Exergy
Encyclopedia
In thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, the exergy of a system is the maximum useful work
Mechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...

possible during a process that brings the system into equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

with a heat reservoir
Heat reservoir
In thermodynamics, a heat reservoir, thermal reservoir, or heat bath is a system whose heat capacity is so large that when it is in thermal contact with some other system of interest its temperature remains effectively constant. The heat bath is effectively an infinite reservoir of energy and...

. 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
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

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
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

.

Energy is never destroyed during a process; it changes from one form to another (see First Law of Thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

). In contrast, exergy accounts for the irreversibility
Irreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....

of a process due to increase in entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

(see Second Law of Thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

). Exergy is always destroyed when a process involves a temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

change. This destruction is proportional to the entropy increase of the system together with its surroundings. The destroyed exergy has been called anergy. For an isothermal process
Isothermal process
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir , and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir...

, exergy and energy are interchangeable terms, and there is no anergy.

Exergy analysis is performed in the field of industrial ecology
Industrial ecology
Industrial Ecology is the study of material and energy flows through industrial systems. The global industrial economy can be modeled as a network of industrial processes that extract resources from the Earth and transform those resources into commodities which can be bought and sold to meet the...

to use energy more efficiently. The term was coined by Zoran Rant
Zoran Rant
Zoran Rant was a Slovene mechanical engineer, scientist and professor, associate member of SAZU. He invented terms known today as "exergy and anergy"....

in 1956, but the concept was developed by J. Willard Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...

in 1873. Ecologists and design engineers often choose a reference state for the reservoir that may be different from the actual surroundings of the system.

Exergy is a combination property of a system and its environment because unlike energy 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 joule
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

s. The Internal Energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...

of a system is always measured from a fixed reference state and is therefore always a state function
State function
In thermodynamics, a state function, function of state, state quantity, or state variable is a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state . A state function describes the equilibrium state of a system...

. 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.

The term exergy is also used, by analogy with its physical definition, in information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

related to reversible computing
Reversible computing
Reversible computing is a model of computing where the computational process to some extent is reversible, i.e., time-invertible. A necessary condition for reversibility of a computational model is that the transition function mapping states to their successors at a given later time should be...

. 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
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...

work
, and ideal work.

### Carnot

Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...

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
Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

, and proved by a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

that any heat engine performing better than this engine would be a perpetual motion
Perpetual motion
Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not....

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
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

and of sound physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

. 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
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. Carnot's focus on heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...

s, equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

, and heat reservoir
Heat reservoir
In thermodynamics, a heat reservoir, thermal reservoir, or heat bath is a system whose heat capacity is so large that when it is in thermal contact with some other system of interest its temperature remains effectively constant. The heat bath is effectively an infinite reservoir of energy and...

s is also the best entry point for understanding the closely related concept of exergy.

Carnot believed in the incorrect caloric theory
Caloric theory
The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores in solids and liquids...

of heat that was popular during his time, but his thought experiment nevertheless described a fundamental limit of nature. As kinetic theory
Kinetic theory
The kinetic theory of gases describes a gas as a large number of small particles , all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container...

replaced caloric theory through the early and mid-19th century (see timeline
Timeline of thermodynamics, statistical mechanics, and random processes
A timeline of events related to thermodynamics.- Before 1800 :* 1650 – Otto von Guericke builds the first vacuum pump* 1660 – Robert Boyle experimentally discovers Boyle's Law, relating the pressure and volume of a gas...

), several scientists added mathematical precision to the first and second laws of thermodynamics
Laws of thermodynamics
The four laws of thermodynamics summarize its most important facts. They define fundamental physical quantities, such as temperature, energy, and entropy, in order to describe thermodynamic systems. They also describe the transfer of energy as heat and work in thermodynamic processes...

and developed the concept of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

. Carnot's focus on processes at the human scale (above the thermodynamic limit
Thermodynamic limit
In thermodynamics, particularly statistical mechanics, the thermodynamic limit is reached as the number of particles in a system, N, approaches infinity...

) led to the most universally applicable concepts in physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

. Entropy and the second-law are applied today in fields ranging from quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

to physical cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

.

### Gibbs

In the 1870s, Josiah Willard Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...

unified a large quantity of 19th century thermochemistry
Thermochemistry
Thermochemistry is the study of the energy and heat associated with chemical reactions and/or physical transformations. A reaction may release or absorb energy, and a phase change may do the same, such as in melting and boiling. Thermochemistry focuses on these energy changes, particularly on the...

into one compact theory. Gibbs's theory incorporated the new concept of a chemical potential
Chemical potential
Chemical potential, symbolized by μ, is a measure first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. It is the potential that a substance has to produce in order to alter a system...

to cause change when distant from a chemical equilibrium
Chemical equilibrium
In a chemical reaction, chemical equilibrium is the state in which the concentrations of the reactants and products have not yet changed with time. It occurs only in reversible reactions, and not in irreversible reactions. Usually, this state results when the forward reaction proceeds at the same...

into the older work begun by Carnot in describing thermal and mechanical equilibrium
Mechanical equilibrium
A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

and their potentials for change. Gibbs's unifying theory resulted in the thermodynamic potential state function
State function
In thermodynamics, a state function, function of state, state quantity, or state variable is a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state . A state function describes the equilibrium state of a system...

s describing differences from thermodynamic equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

.

In 1873, Gibbs derived the mathematics of "available energy of the body and medium" into the form it has today. (See the equations below). The physics describing exergy has changed little since that time. The term exergy was suggested in 1956 by Zoran Rant
Zoran Rant
Zoran Rant was a Slovene mechanical engineer, scientist and professor, associate member of SAZU. He invented terms known today as "exergy and anergy"....

(1904–1972) by using the Greek ex and ergon meaning "from work
Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

."

### 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
Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

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 Stotal, the entropy of the system and its reference environment enclosed together in a larger isolated system
Isolated system
In the natural sciences an isolated system, as contrasted with an open system, is a physical system without any external exchange. If it has any surroundings, it does not interact with them. It obeys in particular the first of the conservation laws: its total energy - mass stays constant...

, increase with time:

For macroscopic systems (above the thermodynamic limit
Thermodynamic limit
In thermodynamics, particularly statistical mechanics, the thermodynamic limit is reached as the number of particles in a system, N, approaches infinity...

), these statements are both expressions of the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

if the following expression is used for exergy:

where the extensive quantities for the system are: U = Internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...

, V = Volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

, and Ni = Moles
Mole (unit)
The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12 , the isotope of carbon with atomic weight 12. This corresponds to a value...

of component i

The intensive quantities for the surroundings are: PR = Pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

, TR = temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, &mui, R
= Chemical potential
Chemical potential
Chemical potential, symbolized by μ, is a measure first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. It is the potential that a substance has to produce in order to alter a system...

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
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...

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
William Thomson, 1st Baron Kelvin OM, GCVO, PC, PRS, PRSE, was a mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging...

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
Rudolf Clausius
Rudolf Julius Emanuel Clausius , was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis...

recognized the presence of a proportionality
Proportionality (mathematics)
In mathematics, two variable quantities are proportional if one of them is always the product of the other and a constant quantity, called the coefficient of proportionality or proportionality constant. In other words, are proportional if the ratio \tfrac yx is constant. We also say that one...

constant in Kelvin's analysis and gave it the name entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

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
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....

.

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
Anthropocentrism
Anthropocentrism describes the tendency for human beings to regard themselves as the central and most significant entities in the universe, or the assessment of reality through an exclusively human perspective....

. Laws derived using such a property may not describe the universe but instead describe what people wish to see.

The field of statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

(beginning with the work of Ludwig Boltzmann
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...

in developing the Boltzmann equation
Boltzmann equation
The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...

) 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
Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an "absolute" scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the...

). 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
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...

, the interactions among systems (mostly ecosystem
Ecosystem
An ecosystem is a biological environment consisting of all the organisms living in a particular area, as well as all the nonliving , physical components of the environment with which the organisms interact, such as air, soil, water and sunlight....

s) 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
Systems ecology
Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem...

, 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
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...

H is used in the expression:

For a given set of chemicals at a given temperature and volume, Helmholtz free energy
Helmholtz free energy
In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the “useful” work obtainable from a closed thermodynamic system at a constant temperature and volume...

A is used in the expression:

For a given set of chemicals at a given temperature and pressure, Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...

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
Thermodynamic free energy
The thermodynamic free energy is the amount of work that a thermodynamic system can perform. The concept is useful in the thermodynamics of chemical or thermal processes in engineering and science. The free energy is the internal energy of a system less the amount of energy that cannot be used to...

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
Fuel cell
A fuel cell is a device that converts the chemical energy from a fuel into electricity through a chemical reaction with oxygen or another oxidizing agent. Hydrogen is the most common fuel, but hydrocarbons such as natural gas and alcohols like methanol are sometimes used...

.
) This is true of every isothermal process. Examples are gravitational potential energy, kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which 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 acceleration, the body maintains this kinetic energy unless its speed changes...

(on a macroscopic scale), solar energy, electrical energy, and many others. If friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

, absorption, electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

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.

## Applications

Applying equation (1) to a subsystem yields:

This expression applies equally well for theoretical ideals in a wide variety of applications: electrolysis
Electrolysis
In chemistry and manufacturing, electrolysis is a method of using a direct electric current to drive an otherwise non-spontaneous chemical reaction...

(decrease in G), galvanic cell
Galvanic cell
A Galvanic cell, or Voltaic cell, named after Luigi Galvani, or Alessandro Volta respectively, is an electrochemical cell that derives electrical energy from spontaneous redox reaction taking place within the cell...

s and fuel cell
Fuel cell
A fuel cell is a device that converts the chemical energy from a fuel into electricity through a chemical reaction with oxygen or another oxidizing agent. Hydrogen is the most common fuel, but hydrocarbons such as natural gas and alcohols like methanol are sometimes used...

s (increase in G), explosives (increase in A), heating and refrigeration
HVAC
HVAC refers to technology of indoor or automotive environmental comfort. HVAC system design is a major subdiscipline of mechanical engineering, based on the principles of thermodynamics, fluid mechanics, and heat transfer...

(exchange of H), motors
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...

(decrease in U) and generators
Electrical generator
In electricity generation, an electric generator is a device that converts mechanical energy to electrical energy. A generator forces electric charge to flow through an external electrical circuit. It is analogous to a water pump, which causes water to flow...

(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 operation
Unit operation
In chemical engineering and related fields, a unit operation is a basic step in a process.Unit operation involves bringing a physical change such as separation, crystallization, evaporation, filtration etc.. For example in milk processing, homogenization, pasteurization, chilling, and packaging are...

s in chemical plant
Chemical plant
A chemical plant is an industrial process plant that manufactures chemicals, usually on a large scale. The general objective of a chemical plant is to create new material wealth via the chemical or biological transformation and or separation of materials. Chemical plants use special equipment,...

s was partially responsible for the huge growth of the chemical industry
Chemical industry
The chemical industry comprises the companies that produce industrial chemicals. Central to the modern world economy, it converts raw materials into more than 70,000 different products.-Products:...

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
Standard conditions for temperature and pressure
Standard condition for temperature and pressure are standard sets of conditions for experimental measurements established to allow comparisons to be made between different sets of data...

. Individual processes on Earth like combustion in a power plant often eventually result in products that are incorporated into a large 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 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 appear on paper to be 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
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

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
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

for real processes. After the input and output are completed, the engineer will often want to select the most efficient process. An energy efficiency
Energy conversion efficiency
Energy conversion efficiency is the ratio between the useful output of an energy conversion machine and the input, in energy terms. The useful output may be electric power, mechanical work, or heat.-Overview:...

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
Exergy efficiency
Exergy efficiency computes the efficiency of a process taking the second law of thermodynamics into account.-Motivation:...

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.

Design engineer
Design engineer
Design Engineer is a general term that covers multiple engineering disciplines including electrical, mechanical, industrial design and civil engineering, architectural engineers in the U.S...

s have recognized that a higher exergy efficiency involves building a more expensive plant, and a balance between capital investment and operating efficiency must be determined in the context of economic competition.

### 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
Industrial Ecology is the study of material and energy flows through industrial systems. The global industrial economy can be modeled as a network of industrial processes that extract resources from the Earth and transform those resources into commodities which can be bought and sold to meet the...

, ecological economics
Ecological economics
Image:Sustainable development.svg|right|The three pillars of sustainability. Clickable.|275px|thumbpoly 138 194 148 219 164 240 182 257 219 277 263 291 261 311 264 331 272 351 283 366 300 383 316 394 287 408 261 417 224 424 182 426 154 423 119 415 87 403 58 385 40 368 24 347 17 328 13 309 16 286 26...

, systems ecology
Systems ecology
Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem...

, and energetics
Energetics
Energetics is the study of energy under transformation. Because energy flows at all scales, from the quantum level to the biosphere and cosmos, energetics is a very broad discipline, encompassing for example thermodynamics, chemistry, biological energetics, biochemistry and ecological 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
Natural environment
The natural environment encompasses all living and non-living things occurring naturally on Earth or some region thereof. It is an environment that encompasses the interaction of all living species....

. As with ambient air, this often requires the unrealistic substitution of properties from a natural environment in place of the reference state
Heat reservoir
In thermodynamics, a heat reservoir, thermal reservoir, or heat bath is a system whose heat capacity is so large that when it is in thermal contact with some other system of interest its temperature remains effectively constant. The heat bath is effectively an infinite reservoir of energy and...

environment of Carnot. For example, ecologists and others have developed reference conditions for the ocean
Ocean
An ocean is a major body of saline water, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas.More than half of this area is over 3,000...

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
Natural Resources
Natural Resources is a soul album released by Motown girl group Martha Reeves and the Vandellas in 1970 on the Gordy label. The album is significant for the Vietnam War ballad "I Should Be Proud" and the slow jam, "Love Guess Who"...

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 producution 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 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
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...

, solids within the Earth’s crust, and molecules or ions 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 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
Exhaust gas
Exhaust gas or flue gas is emitted as a result of the combustion of fuels such as natural gas, gasoline/petrol, diesel fuel, fuel oil or coal. According to the type of engine, it is discharged into the atmosphere through an exhaust pipe, flue gas stack or propelling nozzle.It often disperses...

, fuels, and other sources of energy. Combustion
Combustion
Combustion or burning is the sequence of exothermic chemical reactions between a fuel and an oxidant accompanied by the production of heat and conversion of chemical species. The release of heat can result in the production of light in the form of either glowing or a flame...

of fossil fuels, for example, is examined with respect to assessing the environmental impacts of burning coal
Coal
Coal is a combustible black or brownish-black sedimentary rock usually occurring in rock strata in layers or veins called coal beds or coal seams. The harder forms, such as anthracite coal, can be regarded as metamorphic rock because of later exposure to elevated temperature and pressure...

, oil
Oil
An oil is any substance that is liquid at ambient temperatures and does not mix with water but may mix with other oils and organic solvents. This general definition includes vegetable oils, volatile essential oils, petrochemical oils, and synthetic oils....

, and natural gas
Natural gas
Natural gas is a naturally occurring gas mixture consisting primarily of methane, typically with 0–20% higher hydrocarbons . It is found associated with other hydrocarbon fuel, in coal beds, as methane clathrates, and is an important fuel source and a major feedstock for fertilizers.Most natural...

. The current methods for analyzing the emissions
Exhaust gas
Exhaust gas or flue gas is emitted as a result of the combustion of fuels such as natural gas, gasoline/petrol, diesel fuel, fuel oil or coal. According to the type of engine, it is discharged into the atmosphere through an exhaust pipe, flue gas stack or propelling nozzle.It often disperses...

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
Atmosphere
An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature 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
Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem...

, researchers sometimes consider the exergy of the current formation of natural resources from a small number of exergy inputs (usually solar radiation, tidal force
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

s, 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
Pseudoscience
Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...

or pseudo-engineering.

The field describes this accumulated exergy in a natural resource over time as embodied energy
Embodied energy
Embodied energy is defined as the sum of energy inputs that was used in the work to make any product, from the point of extraction and refining materials, bringing it to market, and disposal / re-purposing of it...

with units of the "embodied joule" or "emjoule".

The important application of this research is to address sustainability
Sustainability
Sustainability is the capacity to endure. For humans, sustainability is the long-term maintenance of well being, which has environmental, economic, and social dimensions, and encompasses the concept of union, an interdependent relationship and mutual responsible position with all living and non...

issues in a quantitative fashion through a sustainability measurement
Sustainability measurement
Sustainability measurement is a term that denotes the measurements used as the quantitative basis for the informed management of sustainability...

:
Does the human production of an economic good deplete the exergy of Earth's natural resources
Natural Resources
Natural Resources is a soul album released by Motown girl group Martha Reeves and the Vandellas in 1970 on the Gordy label. The album is significant for the Vietnam War ballad "I Should Be Proud" and the slow jam, "Love Guess Who"...

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
Emergy
Emergy is the available energy of one kind that is used up in transformations directly and indirectly to make a product or service. Emergy accounts for, and in effect, measures quality differences between forms of energy. Emergy is an expression of all the energy used in the work processes that...

) 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
Energetics is the study of energy under transformation. Because energy flows at all scales, from the quantum level to the biosphere and cosmos, energetics is a very broad discipline, encompassing for example thermodynamics, chemistry, biological energetics, biochemistry and ecological 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
Protoscience
In the philosophy of science, a protoscience is an area of scientific endeavor that is in the process of becoming established. Protoscience is distinguished from pseudoscience by its standard practices of good science, such as a willingness to be disproven by new evidence, or to be replaced by a...

being regarded by many as a pseudoscience
Pseudoscience
Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...

. 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
Embodied energy
Embodied energy is defined as the sum of energy inputs that was used in the work to make any product, from the point of extraction and refining materials, bringing it to market, and disposal / re-purposing of it...

. 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
Maximum power
Maximum power can refer to different concepts:* In electronics, the maximum power theorem* In systems theory, the maximum power principle...

). Researchers in these fields describe biological evolution
Evolution
Evolution is any change across successive generations in the heritable characteristics of biological populations. Evolutionary processes give rise to diversity at every level of biological organisation, including species, individual organisms and molecules such as DNA and proteins.Life on Earth...

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
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...

of an infinite number of infinitesimal
Infinitesimal
Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...

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
Biocentrism (ethics)
Biocentrism , in a political and ecological sense, is an ethical point of view which extends inherent value to non-human species, ecosystems, and processes in nature - regardless of their sentience...

or ecocentric alternative for terms like quality and value
Value theory
Value theory encompasses a range of approaches to understanding how, why and to what degree people should value things; whether the thing is a person, idea, object, or anything else. This investigation began in ancient philosophy, where it is called axiology or ethics. Early philosophical...

. The "deep ecology
Deep ecology
Deep ecology is a contemporary ecological philosophy that recognizes an inherent worth of all living beings, regardless of their instrumental utility to human needs. The philosophy emphasizes the interdependence of organisms within ecosystems and that of ecosystems with each other within the...

" movement views economic usage of these terms as an anthropocentric philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

which should be discarded. A possible universal thermodynamic concept of value or utility appeals to those with an interest in monism
Monism
Monism is any philosophical view which holds that there is unity in a given field of inquiry. Accordingly, some philosophers may hold that the universe is one rather than dualistic or pluralistic...

.

For some, the end result of this line of thinking about tracking exergy into the deep past is a restatement of the cosmological argument
Cosmological argument
The cosmological argument is an argument for the existence of a First Cause to the universe, and by extension is often used as an argument for the existence of an "unconditioned" or "supreme" being, usually then identified as God...

that the universe was once at equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

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
Timeline of the Big Bang
This timeline of the Big Bang describes the history of the universe according to the prevailing scientific theory of how the universe came into being, using the cosmological time parameter of comoving coordinates...

). An external reference state is not able to be defined for such an event, and (regardless of its merits), such an arguments may be better expressed in terms of entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

.

## Exergy is highly multidisciplinary

(This section will probably be shortened and added to the "Utilization" section as a table if possible)
The cumulative exergy consumption of a good is a sum
SUM
SUM can refer to:* The State University of Management* Soccer United Marketing* Society for the Establishment of Useful Manufactures* StartUp-Manager* Software User’s Manual,as from DOD-STD-2 167A, and MIL-STD-498...

of the exergy decreases that occurred in order to create it. An initial state for an analysis might consist of exergy contributions from:
1) the material entering individual reactors or other unit
2) the material delivered to the industry and used for all the units in the industrial process.
3) the material purchased from other industries and all the associated indirect exergy decreases involved in transport and administration to get the material and process it.
4) all the initial natural resource
Natural resource
Natural resources occur naturally within environments that exist relatively undisturbed by mankind, in a natural form. A natural resource is often characterized by amounts of biodiversity and geodiversity existent in various ecosystems....

s used directly or indirectly to make the good.
5) all the initial ecological inputs (such as solar radiation, tidal force
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

s, and geothermal heat) that created the natural resources.
6) These multiple inputs related to a single reference input (such as solar radiation).
7) This reference input is related to a single input of exergy to the universe from some external source at a time in the past when the entire universe was at equilibrium
Thermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...

.

Choice 1 (if there are few components) is a tricky undergraduate homework problem in chemical engineering if a chemical reaction occurs in an open system. The worked example above utilizes choice 1 for a closed system with no reaction.

Choice 2 would require an in-house exergy accounting analogous to a process mass balance
Mass balance
A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...

or energy balance
Energy balance
Energy balance may refer to:* First law of thermodynamics, according to which energy cannot be created or destroyed, only modified in form* Energy balance , a measurement of the biological homeostasis of energy in living systems...

. If there are a reasonable number of unit operations, a professional chemical engineer could do this in a short period of time with a good software package to determine exergy flows in the plant.

Choice 3 would require all of choice 2 and converting multiple items usually thought of as economic overhead into terms of exergy. This could be a challenging task requiring considerable thought, but with several assumptions here and there (and more software to keep track of the accounting), it could be done.

Choice 4 would require a repetition of choice 3 for multiple industries, governmental agencies, and all other human activity to convert raw materials to the product. It seems unlikely that many producers would take the time to determine the complete exergy history of their product, but if we ever live in a world where producers were required to perform choice 3, we might be able to get a reasonable estimate of choice 4.

Choice 5 in combination with choice 4 is the only option that is relevant to environmental sustainability
Sustainability
Sustainability is the capacity to endure. For humans, sustainability is the long-term maintenance of well being, which has environmental, economic, and social dimensions, and encompasses the concept of union, an interdependent relationship and mutual responsible position with all living and non...

. Choice 5 requires exergy information from the field of systems ecology
Systems ecology
Systems ecology is an interdisciplinary field of ecology, taking a holistic approach to the study of ecological systems, especially ecosystems. Systems ecology can be seen as an application of general systems theory to ecology. Central to the systems ecology approach is the idea that an ecosystem...

and many additional assumptions. However, with this information, we may address the questions:
Does the human production of this item deplete the Earth's natural resources
Natural Resources
Natural Resources is a soul album released by Motown girl group Martha Reeves and the Vandellas in 1970 on the Gordy label. The album is significant for the Vietnam War ballad "I Should Be Proud" and the slow jam, "Love Guess Who"...

more quickly than those resources are able to regenerate themselves?
If so, how does this numerically compare to the depletion caused by producing an entirely different item using an entirely different set of natural resources?

Choice 6 represents all exergy changes on Earth in terms of one "currency" that may be used to estimate the relative value
Relative value
Relative value is the attractiveness measured in terms of risk, liquidity, and return of one instrument relative to another, or for a given instrument, of one maturity relative to another...

of different natural resources, but this value appraisal would not be on a time scale relevant to human activity. Choice 6 is useful for systems ecologists to consider exergy concepts as a driving force for the emergence
Emergence
In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....

structures in nature using a concept like emergy
Emergy
Emergy is the available energy of one kind that is used up in transformations directly and indirectly to make a product or service. Emergy accounts for, and in effect, measures quality differences between forms of energy. Emergy is an expression of all the energy used in the work processes that...

.

Choice 7 is the consequence of this line of thinking carried out to its fullest extent. It is a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

to restate the cosmological argument
Cosmological argument
The cosmological argument is an argument for the existence of a First Cause to the universe, and by extension is often used as an argument for the existence of an "unconditioned" or "supreme" being, usually then identified as God...

.

## Quality of energy types

The ratio of exergy to energy in a substance can be considered a measure of energy quality
Energy quality
Energy quality is the contrast between different forms of energy, the different trophic levels in ecological systems and the propensity of energy to convert from one form to another. The concept refers to the empirical experience of the characteristics, or qualia, of different energy forms as they...

. Forms of energy such as macroscopic kinetic energy, electrical energy, and chemical Gibbs free energy
Gibbs free energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure...

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
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

.

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
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

.

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
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

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
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

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.

However, it appears that the ability to do work is relative to the energy transforming mechanism that applies a force. This is to say that some forms of energy perform no work with respects to some mechanisms, but perform work with respects to others. For example, water does not have a propensity to combust in an internal combustion engine, whereas gasoline does. Relative to the internal combustion engine, water has little ability to do work that provides a motive force. If “energy” is defined as the ability to do work then a consequence of this simple example is that water has no energy — according to this definition. Nevertheless, water, raised to a height, does have the ability to do work like driving a turbine, and so does have energy.

This example means to demonstrate that the ability to do work can be considered relative to the mechanism that transforms energy, and through such a conversion applies a force. From this observation we might wish to use the word “quality”, and the term “energy quality” to characterise the energetic differences between substances and their propensities to perform work given a specific mechanism. That is the abilities of different energy forms to flow and be transformed in certain mechanisms. With this lexicon, we can say that energy quality is mechanism-relative, and the energy efficiency of a mechanism is energy quality-relative – an internal combustion engine running on water has nearly 0% efficiency since it has the propensity to transform little or no water-energy into thermal-energy. In order to clarify things here we might think of this as the “water-efficiency”. The mechanism of interest is also our system of reference, such that the choice of energy quality specifies a certain system of reference. Thus with respects to the internal combustion system of reference, it has a low “water-efficiency”.

### Exergy of heat available at a temperature

Maximal possible conversion of heat to work, or exergy content of heat, depends on the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

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
Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...

Carnot heat engine
A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824...

.

Carnot efficiency is

where TH is the higher temperature and TC is the lower temperature, both as absolute temperature. From Equation 1 it is clear that in order to maximize efficiency one should maximize TH and minimize TC.

For calculation of exergy of heat available at a temperature there are two cases: the body releasing heat is higher than the surrounding, or, the temperature of the body is lower than the surrounding.

Exergy exchanged is then:

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