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Thermodynamics of Refrigeration Systems

by Aron Dobos (

Historical Aspects of Thermodynamic Theory and Practical Implementation

In the early nineteenth century, the abundance of industrializing spirit in the Western world resulted in the invention of various types of engines to power machinery. As the designs became more complicated and efficiency concerns arose, scientists began exploring possible relationships between heat and work. In 1824, Sadi Nicholas Leonard Carnot published a book that attempted to discover a mathematical expression for the amount of work produced by one kilogram of steam. Through his observations, temperature emerged as a gauge of attainable work. He likened temperature analogous to releasing water from varying heights. Water released from a greater height could produce more mechanical work than from a low one, just as a pot of water raised to a higher temperature could perform more work on its surroundings. These elementary observations later became embodied in the modernly accepted Second Law of Thermodynamics. Shortly after Carnot, Englishman James Joule experiments on heat transfer resulted in a statement of the First Law of Thermodynamics. His discoveries, published in 1850, explained how the seemingly "lost" heat in a system actually reemerged as physical work in varying forms.

The efforts of Carnot and Joule helped forward the invention of everyday heat transfer machines. In 1851, American physician Dr. John Gorrie invented a dense air compression machine, which was the first commercial product used for refrigeration and air conditioning. Soon after in 1853, Alexander Twining received a U.S. Patent for his machine that produced ice using vapor compression mechanisms. Further developments in refrigeration technology included the invention of cold-air refrigerators tailored especially for the international frozen meat trade circa 1870, and by World War II, air conditioning systems had become commonplace in department stores, restaurants, and hospitals. The modern day refrigerator also emerged as a common household appliance.

Basic Thermodynamic Definitions and Laws

An understanding of basic thermodynamic principles remains prerequisite to fully comprehending the refrigeration mechanisms used in the aforementioned modern appliances. Thermodynamics, in its simplest form, involves the relationships between heat, work, and properties of different types of systems. A few definitions beg mention:

The whole of thermodynamics can be described in the standard four rules of thermodynamics. Only the first three seem directly relevant to explaining the thermodynamic aspects of refrigeration, and are reproduced below:

The Zeroth Law: If body A and body B both have temperatures equal to that of body C, then the temperature of body A equals the temperature of body B. Note that this law seems extremely obvious, but still remains the basis for temperature measurement.

The First Law: Energy is conserved. Refer to the definition of an isolated system for a brief overview. In equation form, the first law takes the form:

Esystem + Esurroundings = 0

Energy and work are accounted for in the equation where q is heat and w is work:

E = q + w

The Second Law:

These definitions and laws are helpful in describing the functioning of a basic heat engine.

Heat Engines

Heat engines, technically speaking, are "continuously operating thermodynamic systems at the boundary of where there are heat and work interactions." (Spalding 203) Simply, a heat engine converts heat to work energy or vice versa.

An example of a common heat engine is a power plant. It consists of four main elements, a boiler, turbine, condenser, and feed pump, and the main circulating heat transfer entity is water. If we consider the power plant to be a closed system with its boundary enclosing the operating components, we can apply the First Law of Thermodynamics. The boiler burns a fuel source, causing a transfer of qcombustion heat to water inside, vaporizing it. The high pressure vapor enters the turbine, resulting in a work output of wturbine, and then leaves still as steam but at lower pressure and temperature. The vapor moves through the condenser where it condenses back into water, losing qcondensation heat to the surroundings. The water is pumped back into the boiler, requiring wpump work. Since E = q + w, and assuming a steady state of operation (E=0),

( qcombustion - qcondensation ) + ( wpump - wturbine ) = 0


qcombustion - qcondensation = wturbine - wpump

Generally, wpump is significantly less than the wturbine attained. However, qcondensation may be even more than two-thirds the magnitude of qcombustion, meaning that the total useful work obtained from the combustion of fuel is less than one third of the total work theoretically possible from a complete conversion of qcombustion. The second law of thermodynamics embodies the fact that no engine can be constructed that is 100% efficient.

Refrigeration systems are also heat engines, except running in reverse. The four components of a refrigeration cycle closely mirror those of the steam power plant, reversed. The steam engine's boiler (acting as an evaporator), becomes the refrigerator's condenser, the turbine (an expansion device) reverses and becomes a compressor, the condenser becomes evaporator, and the pump, a compressing device, is replaced by the throttle valve, a expansion device.

The form of the steam power plant's equation still holds true, except there is no physical work extracted from the system:

( qevaporation - qcondensation ) + ( 0 - wcompressor ) = 0


qevaporation - qcondensation = wcompressor

However, the reasons behind the seeming simplicity of refrigeration as a reversed heat engine remain elusive. Refrigeration at its core depends on the rather unintuitive phenomenon that expanding gases cool down. A brief digression into expansion work and its relation to the first law of thermodynamics might prove useful. Assume an ideal gas. If it is allowed to expand at constant temperature, the average kinetic energy of the gas molecules must also remain constant. Since no attraction exists between the molecules in an ideal gas, potential energy is zero. Thus, the net change of the system's total energy must be zero as well. If E = 0, and E = q + w, then:

q = -w

This means that if a gas performs work on its surroundings while expanding, it must absorb heat from the surroundings for E to be zero. For real world gases, E is not zero, but is still quite small.

Another way to observe this peculiarity is to consider that if the pressure over a liquid is lowered enough, the liquid will begin to evaporate since the liquid molecules may occupy a greater volume. Thus, the liquid will draw heat from the surroundings, since the total energy of the system remains constant while the kinetic energy of the molecules has increased, while the potential energy increase in a real world gas remains small. This allows for refrigeration to occur, since high pressure liquid refrigerant is sent through the expansion valve into a low pressure area where the liquid evaporates and expands, drawing heat from the surroundings. The implementation details of a refrigeration system will be discussed in greater detail shortly.

Both the power plant and refrigeration processes described are thus heat engines, and obey thermodynamic laws. A steam power plant is a direct heat engine since heat is converted to work, while a refrigeration system is a reversed heat engine: that is, work causes a heat transfer. Note well that the formal definition of a heat engine gives no indication of the direction of the process. For reference, thermodynamic schematics of both processes are indicated below:

Implementation of Vapor-Compression Refrigeration

Modern refrigerators are frequently based on the vapor-compression refrigeration cycle. Vapor compression systems center around the transfer of heat from a low-temperature region to a higher temperature region. Such a process requires an input of energy to move forward, and is usually supplied in the form of electricity powering. Refrigerators involve four main components: a compressor, condenser, throttling expansion valve, and an evaporator. The basic steps in the cycle are documented below.


1. The compressor powered by an external energy source (usually electricity) compresses the refrigerant gas that enters from the evaporator to a temperature that exceeds the surroundings of the condensing element. The refrigerant thus enters the condenser as a super-heated vapor, and the heat-exchanging coils and fins of the condenser dissipate the heat caused by pressurization to the surroundings.

2. The refrigerant slowly cools as it passes through the condenser coils, and condenses into liquid form. The pressure inside the condenser remains significant as the liquid refrigerant nears the throttling expansion valve.

3. The throttling expansion valve controls the rate at which the liquid refrigerant flows from the high pressure condenser element into the low pressure evaporator coil that resides with the subject of the refrigeration process. An expansion valve may be as simple as a capillary tube that simply restricts the flow of liquid into the evaporator. The pressure drop between the condenser and the evaporator causes the liquid refrigerant to immediately boil and evaporate, thus drawing heat from itself, resulting in a reduction of temperature of the evaporator coil.

4. The coil-fin arrangement of the evaporator is distinctly similar to the condenser, except that the evaporating gas inside the coil absorbs heat from the surroundings of the evaporator. The refrigerant then returns to the condenser, where the compression cycle begins once more. Note that the pressure difference required for cooling is maintained since the compressor continually sucks gas from the "out" end of the evaporator.

Below are pictures of actual refrigerator components.



Expansion Valve

Considerations for Refrigeration Systems

While the phase changes for water work will in a direct heat engine application like a power plant, the circulating heat transfer medium in a refrigerator must possess specific characteristics. The refrigerant must be recyclable: that is, it can be condensed and evaporated repeatedly. Furthermore, it must be able to easily absorb and expend heat at normal operating temperatures for the device. Water fails as an efficient refrigerant: its boiling point greatly exceeds normal operating conditions, and its freezing point also is too high for good cooling. As a result, special liquids emerged as refrigerants that possessed many of the desired characteristics:

(Sauer 38)

Early refrigerants included ammonia (NH3), sulfur dioxide (SO2), propane (C3H8), and methane (CH4). Each of these failed to meet all of the desired criteria necessary for safe refrigerator operation, especially for widespread consumer use. One of the first commercial liquids developed was refrigerant-12, more commonly known by the manufacturer's name (Freon-12, Arcton-12, etc). Chemically, it was dichlorodiflourmethane (CCl2F2). However, recent environmental studies have indicated that the chlorine in the liquid destroys ozone, and thus Freon-12 has been removed from the marketplace and succeeded by new refrigerant technology.

Information on Source Retrieval

My sudden desire to explore the thermodynamics of refrigeration systems arose the dank crevices of my mind late one night. Possessing but a cursory (or perhaps previously learned but forgotten) knowledge of thermodynamics, my first tasks involved wrapping my mind around a smorgasbord of general chemistry, general physics, and specialized texts. After replenishing my mental store of thermodynamic theory, I proceeded to investigate refrigerators specifically. Significant sources of information emerged from the Cornell Science Library, since most of the online resources I encountered failed to tackle the subject in a non-abbreviated manner.


Black, William Z., and James G. Hartley. Thermodynamics. New York: Harper & Row , 1985.

Brady, James E. General Chemistry: Principles and Structure. New York: John Wiley & Sons, 1990.

Brian, Marshall. Howstuffworks - How Refrigerators Work. 24 Oct. 2002

Cole, E. H., and D. B. Spalding. Engineering Thermodynamics. London: Edward Arnold Ltd, 1973.

Fitzpatrick, Richard. Classical Thermodynamics. University of Texas. 24 Oct. 2002

Harwood, William S., and Ralph H. Petrucci. General Chemistry: Principles and Modern Applications. 7th ed. Upper Saddle River, NJ: Prentice HaGeneral Chemistry: Principles and Modern Applications. 7th ed.ll, 1997.

Heat Transfer from Cold to Warmer Region. Georgia State University. 24 Oct. 2002

Howell, Ronald H., and Harry J. Sauer. Heat Pump Systems. New York: John Wiley & Sons, 1983.

Wieseler, Chad. Heat and Thermodynamics. Doane College. 24 Oct. 2002

Wrangham, D A. The Theory and Practice of Heat Engines. New York: The Macmillan Company, 1942.