In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
, the exergy of a
system is the maximum useful
work possible during a
process that brings the system into
equilibrium with a
heat reservoir
A thermal reservoir, also thermal energy reservoir or thermal bath, is a thermodynamic system with a heat capacity so large that the temperature of the reservoir changes relatively little when a much more significant amount of heat is added o ...
, reaching maximum
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
. 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
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
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
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws o ...
. The term "exergy" was coined in 1956 by
Zoran Rant (1904–1972) by using the Greek ''
ex'' and ''
ergon
Ergon may refer to:
* Ergon, alien from the ''Doctor Who'' serial ''Arc of Infinity''
* Ergon, concept from Aristotle's ''Nicomachean Ethics'' that is most often translated as function, task, or work
* Ergon, Inc., petroleum company based in Jacks ...
'' meaning "from
work", but the concept had been earlier developed by
J Willard Gibbs (the namesake of
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work (physics), work that may be performed by a closed system, thermodynamically closed system a ...
) in 1873.
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
Irreversible may refer to:
* Irreversible process, in thermodynamics, a process that is not reversible
*'' Irréversible'', a 2002 film
* ''Irréversible'' (soundtrack), soundtrack to the film ''Irréversible''
* An album recorded by hip-hop artis ...
, for example loss of heat to the environment (''see
Second Law of Thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
''). This destruction is proportional to the
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
increase of the system together with its surroundings (''see
Entropy production
Entropy production (or generation) 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, anelastic ...
''). The destroyed exergy has been called anergy. For an
isentropic process, exergy and energy are interchangeable terms, and there is no anergy.
Definitions
Exergy is a combination property 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 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.
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.
The term exergy is also used, by analogy with its physical definition, in
information theory
Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...
related to
reversible computing
Reversible computing is any model of computation 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 c ...
. Exergy is also synonymous with: ''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''.
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 processes by considering the entire cycle as a single process and using one of the exergy destruction equations.
Heat engine
For a
heat engine, the exergy can be simply defined as the energy input times the
Carnot efficiency
A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynam ...
. Since many systems can be modeled as a heat engine, this definition can be useful for many applications.
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.
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 ''S''
total, 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
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
if the following expression is used for exergy:
where the
extensive quantities
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one ...
for the system are: ''U'' =
Internal energy, ''V'' =
Volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
, and ''N''
i =
Moles of component ''i''
The
intensive quantities
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one ...
for the surroundings are: ''P''
R =
Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
, ''T''
R =
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied on ...
, ''μ''
i, 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 () is useful for processes where system volume, entropy, and the 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 ()) 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
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy at the University of Glasgow for 53 years, he did importan ...
, 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 (), 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 ():
Rudolf Clausius
Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
recognized the presence of a
proportionality constant in Kelvin's analysis and gave it the name
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
in 1865 from the Greek for "transformation" because it describes the quantity of energy lost during the 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
Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrati ...
.
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
The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Ler ...
) 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
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic ...
''). 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.
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
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature ( isothermal). The change in the Helmholtz e ...
''A'' is used in the expression:
For a given set of chemicals at a given temperature and pressure,
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work (physics), work that may be performed by a closed system, thermodynamically closed system a ...
''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
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen fuel, hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most bat ...
.'') This is true of every isothermal process. Examples are
gravitational potential energy
Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conv ...
,
kinetic energy
In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its a ...
(on a macroscopic scale),
solar energy
Solar energy is radiant light and heat from the Sun that is harnessed using a range of technologies such as solar power to generate electricity, solar thermal energy (including solar water heating), and solar architecture. It is an ...
,
electrical energy
Electrical energy is energy related to forces on electrically charged particles and the movement of electrically charged particles (often electrons in wires, but not always). This energy is supplied by the combination of electric current and electr ...
, and many others. If
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding (motion), sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative la ...
,
absorption,
electrical resistance
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...
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 the 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.
[
]
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. 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 N
2=75.67%, O
2=20.35%, H
2O(g)=3.12%, CO
2=0.03% and other gases=0.83%.
These molar fractions will become of use when applying Equation 8 below.
C
aH
bO
c 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. These values can be found in thermodynamic books or in online tables.
Important equations
where:
*
is the Gibbs function of the specific substance in the system at
. (
refers to the substance that is entering the system)
*
is the Universal gas constant (8.314462 J/mol•K)
*
is the temperature that the system is being evaluated at in absolute temperature
*
is the molar fraction of the given substance in the environment, i.e. air
where
is 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 environmental 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
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:
[
]
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 to the difference in exergy at inlet and outlet of the system:
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 the irreversibility of that system.
Applications
Applying equation () to a subsystem yields:
This expression applies equally well for theoretical ideals in a wide variety of applications:
electrolysis (decrease in ''G''),
galvanic cell
A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous Oxidation-Reduction reactions. A common apparatus ...
s and
fuel cell
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen fuel, hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most bat ...
s (increase in ''G''),
explosives (increase in ''A''),
heating and refrigeration (exchange of ''H''),
motors
An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy.
Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power ...
(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
One goal of energy and exergy methods in engineering is to compute what comes into and out of several possible designs before a design 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 equal the exergy input for real processes since a part of the exergy input is always destroyed according to the
Second Law of Thermodynamics
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
for real processes. After the input and output are calculated, an 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.
Exergy has been applied in a number of design applications in order to optimize systems or identify components or subsystems with the greatest potential for improvement. For instance, an exergy analysis of
environmental control systems on the
international space station
The International Space Station (ISS) is the largest Modular design, modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos ( ...
revealed the oxygen generation assembly as the subsystem which destroyed the most exergy.
Exergy is particularly useful for broad engineering analyses with many systems of varied nature, since it can account for mechanical, electrical, nuclear, chemical, or thermal systems. For this reason, Exergy analysis has also been used to optimize the performance of rocket vehicles. Exergy analysis affords a more detailed analysis compared to energy analysis because it also considers the relationship between the system and its environment. For example, exergy analysis has been used to compare possible power generation and storage systems on the moon, since exergy analysis considers both the system and its relationship with its environment.
Application of exergy to
unit operations in
chemical plants was partially responsible for the huge growth of the
chemical industry
The chemical industry comprises the companies that produce industrial chemicals. Central to the modern world economy, it converts raw materials ( oil, natural gas, air, water, metals, and minerals) into more than 70,000 different products. T ...
during the 20th century. 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%. Without taking into account the non-standard atmospheric temperature variation, these calculations 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.
Applications in natural resource utilization
In recent decades, utilization of exergy has spread outside of physics and engineering to the fields of
industrial ecology
Industrial ecology (IE) is the study of material and energy flows through industrial systems. The global industrial economy can be modelled as a network of industrial processes that extract resources from the Earth and transform those resou ...
,
ecological economics,
systems ecology
Systems ecology is an interdisciplinary field of ecology, a subset of Earth system science, that takes a holism, holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general ...
, and
energetics Energetics is the study of energy, and may refer to:
* Thermodynamics
* Bioenergetics
* Energy flow (ecology)
Energy flow is the flow of energy through living things within an ecosystem. All living organisms can be organized into producers and ...
. 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
The natural environment or natural world encompasses all living and non-living things occurring naturally, meaning in this case not artificial. The term is most often applied to the Earth or some parts of Earth. This environment encompasses ...
. As with ambient air, this often requires the unrealistic substitution of properties from a natural environment in place of the
reference state environment
Environment most often refers to:
__NOTOC__
* Natural environment, all living and non-living things occurring naturally
* Biophysical environment, the physical and biological factors along with their chemical interactions that affect an organism or ...
of Carnot. For example, ecologists and others have developed reference conditions for the
ocean
The ocean (also the sea or the world ocean) is the body of salt water that covers approximately 70.8% of the surface of Earth and contains 97% of Earth's water. An ocean can also refer to any of the large bodies of water into which the wo ...
and for the
Earth's crust
Earth's crust is Earth's thin outer shell of rock, referring to less than 1% of Earth's radius and volume. It is the top component of the lithosphere, a division of Earth's layers that includes the crust and the upper part of the mantle. The ...
. Exergy values for human activity using this information can be useful for comparing policy alternatives based on the efficiency of utilizing
natural resources
Natural resources are resources that are drawn from nature and used with few modifications. This includes the sources of valued characteristics such as commercial and industrial use, aesthetic value, scientific interest and cultural value. ...
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.
[
] 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,
[
] and how human interference alters this potential.
Referencing the inherent qualities of a system in place of a reference state environment
is the most direct way that ecologists determine the exergy of a natural resource. Specifically, it is easiest to examine the
thermodynamic
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of t ...
properties of a system, and the reference substances
[
] that are acceptable within the reference environment.
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
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. ...
, solids within the Earth's crust, and
molecules
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...
or
ions
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
in seawater.
By understanding these basic models, it's possible to determine the exergy of multiple earth systems interacting, like the effects of
solar radiation
Solar irradiance is the power per unit area ( surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre ...
on plant life. 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.
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.
Today, it is becoming increasingly popular to analyze the environmental impacts of natural resource utilization, especially for energy usage.
[
] 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.
Combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combust ...
of fossil fuels, for example, is examined with respect to assessing the environmental impacts of burning
coal
Coal is a combustible black or brownish-black sedimentary rock, formed as stratum, rock strata called coal seams. Coal is mostly carbon with variable amounts of other Chemical element, elements, chiefly hydrogen, sulfur, oxygen, and nitrogen ...
,
oil, and
natural gas
Natural gas (also called fossil gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbon ...
. 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
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. ...
.
In this way, it is easier to determine how human action is affecting the natural environment.
Applications in sustainability
In
systems ecology
Systems ecology is an interdisciplinary field of ecology, a subset of Earth system science, that takes a holism, holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general ...
, researchers sometimes consider the exergy of the current formation of natural resources from a small number of exergy inputs (usually
solar radiation
Solar irradiance is the power per unit area ( surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre ...
,
tidal force
The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenom ...
s, and
geothermal heat
Geothermal heating is the direct use of geothermal energy for some heating applications. Humans have taken advantage of geothermal heat this way since the Paleolithic era. Approximately seventy countries made direct use of a total of 270 PJ of ...
). 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
Specific definitions of sustainability are difficult to agree on and have varied in the literature and over time. The concept of sustainability can be used to guide decisions at the global, national, and individual levels (e.g. sustainable livin ...
issues in a quantitative fashion through a
sustainability measurement
Sustainability measurement are tools and methods that attempt to measure the degree of sustainability of processes, products, services, businesses and so forth. Sustainability is difficult to quantify, perhaps even immeasurable. The metrics used to ...
:
:Does the human production of an economic good deplete the exergy of Earth's
natural resources
Natural resources are resources that are drawn from nature and used with few modifications. This includes the sources of valued characteristics such as commercial and industrial use, aesthetic value, scientific interest and cultural value. ...
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 Energetics is the study of energy, and may refer to:
* Thermodynamics
* Bioenergetics
* Energy flow (ecology)
Energy flow is the flow of energy through living things within an ecosystem. All living organisms can be organized into producers and ...
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
Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variation ...
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
An economy is an area of the production, distribution and trade, as well as consumption of goods and services. In general, it is defined as a social domain that emphasize the practices, discourses, and material expressions associated with t ...
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
Monism attributes oneness or singleness (Greek: μόνος) to a concept e.g., existence. Various kinds of monism can be distinguished:
* Priority monism states that all existing things go back to a source that is distinct from them; e.g., i ...
.
For some, the 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
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
.
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
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work (physics), work that may be performed by a closed system, thermodynamically closed system a ...
are 100% recoverable as work, and therefore have 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
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
.
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
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
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
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied on ...
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
A Carnot cycle is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynam ...
and was discovered by
Nicolas Léonard Sadi Carnot
''Sous-lieutenant'' Nicolas Léonard Sadi Carnot (; 1 June 1796 – 24 August 1832) was a French mechanical engineer in the French Army, military scientist and physicist, and often described as the "father of thermodynamics". He published on ...
in 1824. See also
Carnot heat engine.
Carnot efficiency is
where ''T''
''H'' is the higher temperature and ''T''
''C'' is the lower temperature, both as
absolute temperature. From Equation 15 it is clear that in order to maximize efficiency one should maximize ''T''
''H'' and minimize ''T''
''C''.
Exergy exchanged is then:
where ''T''
''source'' is the temperature of the heat source, and ''T''
''o'' is the temperature of the surrounding.
Connection with economic value
Exergy in a sense can be understood as a measure of the value of energy. Since high-exergy energy carriers can be used 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 the 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 the 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.
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. Wall clearly states the relation between exergy analysis and resource accounting. This intuition confirmed by Dewulf Sciubba lead to exergo-economic accounting and to methods specifically dedicated to LCA such as exergetic material input per unit of service (EMIPS).
[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] 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 the transport system and allows an effective coupling with
life cycle assessment.
The exergy analysis according to EMIPS allowed the definition of a precise strategy for reducing
environmental impacts of transport toward more
sustainable transport.
Such a strategy requires the reduction of the weight of vehicles, sustainable styles of driving, reducing the friction of tires, encouraging electric and hybrid vehicles, improving the walking and
cycling environment in cities, and by enhancing the role of public transport, especially
electric rail.
[VV. AA., “Transport Energy Efficiency,” IEA, International Energy Agency, 2010.]
History
Carnot
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
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anci ...
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
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
. It is inadmissible."
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
The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...
. Because it involves no mathematics, it still often serves as the entry point for a modern understanding of both the second law and
entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
. Carnot's focus on
heat engines,
equilibrium, and
heat reservoir
A thermal reservoir, also thermal energy reservoir or thermal bath, is a thermodynamic system with a heat capacity so large that the temperature of the reservoir changes relatively little when a much more significant amount of heat is added o ...
s 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
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodyna ...
. Carnot's focus on processes at the human scale (above the
thermodynamic limit) led to the most universally applicable concepts in
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
. Entropy and the second-law are applied today in fields ranging from
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, q ...
to
physical cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of f ...
.
Gibbs
In the 1870s,
Josiah Willard Gibbs unified a large quantity of 19th century
thermochemistry
Thermochemistry is the study of the heat energy which is associated with chemical reactions and/or phase changes such as melting and boiling. A reaction may release or absorb energy, and a phase change may do the same. Thermochemistry focuses on ...
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
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 ther ...
.
In 1873, Gibbs derived the mathematics of "available energy of the body and medium" into the form it has today. (See the equations
above). The physics describing exergy has changed little since that time.
Helmholtz
In the 1880s, German scientist
Herman Von Helmholtz derived the equation for the maximum work which can be reversibly obtained from a closed system.
Rant
In 1956, Yugoslav scholar
Zoran Rant proposed the concept of Exergy, extending Gibbs and Helmholtz' work. Since then, continuous development in exergy analysis has seen many applications in thermodynamics, and exergy has been accepted as the maximum theoretical useful work which can be obtained from a system with respect to its environment.
See also
*
Thermodynamic free energy
*
Entropy production
Entropy production (or generation) 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, anelastic ...
*
Energy: world resources and consumption
*
Emergy
Notes
References
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Further reading
*
*Stephen Jay Kline (1999). ''The Low-Down on Entropy and Interpretive Thermodynamics'', La Cañada, CA: DCW Industries. .
External links
Energy, Incorporating Exergy, An International Journal''Exergy – a useful concept'' by Göran Wall''Exergetics'' textbook for self-study by Göran Wall''Exergy calculator'' by The Exergoecology Portal*
ttp://www.lowex.net/english/inside/frames/text/material_in.html ''Introduction to the Concept of Exergy''
{{Industrial ecology
Thermodynamic free energy
State functions
Ecological economics