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Exergy


Exergy is the maximum amount of work that can be extracted from a physical system by exchanging matter and energy with large reservoirs in a reference state. This work potential is due to either a potential due to a force, temperature, or the degree of physical disorder. While energy is conserved, exergy can be destroyed. While there is a constant amount of energy in the universe, the amount of exergy is constantly decreasing with every physical process.

The term essergy is also used for the same concept.

Contents

Quality of energy types

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

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

The quantification of exergy depends on the conditions of the surrounding environment, or reference state. Exergy, in a general sense, is a measure of how different a substance is from the surroundings. Work can be subtracted by making this substance more like the surroundings. In order to extract gravitational potential energy, you need to allow a substance to fall. Exergy-containing chemicals react with species in the environment, creating products that can be diffused to the concentration they are found in the environment, releasing energy. A technically correct reference state has homogenous matter and energy that cannot undergo a process in which work is done. While the Earth's environment is hardly a perfect reference state, local conditions can be used for practical calculations. In order to extract work from something hot, you need a reservoir of relative cold.

Work can be extracted also from bodies colder than the surroundings. When the flow of energy is comming into the body, work is performed by this energy obtained from the large reservoir, the surrounding.

Gravitational, Electric, and Kinetic Exergy

As stated above, gravitational, electric and kinetic energy can be completely recovered as mechanical work. Therefore, the exergy and energy are equal for these types of energy. The amount of exergy must be established relative to a reference state, such as motionless at sealevel.

Chemical Exergy

The chemical potential, or Gibbs free energy, of a substance is equal to its chemical exergy. This potential is completely recoverable, allowing devices that convert chemical potential directly to entropy-free forms of energy like electricity like fuel cells to be theoretically 100% efficient. The chemical potential includes the difference in bond energy of the reacting molecules relative to reference species in the environment in addition to the diffusive energy of the products. When one species is at a high concentration relative to its concentration in the environment, work can be extracted by allowing the substance to diffuse to the reference state concentration. The reference species for a reaction of a hydrocarbon fuel with oxygen are carbon dioxide and water. In most chemical energy conversion devices, the chemical exergy is converted to lower quality thermal energy, destroying a portion of the exergy.

Exergy of heat available at a temperature

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

Carnot efficiency is

\eta = 1 - \frac{T_C}{T_H} \qquad \mbox{(1)}

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 fraction of heat available at a temperature higher than the surrounding is:

\frac{E}{Q} \ = 1 - \frac{T_o}{T_h} \qquad \mbox{(2)}

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

Exergy of cold is though:

\frac{E}{Q} \ = 1 - \frac{T_c}{T_o} \qquad \mbox{(3)}


where Tc is the temperature of the cold body that is receiving heat from the surroundings.

Exergy of heat available from a body

A body can deliver heat either from the sensible heat that is exhibited as temperature of the body, or from the latent heat. In the case of sensible heat the heat is not available at a constant temperature, as the temperature decreases as it gives away the heat. For the latent heat components, the Carnot factor can be employed. In practice, exergy is determined by use of the state equations of the material or materials of the body, or pre-calculated tables.

+ formulae!

Radiation Exergy

For radiation interpreted as electro-magnetic waves, exergy content is equal to energy content. At the quantum mechanics level finite bodies are involved so that a minute part of the radiationenergy can not be extracted as mechanical work.

In practical energy conversions, such as photosynthesis, photovoltaics and in solar thermal devices the exergy efficiency is limitted by the details of the process involved.

When solar raditaion is coverted to heat (solar thermal conversion), the limitting factors to exergy content are the ability of concentrating the radiation and the temperature which the materials involved in the apparatus can withstand. As the maximal achievable temperature of the working medium is well below 1000oC, one third of the theoretical exergy is lost at the start of further conversion of heat to work (see: #Exergy of heat at a temperature).

Nuclear Exergy

+ similar to above

Exergy History

The general concept of maximum obtainable work from a system was first analysed by Willard Gibbs in 1878. Gibbs called the quantity available energy of a system. A definition of available energy useful in technical system analysis and the term exergy has been proposed by Zoran Rant in 1956.

External links

References

  • Z. Rant, "Exergie, ein neues Wort fur Technische Arbeitsfahigkeit", Forschung Ing. Wes., 22 (1956) 36.


Last updated: 08-22-2005 19:39:55
Last updated: 10-29-2005 02:13:46