency.

Can the log p-h diagram be used for other types of refrigeration cycles, such as absorption refrigeration?

Yes, the log p-h diagram can be used for other types of refrigeration cycles, including absorption refrigeration. While the specific regions and processes may differ, the log p-h diagram provides a general framework for analyzing the thermodynamic state changes of the refrigerant. By adapting the diagram to the specific characteristics of the absorption refrigeration cycle, engineers can use it to analyze and optimize the performance of these systems.

How does the log p-h diagram relate to other thermodynamic diagrams, such as the T-s diagram?

The log p-h diagram is related to other thermodynamic diagrams, such as the T-s diagram, in that they all provide visual representations of the thermodynamic state changes of a system. While the log p-h diagram plots pressure against enthalpy, the T-s diagram plots temperature against entropy. Both diagrams can be used to analyze the refrigeration cycle, but the log p-h diagram is particularly useful for refrigeration systems due to its ability to show the relationships between pressure, temperature, and enthalpy.