Exergy

Exergy, often referred to as "available energy" or "useful work potential", is a fundamental concept in the field of thermodynamics and engineering. It plays a crucial role in understanding and quantifying the quality of energy within a system and its potential to perform useful work. Exergy analysis has widespread applications in various fields, including energy engineering, environmental science, and industrial processes.
From a scientific and engineering perspective, second-law-based exergy analysis is valuable because it provides a number of benefits over energy analysis alone. These benefits include the basis for determining energy quality, enhancing the understanding of fundamental physical phenomena, and improving design, performance evaluation and optimization efforts. In thermodynamics, the exergy of a system is the maximum useful work that can be produced as the system is brought into equilibrium with its environment by an ideal process. The specification of an "ideal process" allows the determination of "maximum work" production. From a conceptual perspective, exergy is the "ideal" potential of a system to do work or cause a change as it achieves equilibrium with its environment. Exergy is also known as "availability". Exergy is non-zero when there is dis-equilibrium between the system and its environment, and exergy is zero when equilibrium is established.
Determining exergy was one of the original goals of thermodynamics. The term "exergy" was coined in 1956 by Zoran Rant by using the Greek ex and ergon, meaning "from work", but the concept had been earlier developed by J. Willard Gibbs in 1873.
Energy is neither created nor destroyed, but is simply converted from one form to another. In contrast to energy, exergy is always destroyed when a process is non-ideal or irreversible. To illustrate, when someone states that "I used a lot of energy running up that hill", the statement contradicts the first law. Although the energy is not consumed, intuitively we perceive that something is. The key point is that energy has quality or measures of usefulness, and this energy quality is what is consumed or destroyed. This occurs because everything, all real processes, produce entropy and the destruction of exergy or the rate of "irreversibility" is proportional to this entropy production. Where entropy production may be calculated as the net increase in entropy of the system together with its surroundings. Entropy production is due to things such as friction, heat transfer across a finite temperature difference and mixing. In distinction from "exergy destruction", "exergy loss" is the transfer of exergy across the boundaries of a system, such as with mass or heat loss, where the exergy flow or transfer is potentially recoverable. The energy quality or exergy content of these mass and energy losses are low in many situations or applications, where exergy content is defined as the ratio of exergy to energy on a percentage basis. For example, while the exergy content of electrical work produced by a thermal power plant is 100%, the exergy content of low-grade heat rejected by the power plant, at say, 41 degrees Celsius, relative to an environment temperature of 25 degrees Celsius, is only 5%.

Definitions

Exergy is a combination property of a system and its environment because it depends on the state of both and is a consequence of dis-equilibrium between them. Exergy is neither a thermodynamic property of matter nor a thermodynamic potential of a system. Exergy and energy always have the same units, and the joule is the unit of energy in the International System of Units. 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. Yet, with such an approach one has to abandon the requirement that the environment is large enough relative to the "system" such that its intensive properties, such as temperature, are unchanged due to its interaction with the system. So that exergy is defined in an absolute sense, it will be assumed in this article that, unless otherwise stated, that the environment's intensive properties are unchanged by its interaction with the system.
For a heat engine, the exergy can be simply defined in an absolute sense, as the energy input times the Carnot efficiency, assuming the low-temperature heat reservoir is at the temperature of the environment. Since many systems can be modeled as a heat engine, this definition can be useful for many applications.

Terminology

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

Implications

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.

Examples

For two thermal reservoirs at temperatures T_H and T_C < T_H, as considered by Carnot, the exergy is the work W that can be done by a reversible engine. Specifically, with Q_H the heat provided by the hot reservoir, Carnot's analysis gives W/''Q_H = /T''_H. Although, exergy or maximum work is determined by conceptually utilizing an ideal process, it is the property of a system in a given environment. Exergy analysis is not merely for reversible cycles, but for all cycles, and indeed for all thermodynamic processes.
As an example, consider the non-cyclic process of expansion of an ideal gas. For free expansion in an isolated system, the energy and temperature do not change, so by energy conservation no work is done. On the other hand, for expansion done against a moveable wall that always matched the pressure of the expanding gas, with no heat transfer, the maximum work would be done. This corresponds to the exergy. Thus, in terms of exergy, Carnot considered the exergy for a cyclic process with two thermal reservoirs. Just as the work done depends on the process, so the exergy depends on the process, reducing to Carnot's result for Carnot's case.
W. Thomson, as early as 1849 was exercised by what he called “lost energy”, which appears to be the same as “destroyed energy” and what has been called “anergy”. In 1874 he wrote that “lost energy” is the same as the energy dissipated by, e.g., friction, electrical conduction, heat conduction, viscous processes and particle diffusion. On the other hand, Kelvin did not indicate how to compute the “lost energy”. This awaited the 1931 and 1932 works of Onsager on irreversible processes.

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, these statements are both expressions of the second law of thermodynamics if the following expression is used for exergy:
where the extensive quantities for the system are: U = Internal energy, V = Volume, and N_i = Moles of component i. The intensive quantities for the surroundings are: P_R = Pressure, T_R = temperature, μ_{i, R} = Chemical potential of component i. Indeed the total entropy of the universe reads:
the second term being the entropy of the surroundings to within a constant.
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. 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 ) 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.