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# Basics of the refrigeration cycle ph diagram

It is a field that appears in the qualification of refrigerators and the study of thermodynamics.

As an owner-engineer, this is a part that can be left up to the manufacturer, so you may not be aware of it.

It may be positioned as a bit of useful knowledge to know.

If you have a solid level of knowledge about this area, it will actually be useful when analyzing problems.

Also, it is possible to attach foil to the manufacturer.

## Refrigeration cycle and ph diagram

When thinking about the refrigeration cycle, a mysterious relationship called a ph diagram appears.

This time, I will dig a little deeper into this ph diagram.

Let’s consider a textbook refrigeration cycle as shown below.

The main player here is the refrigerant .

Refrigerant circulates in the refrigeration cycle.

The state changes while spinning .

It is very important to know where the refrigerator is and what state it is in.

There are various thermodynamic indices that indicate the state.

This time we will use pressure P and enthalpy H.

The ph diagram looks like this:

Let’s take it slow.

## enthalpy

What is enthalpy anyway?

Enthalpy H is defined as follows using internal energy U, pressure P and volume V.

H is defined as follows using internal energy U, pressure P and volume V.

$$H = U + PV$$

### internal energy

You can think of the internal energy U as the kinetic energy of the molecule.

Matter is made up of many molecules.

These molecules are invisible, but they are always in motion.

This energy is proportional to temperature. Rather, it can be said to be the definition of temperature.

Temperature is sometimes called a state quantity in thermodynamics .

This is a physical quantity necessary to specify the state of matter.

A single state quantity cannot determine the state of a substance, and multiple state quantities are combined.

When we use expressions such as “water at 20°C” or “temperature at 10°C” in our daily life, we use the state quantity temperature to indicate the state of water and air.

### fluid energy

PV can be positioned as fluid energy .

It is the product of pressure P and volume V.

I think something like this is enough.

Thinking about it makes it difficult.

In order to specify the state of the fluid, the pressure P and volume V are required.

Pressure P and volume V are also state quantities, just like temperature T.

When we express things like “water at 20°C” or “temperature at 10°C”, we are actually assuming “atmospheric pressure of 100kPaA” .

### two state quantities

If the temperature and pressure can be specified, the volume of an ideal gas can be determined.

It means that specifying two of the state quantities determines the other state quantities.

Enthalpy H is the sum of internal energy dependent on temperature T and fluid energy determined by pressure P and volume V.

Since temperature T, pressure P, and volume V are all state quantities of matter, enthalpy H is also a state quantity.

Therefore, if we look at the two state quantities, pressure P and enthalpy H , it is convenient to recognize that it is a refrigerator.

### amount of change

Enthalpy H is a state quantity, but I am not really interested in its value itself.

I am interested in the amount of change.

You are interested in absolute values ​​of pressure P and temperature T. Like 100kPa or 20℃.

However, we are not interested in the absolute value of the enthalpy H.

If you want to know the amount of change, you will have to differentiate mathematically.

$$dH = dU + PdV + VdP$$

The relational expression is as follows.

For example, in a solid, the amount of change is so small that dV≈0 can be considered, and there are almost no scenes where pressure changes are a concern, so dH = dU is often considered.

In other words, while saying enthalpy, it means that we are looking at real internal energy.

Of course, the VdP term has an effect in systems that apply excessive pressure.

On the other hand, in gases, both PdV and VdP change.

Actual machines are often operated under conditions of constant volume or constant pressure .

In the case of liquids, PdV≒0 as in solids, but VdP≠0.

A rough understanding would be fine.

## state and ph diagram

The ph diagram shows changes in the state of the refrigerant.

Convenient, isn’t it?

Now, what is the state of each refrigerant on the ph diagram?

There are three categories: supercooled liquid, saturated steam, and superheated steam .

The supercooled liquid is the so-called liquid part, and the superheated steam is the gas part.

Saturated vapor is a mixture of liquid and gas.

The side with the lower enthalpy H is the liquid.

This is easily understood by the fact that liquids are generally cooler than gases (lower U) and that liquids have a smaller volume than gases (lower V in PV) .

### constant pressure

Let me introduce an example of a simple state change on the ph diagram.

First, the constant pressure condition .

In refrigerators, changes in the evaporator and condenser are the constant pressure conditions.

Since the pressure is constant, the vertical axis is constant. Of course.

If the temperature is raised while the pressure is constant, the natural phenomenon that the state changes from liquid to gas can be read on the ph diagram.

The enthalpy H is

$$dH = dU + PdV + VdP = dU + PdV$$

becomes. dP=0, isn’t it?

In this example, we are considering the state change from liquid to gas, so dV is not 0.

It can be seen that dH is now proportional to temperature.

In liquids dV∝dT. It’s a world of thermal expansion.

In the case of gas, from the relationship of PV=nRT,

$$dH = dU + PdV = dU + nRdT$$

and is determined by the temperature T.

A monatomic molecule can be expressed as dU=3/2nRT, so dH=5/2nRT. For your reference.

### exchange of heat

Next, let’s look at the condition of no heat exchange.

I will describe it simply.

Thermodynamically, it is a phenomenon called adiabatic change, which corresponds to the change in the compressor.

In an environment where heat is not exchanged with the outside due to adiabatic changes, a sensory understanding that temperature rises as pressure rises is sufficient.

## refrigeration cycle temperature and ph diagram

Now, let’s superimpose a typical refrigeration cycle and a ph diagram.

The status of the refrigeration cycle is simply shown below.

Condition of refrigeration cycle

Temperature is only an example.

The evaporator is the most important function of the refrigerator and is the main part for cooling the process liquid.

This is probably about 5°C lower than the process liquid.

In this example, you can see that it is a refrigerator that cools the process liquid down to around -10°C.

More than an evaporator, the refrigerant is vaporized at the outlet.

This is transferred to a high pressure and high temperature state with a compressor .

The condenser cools and condenses the refrigerant.

Finally, when the expansion valve releases the pressure, it returns to the low temperature state.

As you can see from here, the refrigerant can be considered as a substance that undergoes a phase change between liquid and gas while obtaining the required temperature in the evaporator and condenser.

The greatest mission of refrigerants is to find a medium that satisfies these conditions while also satisfying the environment and safety. That’s how difficult it is.

## reference

There are many books about refrigerators.

If you don’t use it that much in practice, but want to understand it systematically, the following books are useful.  よくわかる 第1種・第2種 冷凍機械責任者試験 合格テキスト＋問題集 [ 高野 左千夫 ] created by Rinker
¥3,630(2023/09/28 02:35:25時点 楽天市場調べ-詳細)

## lastly

I explained the basics of the refrigeration cycle and the ph diagram.

A ph diagram is a good way to know the characteristics of a refrigerant and its state.

I don’t often do anything while looking at this diagram at the site, but I think I can discuss it on an equal footing with the refrigerator manufacturer if I have the knowledge.

It would be better to know the meaning of attaching foil. 