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In thermodynamics, the exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir, reaching maximum entropy. When the surroundings are the reservoir, exergy is the potential of a system to cause a change as it achieves equilibrium with its environment. Exergy is the energy that is available to be used. After the system and surroundings reach equilibrium, the exergy is zero. Determining exergy was also the first goal of thermodynamics. The term "exergy" was coined in 1956 by Zoran Rant (1904–1972) by using the Greek ex and ergon meaning "from work" [1] [3] , but the concept was developed by J. Willard Gibbs in 1873. [4]

Thermodynamics branch of physics concerned with heat, work, temperature, and thermal or internal energy

Thermodynamics is the branch of physics that deals with heat and temperature, and their relation to energy, work, radiation, and properties of matter. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering, but also in fields as complex as meteorology.

Thermodynamic process energetic development of a thermodynamic system proceeding from an initial state to a final state

Classical thermodynamics considers three main kinds of thermodynamic process by change in a system, cycles in a system, and flow processes.

Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.


Energy is neither created nor destroyed during a process. Energy changes from one form to another (see First Law of Thermodynamics ). In contrast, exergy is always destroyed when a process is irreversible, for example loss of heat to the environment (see Second Law of Thermodynamics ). This destruction is proportional to the entropy increase of the system together with its surroundings (see Entropy production ). The destroyed exergy has been called anergy. [2] For an isothermal process, exergy and energy are interchangeable terms, and there is no anergy.

Reversible process (thermodynamics) process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, while not increasing entropy

In thermodynamics, a reversible process is a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings. Throughout the entire reversible process, the system is in thermodynamic equilibrium with its surroundings. Having been reversed, it leaves no change in either the system or the surroundings. Since it would take an infinite amount of time for the reversible process to finish, perfectly reversible processes are impossible. However, if the system undergoing the changes responds much faster than the applied change, the deviation from reversibility may be negligible. In a reversible cycle, a cyclical reversible process, the system and its surroundings will be returned to their original states if one half cycle is followed by the other half cycle.

Entropy physical property of the state of a system, measure of disorder

In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system. Entropy expresses the number Ω of different configurations that a system defined by macroscopic variables could assume. Under the assumption that each microstate is equally probable, the entropy is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally,

Entropy production

Entropy production is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anaelastic deformation of solids, and any irreversible thermodynamic cycle, including thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners.


Exergy is a combination property [3] of a system and its environment because it depends on the state of both the system and environment. The exergy of a system in equilibrium with the environment is zero. Exergy is neither a thermodynamic property of matter nor a thermodynamic potential of a system. Exergy and energy both have units of joules. The internal energy of a system is always measured from a fixed reference state and is therefore always a state function. Some authors define the exergy of the system to be changed when the environment changes, in which case it is not a state function. Other writers prefer[ citation needed ] a slightly alternate definition of the available energy or exergy of a system where the environment is firmly defined, as an unchangeable absolute reference state, and in this alternate definition exergy becomes a property of the state of the system alone.

Thermodynamic potential scalar physical quantities representing system states

A thermodynamic potential is a scalar quantity used to represent the thermodynamic state of a system. The concept of thermodynamic potentials was introduced by Pierre Duhem in 1886. Josiah Willard Gibbs in his papers used the term fundamental functions. One main thermodynamic potential that has a physical interpretation is the internal energy U. It is the energy of configuration of a given system of conservative forces and only has meaning with respect to a defined set of references. Expressions for all other thermodynamic energy potentials are derivable via Legendre transforms from an expression for U. In thermodynamics, external forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mount Everest than it would at the bottom of the Mariana Trench, the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible. In a large system under even homogeneous external force, like the earth atmosphere under gravity, the intensive parameters should be studied locally having even in equilibrium different values in different places far from each other (see thermodynamic models of troposphere].

The joule is a derived unit of energy in the International System of Units. It is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one metre. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

Internal energy energy contained in a system, excluding energy due to its position as a body in external force fields or its overall motion

In thermodynamics, the internal energy of a system is the total energy contained within the system. It is the energy necessary to create or prepare the system in any given state, but does not include the kinetic energy of motion of the system as a whole, nor the potential energy of the system as a whole due to external force fields which includes the energy of displacement of the system's surroundings. It keeps account of the gains and losses of energy of the system that are due to changes in its internal state.

However, from a theoretical point of view, exergy may be defined without reference to any environment. If the intensive properties of different finitely extended elements of a system differ, there is always the possibility to extract mechanical work from the system. [4] [5]

The term exergy is also used, by analogy with its physical definition, in information theory related to reversible computing. Exergy is also synonymous with: availability, available energy, exergic energy, essergy (considered archaic), utilizable energy, available useful work, maximum (or minimum) work, maximum (or minimum) work content, reversible work, and ideal work.

Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper titled "A Mathematical Theory of Communication". Its impact has been crucial to the success of the Voyager missions to deep space, the invention of the compact disc, the feasibility of mobile phones, the development of the Internet, the study of linguistics and of human perception, the understanding of black holes, and numerous other fields.

Reversible computing is a model of computing where the computational process to some extent is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary condition for reversibility is that the relation of the mapping from (nonzero-probability) states to their successors must be one-to-one. Reversible computing is a form of unconventional computing.

The exergy destruction of a cycle is the sum of the exergy destruction of the processes that compose that cycle. The exergy destruction of a cycle can also be determined without tracing the individual processed by considering the entire cycle as a single process and using one of the exergy destruction equations.

Mathematical description

An application of the second law of thermodynamics

Exergy uses system boundaries in a way that is unfamiliar to many. We imagine the presence of a Carnot engine between the system and its reference environment even though this engine does not exist in the real world. Its only purpose is to measure the results of a "what-if" scenario to represent the most efficient work interaction possible between the system and its surroundings.

Carnot heat engine heat engine

A Carnot heat engine is a theoretical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded upon by Benoît Paul Émile Clapeyron in 1834 and mathematically explored by Rudolf Clausius in 1857 from which the concept of entropy emerged.

If a real-world reference environment is chosen that behaves like an unlimited reservoir that remains unaltered by the system, then Carnot's speculation about the consequences of a system heading towards equilibrium with time is addressed by two equivalent mathematical statements. Let B, the exergy or available work, decrease with time, and Stotal, the entropy of the system and its reference environment enclosed together in a larger isolated system, increase with time:

For macroscopic systems (above the thermodynamic limit), these statements are both expressions of the second law of thermodynamics if the following expression is used for exergy:

where the extensive quantities for the system are: U = Internal energy, V = Volume, and Ni = Moles of component i

The intensive quantities for the surroundings are: PR = Pressure, TR = temperature, μi, R = Chemical potential of component i

Individual terms also often have names attached to them: is called "available PV work", is called "entropic loss" or "heat loss" and the final term is called "available chemical energy."

Other thermodynamic potentials may be used to replace internal energy so long as proper care is taken in recognizing which natural variables correspond to which potential. For the recommended nomenclature of these potentials, see (Alberty, 2001) . Equation (2) is useful for processes where system volume, entropy, and number of moles of various components change because internal energy is also a function of these variables and no others.

An alternative definition of internal energy does not separate available chemical potential from U. This expression is useful (when substituted into equation (1)) for processes where system volume and entropy change, but no chemical reaction occurs:

In this case a given set of chemicals at a given entropy and volume will have a single numerical value for this thermodynamic potential. A multi-state system may complicate or simplify the problem because the Gibbs phase rule predicts that intensive quantities will no longer be completely independent from each other.

A historical and cultural tangent

In 1848, William Thomson, 1st Baron Kelvin, asked (and immediately answered) the question

Is there any principle on which an absolute thermometric scale can be founded? It appears to me that Carnot’s theory of the motive power of heat enables us to give an affirmative answer.

With the benefit of the hindsight contained in equation (3), we are able to understand the historical impact of Kelvin's idea on physics. Kelvin suggested that the best temperature scale would describe a constant ability for a unit of temperature in the surroundings to alter the available work from Carnot's engine. From equation (3):

Rudolf Clausius recognized the presence of a proportionality constant in Kelvin's analysis and gave it the name entropy in 1865 from the Greek for "transformation" because it describes the quantity of energy lost during transformation from heat to work. The available work from a Carnot engine is at its maximum when the surroundings are at a temperature of absolute zero.

Physicists then, as now, often look at a property with the word "available" or "utilizable" in its name with a certain unease. The idea of what is available raises the question of "available to what?" and raises a concern about whether such a property is anthropocentric. Laws derived using such a property may not describe the universe but instead describe what people wish to see.

The field of statistical mechanics (beginning with the work of Ludwig Boltzmann in developing the Boltzmann equation) relieved many physicists of this concern. From this discipline, we now know that macroscopic properties may all be determined from properties on a microscopic scale where entropy is more "real" than temperature itself (see Thermodynamic temperature ). Microscopic kinetic fluctuations among particles cause entropic loss, and this energy is unavailable for work because these fluctuations occur randomly in all directions. The anthropocentric act is taken, in the eyes of some physicists and engineers today, when someone draws a hypothetical boundary, in fact he says: "This is my system. What occurs beyond it is surroundings." In this context, exergy is sometimes described as an anthropocentric property, both by those who use it and those who don't. Entropy is viewed as a more fundamental property of matter.

In the field of ecology, the interactions among systems (mostly ecosystems) and their manipulation of exergy resources is of primary concern. With this perspective, the answer of "available to what?" is simply: "available to the system", because ecosystems appear to exist in the real world. With the viewpoint of systems ecology, a property of matter like absolute entropy is seen as anthropocentric because it is defined relative to an unobtainable hypothetical reference system in isolation at absolute zero temperature. With this emphasis on systems rather than matter, exergy is viewed as a more fundamental property of a system, and it is entropy that may be viewed as a co-property of a system with an idealized reference system.

A potential for every thermodynamic situation

In addition to and , the other thermodynamic potentials are frequently used to determine exergy. For a given set of chemicals at a given entropy and pressure, enthalpy H is used in the expression:

For a given set of chemicals at a given temperature and volume, Helmholtz free energy A is used in the expression:

For a given set of chemicals at a given temperature and pressure, Gibbs free energy G is used in the expression:

The potentials A and G are utilized for a constant temperature process. In these cases, all energy is free to perform useful work because there is no entropic loss. A chemical reaction that generates electricity with no associated change in temperature will also experience no entropic loss. (See Fuel cell.) This is true of every isothermal process. Examples are gravitational potential energy, kinetic energy (on a macroscopic scale), solar energy, electrical energy, and many others. If friction, absorption, electrical resistance or a similar energy conversion takes place that releases heat, the impact of that heat on thermodynamic potentials must be considered, and it is this impact that decreases the available energy.

Chemical exergy

Similar to thermomechanical exergy, chemical exergy depends on the temperature and pressure of a system as well as on the composition. The key difference in evaluating chemical exergy versus thermomechanical exergy is that thermomechanical exergy does not take into account the difference in a system and environment's chemical composition. If the temperature, pressure or composition of a system differs from the environment's state, then the overall system will have exergy. [6]

The definition of chemical exergy resembles the standard definition of thermomechanical exergy, but with a few differences. Chemical exergy is defined as the maximum work that can be obtained when the considered system is brought into reaction with reference substances present in the environment. [7] Defining the exergy reference environment is one of the most vital parts of analyzing chemical exergy. In general, the environment is defined as the composition of air at 25 °C and 1 atm of pressure. At these properties air consists of N2=75.67%, O2=20.35%, H2O(g)=3.12%, CO2=0.03% and other gases=0.83%. [6] These molar fractions will become of use when applying Equation 8 below.

CaHbOc is the substance that is entering a system that one wants to find the maximum theoretical work of. By using the following equations, one can calculate the chemical exergy of the substance in a given system. Below, Equation 8 uses the Gibbs function of the applicable element or compound to calculate the chemical exergy. Equation 9 is similar but uses standard molar chemical exergy, which scientists have determined based on several criteria, including the ambient temperature and pressure that a system is being analyzed and the concentration of the most common components. [8] These values can be found in thermodynamic books or in online tables. [9]

Important equations


Gibbs function of the specific substance in the system at . ( refers to the substance that is entering the system)

The Universal gas constant (8.314462 J/mol•K) [10]

Temperature that the system is being evaluated at in absolute temperature

The molar fraction of the given substance in the environment i.e. air


The standard molar chemical exergy taken from a table for the specific conditions that the system is being evaluated

Equation 9 is more commonly used due to the simplicity of only having to look up the standard chemical exergy for given substances. Using a standard table works well for most cases, even if the environment conditions vary slightly, the difference is most likely negligible.

Total exergy

After finding the chemical exergy in a given system, one can find the total exergy by adding it to the thermomechanical exergy. Depending on the situation, the amount of chemical exergy added can be very small. If the system being evaluated involves combustion, the amount of chemical exergy is very large and necessary to find the total exergy of the system.


Irreversibility accounts for the amount of exergy destroyed in a closed system, or in other words, the wasted work potential. This is also called dissipated energy. For highly efficient systems, the value of I, is low, and vice versa. The equation to calculate the Irreversibility of a closed system, as it relates to the exergy of that system, is as follows: [11]

where: is the entropy generated by the system processes.

If then there are irreversibilities present in the system. If then there are no irreversibilities present in the system.

The value of I, the irreversibility, can not be negative, as it is not a property. On the contrary, the availability is a different story, which is a property of the system.

Exergy analysis is based on the relation between the actual work and the maximal work, that could be obtained in the reversible process:

The first term at the right part is related with the difference in exergy at inlet and outlet of the system: [11]

For an Isolated System:

No heat or work interactions with the surroundings occur, and therefore, there are no transfers of availability between the system and its surroundings. The change in exergy of an isolated system is equivalent, but opposite the value for irreversibility of that system.


Applying equation (1) to a subsystem yields:

This expression applies equally well for theoretical ideals in a wide variety of applications: electrolysis (decrease in G), galvanic cells and fuel cells (increase in G), explosives (increase in A), heating and refrigeration (exchange of H), motors (decrease in U) and generators (increase in U).

Utilization of the exergy concept often requires careful consideration of the choice of reference environment because, as Carnot knew, unlimited reservoirs do not exist in the real world. A system may be maintained at a constant temperature to simulate an unlimited reservoir in the lab or in a factory, but those systems cannot then be isolated from a larger surrounding environment. However, with a proper choice of system boundaries, a reasonable constant reservoir can be imagined. A process sometimes must be compared to "the most realistic impossibility," and this invariably involves a certain amount of guesswork.

Engineering applications

Application of exergy to unit operations in chemical plants was partially responsible for the huge growth of the chemical industry during the 20th century.[ citation needed ] During this time it was usually called availability or available work.

As a simple example of exergy, air at atmospheric conditions of temperature, pressure, and composition contains energy but no exergy when it is chosen as the thermodynamic reference state known as ambient. Individual processes on Earth such as combustion in a power plant often eventually result in products that are incorporated into the atmosphere, so defining this reference state for exergy is useful even though the atmosphere itself is not at equilibrium and is full of long and short term variations.

If standard ambient conditions are used for calculations during chemical plant operation when the actual weather is very cold or hot, then certain parts of a chemical plant might seem to have an exergy efficiency of greater than 100% and without taking into account the non-standard atmospheric temperature variation can give an impression of being a perpetual motion machine. Using actual conditions will give actual values, but standard ambient conditions are useful for initial design calculations.

One goal of energy and exergy methods in engineering is to compute what comes into and out of several possible designs before a factory is built. Energy input and output will always balance according to the First Law of Thermodynamics or the energy conservation principle. Exergy output will not balance the exergy input for real processes since a part of the exergy input is always destroyed according to the Second Law of Thermodynamics for real processes. After the input and output are completed, the engineer will often want to select the most efficient process. An energy efficiency or first law efficiency will determine the most efficient process based on wasting as little energy as possible relative to energy inputs. An exergy efficiency or second-law efficiency will determine the most efficient process based on wasting and destroying as little available work as possible from a given input of available work.

Applications in natural resource utilization

In recent decades, utilization of exergy has spread outside of physics and engineering to the fields of industrial ecology, ecological economics, systems ecology, and energetics. Defining where one field ends and the next begins is a matter of semantics, but applications of exergy can be placed into rigid categories.

Researchers in ecological economics and environmental accounting perform exergy-cost analyses in order to evaluate the impact of human activity on the current natural environment. As with ambient air, this often requires the unrealistic substitution of properties from a natural environment in place of the reference state environment of Carnot. For example, ecologists and others have developed reference conditions for the ocean and for the Earth's crust. Exergy values for human activity using this information can be useful for comparing policy alternatives based on the efficiency of utilizing natural resources to perform work. Typical questions that may be answered are:

Does the human production of one unit of an economic good by method A utilize more of a resource's exergy than by method B?
Does the human production of economic good A utilize more of a resource's exergy than the production of good B?
Does the human production of economic good A utilize a resource's exergy more efficiently than the production of good B?

There has been some progress in standardizing and applying these methods.

Measuring exergy requires the evaluation of a system’s reference state environment. [12] With respect to the applications of exergy on natural resource utilization, the process of quantifying a system requires the assignment of value (both utilized and potential) to resources that are not always easily dissected into typical cost-benefit terms. However, to fully realize the potential of a system to do work, it is becoming increasingly imperative to understand exergetic potential of natural resources, [13] and how human interference alters this potential.

Referencing the inherent qualities of a system in place of a reference state environment [12] is the most direct way that ecologists determine the exergy of a natural resource. Specifically, it is easiest to examine the thermodynamic properties of a system, and the reference substances [14] that are acceptable within the reference environment. [14] This determination allows for the assumption of qualities in a natural state: deviation from these levels may indicate a change in the environment caused by outside sources. There are three kinds of reference substances that are acceptable, due to their proliferation on the planet: gases within the atmosphere, solids within the Earth’s crust, and molecules or ions in seawater. [12] By understanding these basic models, it’s possible to determine the exergy of multiple earth systems interacting, like the effects of solar radiation on plant life. [15] These basic categories are utilized as the main components of a reference environment when examining how exergy can be defined through natural resources.

Other qualities within a reference state environment include temperature, pressure, and any number of combinations of substances within a defined area. [12] Again, the exergy of a system is determined by the potential of that system to do work, so it is necessary to determine the baseline qualities of a system before it is possible to understand the potential of that system. The thermodynamic value of a resource can be found by multiplying the exergy of the resource by the cost of obtaining the resource and processing it. [12]

Today, it is becoming increasingly popular to analyze the environmental impacts of natural resource utilization, especially for energy usage. [16] To understand the ramifications of these practices, exergy is utilized as a tool for determining the impact potential of emissions, fuels, and other sources of energy. [16] Combustion of fossil fuels, for example, is examined with respect to assessing the environmental impacts of burning coal, oil, and natural gas. The current methods for analyzing the emissions from these three products can be compared to the process of determining the exergy of the systems affected; specifically, it is useful to examine these with regard to the reference state environment of gases within the atmosphere. [13] In this way, it is easier to determine how human action is affecting the natural environment.

Applications in sustainability

In systems ecology, researchers sometimes consider the exergy of the current formation of natural resources from a small number of exergy inputs (usually solar radiation, tidal forces, and geothermal heat). This application not only requires assumptions about reference states, but it also requires assumptions about the real environments of the past that might have been close to those reference states. Can we decide which is the most "realistic impossibility" over such a long period of time when we are only speculating about the reality?

For instance, comparing oil exergy to coal exergy using a common reference state would require geothermal exergy inputs to describe the transition from biological material to fossil fuels during millions of years in the Earth's crust, and solar radiation exergy inputs to describe the material's history before then when it was part of the biosphere. This would need to be carried out mathematically backwards through time, to a presumed era when the oil and coal could be assumed to be receiving the same exergy inputs from these sources. A speculation about a past environment is different from assigning a reference state with respect to known environments today. Reasonable guesses about real ancient environments may be made, but they are untestable guesses, and so some regard this application as pseudoscience or pseudo-engineering.

The field describes this accumulated exergy in a natural resource over time as embodied energy with units of the "embodied joule" or "emjoule".

The important application of this research is to address sustainability issues in a quantitative fashion through a sustainability measurement:

Does the human production of an economic good deplete the exergy of Earth's natural resources more quickly than those resources are able to receive exergy?
If so, how does this compare to the depletion caused by producing the same good (or a different one) using a different set of natural resources?

Assigning one thermodynamically obtained value to an economic good

A technique proposed by systems ecologists is to consolidate the three exergy inputs described in the last section into the single exergy input of solar radiation, and to express the total input of exergy into an economic good as a solar embodied joule or sej. (See Emergy ) Exergy inputs from solar, tidal, and geothermal forces all at one time had their origins at the beginning of the solar system under conditions which could be chosen as an initial reference state, and other speculative reference states could in theory be traced back to that time. With this tool we would be able to answer:

What fraction of the total human depletion of the Earth's exergy is caused by the production of a particular economic good?
What fraction of the total human and non-human depletion of the Earth's exergy is caused by the production of a particular economic good?

No additional thermodynamic laws are required for this idea, and the principles of energetics may confuse many issues for those outside the field. The combination of untestable hypotheses, unfamiliar jargon that contradicts accepted jargon, intense advocacy among its supporters, and some degree of isolation from other disciplines have contributed to this protoscience being regarded by many as a pseudoscience. However, its basic tenets are only a further utilization of the exergy concept.

Implications in the development of complex physical systems

A common hypothesis in systems ecology is that the design engineer's observation that a greater capital investment is needed to create a process with increased exergy efficiency is actually the economic result of a fundamental law of nature. By this view, exergy is the analogue of economic currency in the natural world. The analogy to capital investment is the accumulation of exergy into a system over long periods of time resulting in embodied energy. The analogy of capital investment resulting in a factory with high exergy efficiency is an increase in natural organizational structures with high exergy efficiency. (See Maximum power ). Researchers in these fields describe biological evolution in terms of increases in organism complexity due to the requirement for increased exergy efficiency because of competition for limited sources of exergy.

Some biologists have a similar hypothesis. A biological system (or a chemical plant) with a number of intermediate compartments and intermediate reactions is more efficient because the process is divided up into many small substeps, and this is closer to the reversible ideal of an infinite number of infinitesimal substeps. Of course, an excessively large number of intermediate compartments comes at a capital cost that may be too high.

Testing this idea in living organisms or ecosystems is impossible for all practical purposes because of the large time scales and small exergy inputs involved for changes to take place. However, if this idea is correct, it would not be a new fundamental law of nature. It would simply be living systems and ecosystems maximizing their exergy efficiency by utilizing laws of thermodynamics developed in the 19th century.

Philosophical and cosmological implications

Some proponents of utilizing exergy concepts describe them as a biocentric or ecocentric alternative for terms like quality and value. The "deep ecology" movement views economic usage of these terms as an anthropocentric philosophy which should be discarded. A possible universal thermodynamic concept of value or utility appeals to those with an interest in monism.

For some, the end result of this line of thinking about tracking exergy into the deep past is a restatement of the cosmological argument that the universe was once at equilibrium and an input of exergy from some First Cause created a universe full of available work. Current science is unable to describe the first 10−43 seconds of the universe (See Timeline of the Big Bang ). An external reference state is not able to be defined for such an event, and (regardless of its merits), such an argument may be better expressed in terms of entropy.

Quality of energy types

The ratio of exergy to energy in a substance can be considered a measure of energy quality. Forms of energy such as macroscopic kinetic energy, electrical energy, and chemical Gibbs free energy are 100% recoverable as work, and therefore have an exergy equal to their energy. However, forms of energy such as radiation and thermal energy can not be converted completely to work, and have exergy content less than their energy content. The exact proportion of exergy in a substance depends on the amount of entropy relative to the surrounding environment as determined by the Second Law of Thermodynamics.

Exergy is useful when measuring the efficiency of an energy conversion process. The exergetic, or 2nd Law, efficiency is a ratio of the exergy output divided by the exergy input. This formulation takes into account the quality of the energy, often offering a more accurate and useful analysis than efficiency estimates only using the First Law of Thermodynamics.

Work can be extracted also from bodies colder than the surroundings. When the flow of energy is coming into the body, work is performed by this energy obtained from the large reservoir, the surrounding. A quantitative treatment of the notion of energy quality rests on the definition of energy. According to the standard definition, Energy is a measure of the ability to do work. Work can involve the movement of a mass by a force that results from a transformation of energy. If there is an energy transformation, the second principle of energy flow transformations says that this process must involve the dissipation of some energy as heat. Measuring the amount of heat released is one way of quantifying the energy, or ability to do work and apply a force over a distance.

Exergy of heat available at a temperature

Maximal possible conversion of heat to work, or exergy content of heat, depends on the temperature at which heat is available and the temperature level at which the reject heat can be disposed, that is the temperature of the surrounding. The upper limit for conversion is known as Carnot efficiency and was discovered by Nicolas Léonard Sadi Carnot in 1824. See also Carnot heat engine.

Carnot efficiency is

where TH is the higher temperature and TC is the lower temperature, both as absolute temperature. From Equation 15 it is clear that in order to maximize efficiency one should maximize TH and minimize TC.

Exergy exchanged is then:

where Tsource is the temperature of the heat source, and To is the temperature of the surrounding.

Higher exergy content tends to mean higher energy prices. Here the costs of heating (vertical axis) are compared with the exergy content of different energy carriers (horizontal axis) in Finland. Energy carriers included are district heating (D), ground-source heat pump (G), exhaust air heat pump (A), bioenergy meaning firewood (B), heating oil (O) and direct electric heating (E). Red dots and trend line indicates energy prices for consumers, blue dots and trend line indicates total price for consumers including capital expenditure for the heating system. Cost and exergy for heating energy in Finland.jpg
Higher exergy content tends to mean higher energy prices. Here the costs of heating (vertical axis) are compared with the exergy content of different energy carriers (horizontal axis) in Finland. Energy carriers included are district heating (D), ground-source heat pump (G), exhaust air heat pump (A), bioenergy meaning firewood (B), heating oil (O) and direct electric heating (E). Red dots and trend line indicates energy prices for consumers, blue dots and trend line indicates total price for consumers including capital expenditure for the heating system.

Connection with economic value

Exergy in a sense can be understood as a measure of value of energy. Since high-exergy energy carriers can be used in for more versatile purposes, due to their ability to do more work, they can be postulated to hold more economic value. This can be seen in prices of energy carriers, i.e. high-exergy energy carriers such as electricity tend to be more valuable than low-exergy ones such as various fuels or heat. This has led to substitution of more valuable high-exergy energy carriers with low-exergy energy carriers, when possible. An example is heating systems, where higher investment to heating systems allows using low-exergy energy sources. Thus high-exergy content is being substituted with capital investments. [17]

Exergy based Life Cycle Assessment (LCA)

Exergy of a system is the maximum useful work possible during a process that brings the system into equilibrium with a heat reservoir. [18] [19] Wall [20] clearly states the relation between exergy analysis and resource accounting. [21] This intuition confirmed by Dewulf [22] Sciubba [23] lead to exergo-economic accounting [24] and to methods specifically dedicated to LCA such as exergetic material input per unit of service (EMIPS). [25] The concept of material input per unit of service (MIPS) is quantified in terms of the second law of thermodynamics, allowing the calculation of both resource input and service output in exergy terms. This exergetic material input per unit of service (EMIPS) has been elaborated for transport technology. The service not only takes into account the total mass to be transported and the total distance, but also the mass per single transport and the delivery time. The applicability of the EMIPS methodology relates specifically to transport system and allows an effective coupling with life cycle assessment.



In 1824, Sadi Carnot studied the improvements developed for steam engines by James Watt and others. Carnot utilized a purely theoretical perspective for these engines and developed new ideas. He wrote:

The question has often been raised whether the motive power of heat is unbounded, whether the possible improvements in steam engines have an assignable limit—a limit by which the nature of things will not allow to be passed by any means whatever... In order to consider in the most general way the principle of the production of motion by heat, it must be considered independently of any mechanism or any particular agent. It is necessary to establish principles applicable not only to steam-engines but to all imaginable heat-engines... The production of motion in steam-engines is always accompanied by a circumstance on which we should fix our attention. This circumstance is the re-establishing of equilibrium… Imagine two bodies A and B, kept each at a constant temperature, that of A being higher than that of B. These two bodies, to which we can give or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs...

Carnot next described what is now called the Carnot engine, and proved by a thought experiment that any heat engine performing better than this engine would be a perpetual motion machine. Even in the 1820s, there was a long history of science forbidding such devices. According to Carnot, "Such a creation is entirely contrary to ideas now accepted, to the laws of mechanics and of sound physics. It is inadmissible." [4]

This description of an upper bound to the work that may be done by an engine was the earliest modern formulation of the second law of thermodynamics. Because it involves no mathematics, it still often serves as the entry point for a modern understanding of both the second law and entropy. Carnot's focus on heat engines, equilibrium, and heat reservoirs is also the best entry point for understanding the closely related concept of exergy.

Carnot believed in the incorrect caloric theory of heat that was popular during his time, but his thought experiment nevertheless described a fundamental limit of nature. As kinetic theory replaced caloric theory through the early and mid-19th century (see Timeline of thermodynamics ), several scientists added mathematical precision to the first and second laws of thermodynamics and developed the concept of entropy. Carnot's focus on processes at the human scale (above the thermodynamic limit) led to the most universally applicable concepts in physics. Entropy and the second-law are applied today in fields ranging from quantum mechanics to physical cosmology.


In the 1870s, Josiah Willard Gibbs unified a large quantity of 19th century thermochemistry into one compact theory. Gibbs's theory incorporated the new concept of a chemical potential to cause change when distant from a chemical equilibrium into the older work begun by Carnot in describing thermal and mechanical equilibrium and their potentials for change. Gibbs's unifying theory resulted in the thermodynamic potential state functions describing differences from thermodynamic equilibrium.

In 1873, Gibbs derived the mathematics of "available energy of the body and medium" into the form it has today. [3] (See the equations above). The physics describing exergy has changed little since that time.

See also


  1. Rant, Zoran (1956). "Exergie, Ein neues Wort für "technische Arbeitsfähigkeit"". Forschung Auf dem Gebiete des Ingenieurwesens. 22: 36–37.
  2. Honerkamp, J. (2002). Statistical physics. Springer. p. 298. ISBN   978-3-540-43020-9. The maximum fraction of an energy form which (in a reversible process) can be transformed into work is called exergy. The remaining part is called anergy, and this corresponds to the waste heat.
  3. Çengel, Y. A.; Boles, M. A. (2008). Thermodynamics an Engineering Approach (6th ed.). p. 445. ISBN   978-0-07-125771-8.
  4. van Gool, W.; Bruggink, J.J.C. (Eds) (1985). Energy and time in the economic and physical sciences. North-Holland. pp. 41–56. ISBN   978-0444877482.CS1 maint: extra text: authors list (link)
  5. Grubbström, Robert W. (2007). "An Attempt to Introduce Dynamics Into Generalised Exergy Considerations". Applied Energy. 84 (7–8): 701–718. doi:10.1016/j.apenergy.2007.01.003.
  6. 1 2 Moran, Michael (2010). Fundamentals of Engineering Thermodynamics (7th ed.). Hoboken, N.J.: John Wiley & Sons Canada, Limited. pp. 816–817. ISBN   978-0-470-49590-2.
  7. Szargut, Jan. "Towards an International Reference Environment of Chemical Exergy" (PDF). Retrieved 15 April 2012.
  8. Rivero, R.; Garfias, M. (1 December 2006). "Standard chemical exergy of elements updated". Energy. 31 (15): 3310–3326. doi:10.1016/j.energy.2006.03.020.
  9. Zanchini, Enzo; Terlizzese, Tiziano (1 September 2009). "Molar exergy and flow exergy of pure chemical fuels". Energy. 34 (9): 1246–1259. doi:10.1016/j.energy.2009.05.007.
  10. "The Individual and Universal Gas Constant" . Retrieved 15 April 2012.
  11. 1 2 "Exergy (Availability) – Part a (updated 3/24/12)" . Retrieved 1 April 2015.
  12. 1 2 3 4 5 "The Reference Environment". Exergoecology Portal. CIRCE. 2008.
  13. 1 2 Edwards, C.; et al. (2007). "Development of Low-Exergy-Lost, High-Efficiency Chemical Engines" (PDF). GCEP Technology Report: 1–2.
  14. 1 2 Goswami, D. Y.; et al. (2004). The CRC Handbook of Mechanical Engineering (2nd ed.). CRC Press. ISBN   978-0-8493-0866-6.
  15. Svirezhev, Y (2001). "Exergy of solar radiation: Information approach". Ecological Modelling. 145 (2–3): 101–110. doi:10.1016/S0304-3800(01)00409-4
  16. 1 2 Dincer, I.; Rosen, M. A. (2007). Exergy: Energy, Environment, and Sustainable Development. Elsevier. ISBN   978-0-08-044529-8.
  17. 1 2 Müller, A.; Kranzl, L.; Tuominen, P.; Boelman, E.; Molinari, M.; Entrop, A.G. (2011). "Estimating exergy prices for energy carriers in heating systems: Country analyses of exergy substitution with capital expenditures". Energy and Buildings. 43 (12): 3609–3617. doi:10.1016/j.enbuild.2011.09.034.
  18. Rosen, M. A., & Dincer, I. (2001). Exergy as the confluence of energy, environment and sustainable development. Exergy, an International journal, 1(1), 3–13. https://www.academia.edu/download/6421325/kcx1421.pdf%5B%5D
  19. Wall, G., & Gong, M. (2001). On exergy and sustainable development—Part 1: Conditions and concepts. Exergy, An International Journal, 1(3), 128–145. https://www.researchgate.net/profile/Goeran_Wall/publication/222700889_On_exergy_and_sustainable_development__Part_I_Conditions_and_concepts/links/53fdc0470cf2364ccc08fafa.pdf
  20. Wall, G. (1977). Exergy-a useful concept within resource accounting. http://www.diva-portal.org/smash/get/diva2:318565/FULLTEXT01.pdf
  21. Wall, G. (2010). On exergy and sustainable development in environmental engineering. The Open Environmental Engineering Journal, 3, 21–32. http://www.diva-portal.org/smash/get/diva2:318551/FULLTEXT01.pdf
  22. Dewulf, J., Van Langenhove, H., Muys, B., Bruers, S., Bakshi, B. R., Grubb, G. F., ... & Sciubba, E. (2008). Exergy: its potential and limitations in environmental science and technology. Environmental Science & Technology, 42(7), 2221–2232. https://www.researchgate.net/profile/Jo_Dewulf/publication/51393531_Exergy_Its_Potential_and_Limitations_in_Environmental_Science_and_Technology/links/5447ddcc0cf2d62c305220e6.pdf
  23. Sciubba, E. (2004). From Engineering Economics to Extended Exergy Accounting: A Possible Path from Monetary to Resource‐Based Costing. Journal of Industrial Ecology, 8(4), 19–40. https://www.researchgate.net/profile/Sciubba_Enrico/publication/229896297_From_Engineering_Economics_to_Extended_Exergy_Accounting_A_Possible_Path_from_Monetary_to_ResourceBased_Costing/links/5469e6cd0cf2397f782e75e5.pdf
  24. Rocco, M. V., Colombo, E., & Sciubba, E. (2014). Advances in exergy analysis: a novel assessment of the Extended Exergy Accounting method. Applied Energy, 113, 1405–1420. https://www.researchgate.net/profile/Matteo_Rocco/publication/257311375_Advances_in_exergy_analysis_A_novel_assessment_of_the_Extended_Exergy_Accounting_method/links/0f3175314ce7cc6fc5000000.pdf
  25. Dewulf, J., & Van Langenhove, H. (2003). Exergetic material input per unit of service (EMIPS) for the assessment of resource productivity of transport commodities. Resources, Conservation and Recycling, 38(2), 161–174. https://www.researchgate.net/profile/Herman_VAN_LANGENHOVE/publication/228422347_Exergetic_material_input_per_unit_of_service_(EMIPS)_for_the_assessment_of_resource_productivity_of_transport_commodities/links/0c960519a4f6c42d97000000.pdf

Related Research Articles

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

Heat engine System that converts heat or thermal energy to mechanical work

In thermodynamics and engineering, a heat engine is a system that converts heat or thermal energy—and chemical energy—to mechanical energy, which can then be used to do mechanical work. It does this by bringing a working substance from a higher state temperature to a lower state temperature. A heat source generates thermal energy that brings the working substance to the high temperature state. The working substance generates work in the working body of the engine while transferring heat to the colder sink until it reaches a low temperature state. During this process some of the thermal energy is converted into work by exploiting the properties of the working substance. The working substance can be any system with a non-zero heat capacity, but it usually is a gas or liquid. During this process, a lot of heat is lost to the surroundings and so cannot be converted to work.

Thermodynamic free energy

The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether a process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful.

Second law of thermodynamics law of physics stating that systems spontaneously evolve towards states of higher entropy

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. The total entropy of a system and its surroundings can remain constant in ideal cases where the system is in thermodynamic equilibrium, or is undergoing a (fictive) reversible process. In all processes that occur, including spontaneous processes, the total entropy of the system and its surroundings increases and the process is irreversible in the thermodynamic sense. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.

Gibbs free energy gibbs energy of formation

In thermodynamics, the Gibbs free energy is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system ; this maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces.

Thermodynamic system precisely specified macroscopic region of the universe, defined by boundaries

A thermodynamic system is a group of material and/or radiative contents. Its properties may be described by thermodynamic state variables such as temperature, entropy, internal energy, and pressure.

Laws of thermodynamics law that defines fundamental physical quantities that characterize thermodynamic systems and their behavior

The three laws of thermodynamics define physical quantities that characterize thermodynamic systems at thermal equilibrium. The laws describe how these quantities behave under various circumstances, and preclude the possibility of certain phenomena.

Thermodynamic equations

Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process. Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics.

Thermodynamic cycle linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system,while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state

A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. At every point in the cycle, the system is in thermodynamic equilibrium, so the cycle is reversible.

Exergy efficiency computes the effectiveness of a system relative to its performance in reversible conditions. It is defined as the ratio of the thermal efficiency of an actual system compared to an idealized or reversible version of the system for heat engines. It can also be described as the ratio of the useful work output of the system to the reversible work output for work-consuming systems. For refrigerators and heat pumps, it is the ratio of the actual COP and reversible COP.

Thermal efficiency Efficiency in general

In thermodynamics, the thermal efficiency is a dimensionless performance measure of a device that uses thermal energy, such as an internal combustion engine, a steam turbine or a steam engine, a boiler, furnace, or a refrigerator for example. For a heat engine, thermal efficiency is the fraction of the energy added by heat that is converted to net work output. In the case of a refrigeration or heat pump cycle, thermal efficiency is the ratio of net heat output for heating, or removal for cooling, to energy input.

Entropy is a property of thermodynamical systems. The term entropy was introduced by Rudolf Clausius who named it from the Greek word τρoπή, "transformation". He considered transfers of energy as heat and work between bodies of matter, taking temperature into account. Bodies of radiation are also covered by the same kind of reasoning.

Fundamental thermodynamic relation

In thermodynamics, the fundamental thermodynamic relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way.

Carnot cycle Theoretical thermodynamic cycle proposed by Nicolas Leonard Sadi Carnot in 1824

The Carnot cycle is a theoretical ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. It is not an actual thermodynamic cycle but is a theoretical construct.

Introduction to entropy

Entropy is an important concept in the branch of physics known as thermodynamics. The idea of "irreversibility" is central to the understanding of entropy. Everyone has an intuitive understanding of irreversibility. If one watches a movie of everyday life running forward and in reverse, it is easy to distinguish between the two. The movie running in reverse shows impossible things happening – water jumping out of a glass into a pitcher above it, smoke going down a chimney, water in a glass freezing to form ice cubes, crashed cars reassembling themselves, and so on. The intuitive meaning of expressions such as "you can't unscramble an egg", or "you can't take the cream out of the coffee" is that these are irreversible processes. No matter how long you wait, the cream won't jump out of the coffee into the creamer.

Heat energy transfer process, or its amount (and direction), that is associated with a temperature difference

In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter. The mechanisms include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or isochoric mechanical work done by the surroundings on the system of interest; or Joule heating by an electric current driven through the system of interest by an external system; or a combination of these. When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Thermal conduction occurs by the stochastic (random) motion of microscopic particles. In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field. The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body.


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Further reading