principles of the refrigeration cycle

MCAST BTEC NATIONAL DIPLOMA IN BUILDING SERVICES ENGINEERING

Refrigeration Technology in Building Services Engineering

Principles of the Refrigeration Cycle

Joseph Gatt

Principles of the Refrigeration Cycle 19/11/2009

Joseph Gatt of 22

Contents

Section A - P.37.1 ...............................................................................................................................................4

1. Temperature Conversions ..........................................................................................................................4

2. Laws of Thermodynamics as Regards to Refrigeration and A/C ................................................................4

First Law of Thermodynamics .....................................................................................................................4

Second Law of Thermodynamics ................................................................................................................4

3. Heat Transfer ..............................................................................................................................................4

Conduction ..................................................................................................................................................4

Convection ...................................................................................................................................................5

Radiation .....................................................................................................................................................5

4. Pressure Conversions .................................................................................................................................5

5. Boiling Point of a Liquid Refrigerant ............................................................................................................5

6. Calculations .................................................................................................................................................6

7. Dew Point, Wet Bulb and Dry Bulb Temperatures ......................................................................................7

Dew Point Temperature ..............................................................................................................................7

Dry Bulb Temperature .................................................................................................................................7

Wet Bulb Temperature ................................................................................................................................7

Section B – P.37.2 ..............................................................................................................................................9

8. Boiling Points, Specific Heat Capacities, and Latent Heat Values for Various Refrigerants ......................9

9. Refrigerants and Their Impact on the Environment ....................................................................................9

CFC – ChloroFloroCarbons .........................................................................................................................9

HCFC – HydroChloroFloroCarbons ............................................................................................................9

HFC – HydroFloroCarbons ....................................................................................................................... 10

HC – HydroCarbons ................................................................................................................................. 10

Section C – P.37.3 ........................................................................................................................................... 11

10. Refrigeration Vapour Compression Cycle.............................................................................................. 11

Compressor .............................................................................................................................................. 11

Condenser ................................................................................................................................................ 11

Liquid Receiver ......................................................................................................................................... 12

Filter Dryer ................................................................................................................................................ 12

Expansion Valve ....................................................................................................................................... 12

Evaporator ................................................................................................................................................ 12


Joseph Gatt of 22

11. Compressors and Metering Devices ...................................................................................................... 12

Compressors ............................................................................................................................................ 12

Metering Devices ...................................................................................................................................... 14

Section C – M.37.1 .......................................................................................................................................... 17

About Hilton A660 Air Conditioning Laboratory Unit .................................................................................... 17

Procedure ................................................................................................................................................. 18

Pressure/Enthalpy Chart and Thermodynamic States of R134a ............................................................. 18

References ...................................................................................................................................................... 22


Joseph Gatt of 22

Section A - P.37.1

1. Temperature Conversions

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2. Laws of Thermodynamics as Regards to Refrigeration and A/C

First Law of Thermodynamics

Energy cannot be created nor destroyed. Energy can only be converted into other forms. The work done

in a system is equal to the heat supplied to the system. By means of mechanical energy and by the

process of heating or cooling, heat is transferred to and from its surroundings. Whether it becomes cool

or warm, the refrigerant returns to its original state, hence it will have the same amount of energy.

Second Law of Thermodynamics

Heat only travels from a warmer body to a cooler body. The process cannot be reversed. In a freezing

compartment, the heat energy stored in the food travels to the cooler refrigerant in order to emit the heat

away, until the food reach the same temperature of the compartment.

3. Heat Transfer

Heat transfer may be described as the transfer of thermal energy or heat exchange. Heat Transfer occurs

due to temperature difference between two bodies. Heat transfer process ends once the two bodies reach

thermal equilibrium. The greater the temperature difference, the greater the rate of heat transfer required.1

Heat transfer travels from a hotter body to a cooler body by means of three basic processes.

Conduction

Conduction is the transfer of heat energy through a material without the molecules of the material

changing their basic position.2 Conductive heat occurs in solids, liquids, and gases. Heat transfer by

conduction occurs in such way that two bodies are touching directly with each other. A practical example

is the heat conduction through copper pipes found in refrigerators. Metals are the best conductors of heat

and are widely used in building services engineering, such as heat pumps.

1 What is the Transfer of Heat? – C.Cassar & D. Privitera – Pg. 2

2 Environmental Science in Buildings – 4

th Edition - Randall McMullan – Pg. 17


Joseph Gatt of 22

Convection

Convection is the transfer of heat energy through a material by the bodily movement of particles.3

Convectional heat occurs in fluids (liquids or gases). Heat by convection is divided into two.

Natural Convection

A practical example of natural convection is a refrigerator. The food in the compartment cools by natural

convectional.

Forced Convection

Forced convectional current occurs by means of a mechanical source, such as pump or fan. The air

conditioner cools a room by means of a blower or fan, hence forced convection.

Radiation

Radiation is the transfer of heat energy by electromagnetic waves.4 Radiant heat occurs only from a heat

source (warm element). All materials radiate heat in relation with their temperature. A practical example of

radiant heat is the black surface of a compressor. Actually, bodies with black surfaces emit heat very

quickly.

4. Pressure Conversions

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5. Boiling Point of a Liquid Refrigerant

The temperature (boiling point) of a liquid refrigerant varies in relation to the pressure applied. The higher

the pressure, the higher is the boiling point. The following table illustrates the boiling point for R22.

Temperature (T) °C Pressure (p) Bar

-41 1

-25 2






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6. Calculations

Calculate the heat required to convert 15kg of ice at -10°C into steam at 100°C. The specific heat

capacities of water and ice are, respectively, 4,200J/kgK and 2,100J/kgK; the specific latent heat of fusion

of ice is 340,000J/kg, and the specific latent heat of vaporization of water is 2,300,000J/kg.

Data: m = 15 kg

T1 = -15 °C

T2 = 100 °C

Cwater = 4,200 J/kgK

Cice = 2,100 J/kgK

Cfusion = 340,000 J/kg

Cvaporisation = 2,300,000 J/kg

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Joseph Gatt of 22

7. Dew Point, Wet Bulb and Dry Bulb Temperatures

http://userpages.umbc.edu/~martins/PHYS650/Class8_PsychrometricChart-SeaLevel-SI.jpg

Dew Point Temperature

Dew point can also be referred as the saturated condition. It can be read from the saturation line in the

psychrometric chart. The higher the moisture content of air, the higher is the dew point. Dew point refers

to the water vapour when condenses out of the air, or saturated. At this point in time, the moisture content

remains in the air. The relative humidity is high if the dew point temperature is close to the air

temperature. The relative humidity is low if the dew point temperature is below the air temperature. Dry

bulb, wet bulb, and dew point temperatures are the same when the air is saturated.

Dry Bulb Temperature

Dry bulb measures the temperature of air. It is an indicator of heat content in air. Dry bulb can be

measured either with a normal thermometer or a sling thermometer. It can be read from the vertical lines

in the psychrometric chart.

Wet Bulb Temperature

Wet bulb temperature can also be described as the relative humidity. It is the temperature of adiabatic

saturation. Wet bulb measures the moisture content in air by means of cotton attached to the

thermometer. The cotton absorbs the moisture content in air and gives up some heat, hence reducing the

temperature. The higher the moisture content in air, the higher is the wet bulb temperature. The wet bulb

temperature is always lower than the dry bulb temperature, although both can be equalised when 100%

relative humidity is reached.


Joseph Gatt of 22

Dew point, wet bulb, and dry bulb temperatures do have a relationship between them as follows;

• The dew point temperature is lower than the dry bulb temperature, and the wet bulb temperature

is in between when the air is not saturated but contains some moisture.

• The difference between temperatures becomes less as the amount of moisture in the air

increases and the amount of evaporation decreases.

• The relative humidity becomes 100% when all the three temperatures are the same, hence the

air becomes saturated.


Joseph Gatt of 22

Section B – P.37.2

8. Boiling Points, Specific Heat Capacities, and Latent Heat Values for Various Refrigerants

9. Refrigerants and Their Impact on the Environment

The major worry at the time being is Global Warming. There is so much action in developing alternative

refrigerants due to their impact on the environment. The ideal refrigerant would be non-toxic, non-

flammable, and eco-friendly, but it does not exist. However, refrigerants are being classified in relation to

their impact on the Ozone Depletion Potential – ODP – and Global Warming Potential – GWP.

ODP is a single molecule potential of the refrigerant to destroy the Ozone Layer. R11 is being used as a

datum reference to all refrigerants. R11 has an ODP of 1.0. The less the value, the better is the refrigerant.

GWP is a measurement of effectiveness that a refrigerant has on Global Warming in relation to Carbon

Dioxide; where CO2 has a GWP of 1. The lower the value, the better is the refrigerant.

CFC – ChloroFloroCarbons

All refrigerant under this title contain chlorine. Due to their negative impact on the environment, these

refrigerants are obsolete. Such refrigerants are R11 (ODP 1, GWP 4000), and R12 (ODP 1, GWP 2400).

HCFC – HydroChloroFloroCarbons

R22 (ODP 0.1, GWP 1700) is an example under this classification. HCFC are less harmful than CFC

since they contain hydrogen. Additionally, HCFC are less stable in the atmosphere, hence dissipate more

rapidly.


Joseph Gatt of 22

HFC – HydroFloroCarbons

This classification indicates that the refrigerant is a mixture of Hydrogen, Fluorine, and Carbon. Such

refrigerant is R134a with 0 ODP and 1300 GWP.

HC – HydroCarbons

These contain 0 ODP as well as O GWP. In turn, these alone are highly flammable and fairly toxic. Such

refrigerants are R170, R290, R600a, R610a, R601.

The following table shows the environmental properties of various refrigerants

http://www.engineeringtoolbox.com/Refrigerants-Environment-Properties-d_1220.html


Joseph Gatt of 22

Section C – P.37.3

10. Refrigeration Vapour Compression Cycle

Compressor

The compressor is the heart of the refrigeration cycle, inserted between the condenser and the

evaporator. The refrigerant compressor serves as a heat pump; circulates the flow of refrigerant. The

compressor sucks the vapour from the evaporator. It compresses low pressure, low temperature vapour

into high pressure, high temperature vapour. The compressor is perfectly designed to suck the vapour

from the evaporator at the same rate it forms in the evaporator, which is called a condition of equilibrium.

Condenser

The condenser changes the refrigerant’s state from vapour to liquid by releases the heat away (outwards)

to a lower temperature (air or water). The heat emitted from the condenser is the same heat absorbed by

the evaporator and the heat created into the compressor.


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Liquid Receiver

The receiver is installed after the condenser, before the expansion valve. The liquid from the condenser is

collected in the receiver.

Filter Dryer

As the name implies, it filters any contaminates out of the refrigerant stream, and absorbs any moisture

content out of the liquid refrigerant. The filter dryer ensures that both contaminate and moisture will be

eliminated from the cycle, hence the cycle will be healthy.

Expansion Valve

The expansion has to be inserted in order to lower the pressure to the same level in the evaporator

pressure. It regulates the flow of the refrigerant. After passing through the expansion valve, the liquid

refrigerant begins to boil and evaporate (saturated).

Evaporator

The liquid refrigerant flow through the evaporator, where it absorbs the heat from the surroundings,

increase its boiling point, hence evaporates. Then the vapour will be sucked by the compressor where it

starts another cycle.

The compressor squeezes the vapour to pressurised vapour. The vapour flows through the condenser

where it changes its state to sub-cooled, pressurized liquid. This occurs because the vapour releases its

excessive heat due to temperature difference between the vapour and the medium. The liquid flows

through the receiver, the filter dryer which absorbs any contaminates and moisture content in the liquid

refrigerant, and to the expansion valve where it changes its state to low-pressure, saturated liquid. This

occurs because the liquid refrigerant starts to boil and evaporate after emerging in the expansion valve.

As a result, a sudden drop in pressure occurs. The liquid flows through the evaporator where it changes

its state to low-pressure vapour. This occurs because the liquid absorbs the heat due to temperature

difference between the liquid and medium. The vapour flows back to the compressor as low-pressure

vapour. The thermodynamic cycle is repeated again.

11. Compressors and Metering Devices

Compressors

http://en.wikipedia.org/wiki/Gas_compressor


Joseph Gatt of 22

Reciprocating Compressor

http://www.fscc-online.com/"Passing%20Gas"-article/passing_gas.html

Reciprocating compressors can be found as single or multi-stage, and mostly driven by electric motors.

They are widely used in most residential cooling/heating systems which employ the vapour

compression cycle. This type of compressor has an off-centre shaft which drives the crank shaft. The

crank shaft is connected to the rod which forces the cylinder to move back and forth. The cylinder is

completely tight in the outer cylinder by sealing rings. By its motion, the piston sucks and compresses

the refrigerant.

Suction is created in the cylinder as the piston moves downwards, because the pressure in the suction

line is greater than the pressure in the cylinder. The intake valve opens, allowing the refrigerant to

enter. The intake valve closes as the piston starts to move upwards, because the pressure in the

cylinder is now greater than the pressure in the suction line. The refrigerant is now being compressed,

increasing in pressure as the piston moves upwards. The exhaust valve opens, allowing the refrigerant

to flow out of the cylinder, because the pressure in the cylinder is greater than the pressure in the

discharge line. The cycle is then repeated as the piston reaches its upmost position and starts to move

downwards.

The reciprocating compressor is simply constructed, also maintaining a simple working principle.

Financially speaking, it is the cheapest compressor found on the market. Like everything else,

reciprocating compressors have drawbacks. Those have many moving parts that might result in

efficiency and heat losses. Additionally, all the moving parts tend to vibrate, making a lot of noise. The

valves are brittle in such way that those will be damaged if droplets of liquid enter the cylinder, because

the liquid is not compressible.


Joseph Gatt of 22

Centrifugal Compressor

http://en.wikipedia.org/wiki/Gas_compressor

Centrifugal compressors usually are used widely in various industries where to handling large volume of

low pressure gases or air.

The centrifugal compressor consists of rotating impellers arranged in series, which are closed in

housing. These compressors use centrifugal force in order to compress the refrigerant. The gas flows

from the larger impeller to the smallest one, increasing in velocity and in pressure. The more stages of

impellers, the more is the velocity and pressure of the gas. The centrifugal force depends a lot on the

pitch of the impeller. Moreover, in order to achieve high output pressures, these rotate at very high

revolutions per minutes, in the range of 3000-18000 r.p.m.5

Centrifugal compressors have few moving parts since the impellors rotate on a common shaft, hence

very efficient. Damage might not occur even if liquid refrigerant enters the impellors. If the shaft is a bit

off-centred during its rotation, all the impellers will be damaged and have to be scrapped, and these

cost a lot of money.

Metering Devices

Capillary Tube

http://www.shineyear.com.tw/products/p6/900m.png

The capillary tube is commonly used in refrigeration equipment, mostly in the domestic fridges and air

conditioners. It is a normal coiled tube with a small internal diameter, normally made of copper.

5 Compressors – D. Privitera & C. Cassar


Joseph Gatt of 22

Capillary tubes control the flow of the liquid refrigerant, with no change in temperature along the tube. It

causes the high pressure liquid refrigerant to back up at its inlet, in order to drop it to a lower pressure

liquid at its outlet. It is situated between the condenser and the evaporator. The capacity of the tube is

affected by its length, internal diameter, and pressure.

Capillary tubes are very cheap and simply designed. They have no moving parts and requires low

starting torque compressor.

Thermostatic Expansion Valve

http://www.e-refrigeration.com/index.php?page=metering-device

The thermostatic expansion valve – TXV - is a very common type of metering device. It is widely used

for both commercial and industrial applications due to its high-efficiency. The TXV is practically

adaptable to any type of refrigeration application. TXVs also drop the pressure in the system. It controls

the flow of liquid refrigerant and is the only metering device that stops the liquid refrigerant from entering

in the compressor. This might happen because the liquid refrigerant tends not to boil all off in the

evaporator. The valve operates on three pressures; P1 = bulb pressure, P2 = evaporator pressure, and

P3 = spring pressure. The spring is used to set the superheat.

http://www.hvacmechanic.com/txv.htm

The valve is attached with a sensing bulb by means of a capillary tube filled with refrigerant. The bulb is

mounted on the suction line at the exit of the evaporator. It adjusts how much refrigerant enters in the


Joseph Gatt of 22

evaporator because it senses the temperature difference between the inlet and outlet of the evaporator.

The flow rate in the evaporator must be equal to the rate at which the refrigerant is being boiled off in

the evaporator. Technically speaking, the bulb causes the valve to open or close against the spring

pressure as the temperature on the bulb increases or decreases.

Thermostatic expansion valves are often more efficient than other valves as they control the liquid

content in the refrigerant. In turn, TXVs have many moving parts that they might not give the utmost

performance.


Joseph Gatt of 22

Section C – M.37.1

About Hilton A660 Air Conditioning Laboratory Unit

http://www.p-a-hilton.co.uk/English/Products/Air_Conditioning/air_conditioning.html

A fully modular and upgradeable system enabling the study of air conditioning from the basic principles of

psychrometry, through recirculation and the use of psychrometric and pressure-enthalpy charts using

manual instrumentation, to PID control and computer linking. In addition an environmental chamber is

available for research and student project work. The following upgrade modules can be factory fitted or

purchased individually and installed at a later date by the end user to enhance a teaching programme:

• Digital temperature upgrade;

• Re-circulating duct upgrade;

• PID control upgrade;

• Computer linked upgrade; and

• Environmental chamber.6

6 http://www.p-a-hilton.co.uk/English/Products/Air_Conditioning/air_conditioning.html


Joseph Gatt of 22

The unit consists of; (please refer to the attached block diagram at the end)

• Positive displacement, reciprocating, hermetic compressor equipped with pressure gauge and

thermometer at its outlet;

• Condensing units which includes liquid receiver, filter dryer, pressure gauge and thermometer at its

outlet;

• Glass flow-meter;

• Evaporating unit which includes TXV metering device, pressure gauge and thermometer at its outlet;

• Air chamber which is equipped with two thermometers and variable blower at its inlet, pre-heaters,

two thermometers, evaporator, two thermometers, re-heaters, and two thermometers;

• Steam cylinder; and

• Charged with R134a.

Procedure

We set the equipment on cooling mode, powered the unit and left it to stabilise for about 15 minutes. In

order to determine the superheat, we had to take a reading (H1) from the pressure gauge located at the

evaporator’s outlet. The pressure was 1 Bar (gauge pressure), hence + 1 (atmospheric pressure) = 2 Bar

(absolute pressure). We then checked the boiling point of the R134a at 2 Bar pressure from the PH chart,

which is -10°C. Another reading (H1’) was taken from the thermometer at the evaporator’s outlet, which

was -4°C. Hence the superheat into the compressor was 10 – 4 = +6°C.

The sub-cooling had to be calculated as well in order to plot the refrigerant’s process cycle onto the PH

chart. We took a reading (H3) from the pressure gauge at the condenser’s outlet, which was 9 Bar

(absoulute pressure). From the PH chart, the boiling temperature of R134a at 9 Bar is 36°C. (H3’) was

then taken from the thermometer at the condenser’s outlet, which was 30°C. Hence, the sub-cooling was

-6°C.

Pressure/Enthalpy Chart and Thermodynamic States of R134a

(Please refer to the attached PH chart at the end)

The process cycle of the Refrigerant 134a starts at point H1, at the evaporator’s outlet and in the suction

line. It is also pin-pointed on the saturation line where it starts the superheat. At this point in time, the

refrigerant is at low-pressure saturated vapour state, having a saturated temperature and pressure.

Moreover, the refrigerant has a boiling point temperature (T) of -9.792 °C, pressure (p) of 2.012 Bar,

enthalpy (h) of 391.49 kJ/kg, specific volume (v) of 0.09884 m3/kg, and an entropy (s) of 1.729 kJ/kgK.

The refrigerant flows to point H1’, at the compressor’s inlet but still in the suction line. At this point in time

the gas has a T of -3.898°C, p of 2.012 Bar, h of 396.63 kJ/kg, v of 0.10179 m3/kg, and an s of 1.748

kJ/kgK. Note that there is no change in pressure. Here, the refrigerant is superheated by 6 °C (9.792 –

3.898), which means that the gas is heated to a higher temperature than the saturated temperature. The


Joseph Gatt of 22

gas is now in the vapour region at low-pressure state. The energy in the suction line is 5.22 kJ/kg (396.63

– 391.49).

R134a is now at point H2 after passing through the compressor. It is at the compressor’s outlet in the

discharge line. The working fluid is still in the vapour region; only this time with a higher pressure and

temperature. Actually, T=47.274°C, p=9.174Bar, h=428.93kJ/kg, v=0.002377, and s=1.748kJ/kgK. Note

that the temperature difference is 47.274 - -3.898 = 51.172°C, and the pressure difference is now 9.174 –

2.012 = 7.162Bar. The work done by the compressor is 428.93 – 396.63 = 32.3kJ/kg.

Having a T of 36.225°C, p of 9.174Bar, h of 416.45kJ/kg, v of 0.02211m3/kg, and an s of 1.708kJ/kgK, the

refrigerant is now at point H2’. It is pin-pointed on the saturation line, at the condenser’s inlet, and still in

the discharge line. Here the refrigerant has saturated temperature and pressure, with no change in

pressure. It is noted that at this point in time the refrigerant is de-superheated due to heat losses from the

discharge line. Actually, the heat lost is 47.274 – 36.225 = 11.049°C. The energy in the discharge line is

416.45 – 428.93 = 12.48kJ/kg.

H3 is the next point, where the refrigerant passed through the condenser, hence the mixture zone. It is

also pin-pointed on the saturation line, having saturation temperature and pressure, and starting the sub-

cooling. Note that the refrigerant had neither a change in temperature or in pressure, but had a change in

state (latent heat). It is now condensed liquid. T=36.225°C, p=9.174Bar, h=250.51kJ/kg, v=0.00395m3/kg,

and s=1.172kJ/kgK. The energy by the condenser is 416.45 – 250.51 = 165.94kJ/kg.

The refrigerant is now at point H3, before entering the metering device. It is in the liquid region, having a

T of 29.640°C, p of 9.174Bar, h of 240.96kJ/kg, and an s of 1.141kJ/kgK. There is no change in pressure

at this point in time, but having a lower temperature. This means that the refrigerant is sub-cooled,

therefore cooled to a lower temperature than the saturated temperature. The energy in the line is 250.51

– 240.96 = 9.55kJ/kg.

H4 is the last point of the cycle, where the refrigerant is in the mixture zone, hence saturated liquid.

Where T= -9.714°C, p=2.030Bar, h=240.96kJ/kg, and s=1.157kJ/kgK. It is now low-pressure liquid due to

a sudden drop in pressure after passing through the expansion valve. A sudden drop in temperature also

occurred. Note that the energy in the metering device is 0, thus constant enthalpy. It shall also be noted

that the pressure drop is 9.174 – 2.030 = 7.144Bar. Therefore, the resultant pressure output from the

compressor is 7Bar continuously.

In order to determine the energy in the evaporator to change the sate from liquid to gas, the enthalpy of

point H4 has to be subtracted by the enthalpy of point H1, which gives 150.53kJ/kg (391.49 – 240.96).

After point H4, the refrigerant flows to point H1 where it starts the process cycle again.


Joseph Gatt of 22


Joseph Gatt of 22

References

• http://www.engineeringtoolbox.com/dry-wet-bulb-dew-point-air-d_682.html

• http://www.brighthub.com/engineering/mechanical/articles/39619.aspx

• http://www.tpub.com/content/construction/14279/css/14279_241.htm

• http://en.wikipedia.org/wiki/Laws_of_thermodynamics

• http://www.comfort.uk.com/refrigerants.htm

• http://www.memagazine.org/backissues/membersonly/october98/features/refrig/global.html

• Refrigerants – C. Cassar & D. Privitera

• Introduction to HVAC and Refigeration – C. Cassar & D. Privitera

• http://www.engineeringtoolbox.com/Refrigerants-Environment-Properties-d_1220.html

• The refrigeration Circuit – C. Cassar/ D. Privitera

• http://www.answers.com/topic/piston

• http://en.wikipedia.org/wiki/Gas_compressor

• Compressors – D. Privitera & C. Cassar

• http://www.answers.com/topic/centrifugal-compressor

• http://www.central-air-conditioner-and-refrigeration.com/thermostatic_expansion_valve.html

• http://www.longviewweb.com/expansio.htm

• http://www.crtech.com/txvResponse.html

• http://en.wikipedia.org/wiki/Thermal_expansion_valve

• http://www.hvacmechanic.com/txv.htm

• http://www.e-refrigeration.com/index.php?page=metering-device

• http://www.rparts.com/Catalog/Major_Components/filterdryers/filter_dryers.asp

• http://www.p-a-hilton.co.uk/English/Products/Air_Conditioning/air_conditioning.html

principles of the refrigeration cycle

Documents

wet bulb temperature

dew point temperature

temperature conversions

law of thermodynamics

dry bulb temperatures

heat transfer

laws of thermodynamics

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