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http://en.wikipedia.org/wiki/Energy_density

All text is available under the terms of the GNU Free Documentation License: http://en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License

# Energy density

Energy density is the amount of energy stored in a given system or region of space per unit volume or per unit mass, depending on the context. In some cases it is obvious from context which quantity is most useful: for example, in rocketry, energy per unit mass is the most important parameter, but when studying pressurized gas or magnetohydrodynamics the energy per unit volume is more appropriate. In a few applications (comparing, for example, the effectiveness of hydrogen fuel to gasoline) both figures are appropriate and should be called out explicitly (hydrogen has a higher energy density per unit mass than does gasoline, but a much lower energy density per unit volume in most applications).

Energy density per unit volume has the same physical units as pressure, and in many circumstances is an exact synonym: for example, the energy density of the magnetic field may be expressed as (and behaves as) a physical pressure, and the energy required to compress a gas may be determined by multiplying the pressure of the compressed gas times its final volume.

Note however, that energy density should not be confused with conservation of energy. The energies gained or lost from a system are still conserved, because an equal and opposite energy is gained or lost in another system. In other words, energy has changed form but was never lost or gained.

## Energy density in energy storage and in fuel

In energy storage applications, the energy density relates the mass of an energy store to its stored energy. The higher the energy density, the more energy may be stored or transported for the same amount of mass. In the context of fuel selection, the energy density of a fuel is also called the specific energy of that fuel, though in general an engine using that fuel will yield less energy due to inefficiencies and thermodynamic considerations -- hence the specific fuel consumption of an engine will be greater than the reciprocal of the specific energy of the fuel.

Gravimetric and volumetric energy density of some fuels and storage technologies (modified from the Gasoline article): (Note: some values may not be accurate because of isomers or other irregularities)

By dividing by 3.6 the figures for megajoules per kilogram can be converted to kilowatt-hours per kilogram.

Unfortunately, the useful energy available by extraction from an energy store is always less than the energy put into the energy store, due to the laws of thermodynamics.

No single energy storage method boasts the best in specific power, energy density, and energies per unit mass.

Peukert's Law describes how the amount of energy we get out depends how quickly we pull it out.

## Energy density of electric and magnetic fields

Electric and magnetic fields store energy. In a vacuum, the (volumetric) energy density (in SI units) is given by:

$U = \frac{\varepsilon_0}{2} \mathbf{E}^2 + \frac{1}{2\mu_0} \mathbf{B}^2$,

where E is the electric field and B is the magnetic induction. In the context of magnetohydrodynamics, the physics of conductive fluids, the magnetic energy density behaves like an additional pressure that adds to the gas pressure of a plasma.

In normal (linear) substances, the energy density (in SI units) is:

$U = \frac{1}{2} ( \mathbf{E} \cdot \mathbf{D} + \mathbf{H} \cdot \mathbf{B} )$,

where D is the electric displacement and H is the magnetic field.

## Energy density of empty space

In physics, "vacuum energy" or "zero-point energy" is the volumetric energy density of empty space. More recent developments have expounded on the concept of energy in empty space.

Modern physics is commonly classified into two fundamental theories: quantum field theory and general relativity. Quantum field theory takes quantum mechanics and special relativity into account, and it's a theory of all the forces and particles except gravity. General relativity is a theory of gravity, but it is incompatible with quantum mechanics. Currently these two theories have not yet been reconciled into one unified description, though research into "quantum gravity" seeks to bridge this divide.

In general relativity, the cosmological constant is proportional to the energy density of empty space, and can be measured by the curvature of space. It is subsequently related to the age of the universe, as energy expands outwards with time its density changes.

Quantum field theory considers the vacuum ground state not to be completely empty, but to consist of a seething mass of virtual particles and fields. These fields are quantified as probabilities - that is, the likelihood of manifestation based on conditions. Since these fields do not have a permanent existence , they are called vacuum fluctuations. In the Casimir effect, two metal plates can cause a change in the vacuum energy density between them which generates a measurable force.

Some believe that vacuum energy might be the "dark energy" (also called quintessence) associated with the cosmological constant in general relativity, thought to be similar to a negative force of gravity (or antigravity). Observations that the expanding universe appears to be accelerating seem to support the cosmic inflation theory — first proposed by Alan Guth in 1981 — in which the nascent universe passed through a phase of exponential expansion driven by a negative vacuum energy density (positive vacuum pressure).

## Energy density of food

Energy density is the amount of energy (kilojoules or calories) per amount of food, with food amount being measured in grams or milliliters of food. Energy density is thus expressed in cal/g, kcal/g, J/g, kJ/g, cal/mL, kcal/mL, J/mL, or kJ/mL. This is the energy released when the food is metabolised by a healthy organism when it ingests the food (see food energy for calculation) and the food is metabolized with oxygen, into waste products such as carbon dioxide and water. Typical values of food energy density for high energy-density foods, such as a hamburger, would be 2.5 kcal/g. Purified fats and oils contain the highest energy densities-- about 9 kcal/g.

• Heat of combustion
• Zero-point energy - Vacuum energy
• Virtual particle
• Cosmological constant
• Cosmic inflation

## References

1. ^ C. Knowlen, A.T. Mattick, A.P. Bruckner and A. Hertzberg, "High Efficiency Conversion Systems for Liquid Nitrogen Automobiles", Society of Automotive Engineers Inc, 1988.

## External references

### Zero point energy

1. Eric Weisstein's world of physics - energy density [41]
2. Baez physics - Is there a nonzero cosmological constant? [42]; What's the Energy Density of the Vacuum?.
3. Introductory review of cosmic inflation [43]
4. An exposition to inflationary cosmology [44]

### Density data

•   "Aircraft Fuels." Energy, Technology and the Environment Ed. Attilio Bisio. Vol. 1. New York: John Wiley and Sons, Inc., 1995. 257-259

### Energy storage

• table of energy density
• energy fundamentals
• Energy Density Field Theory

### Books

• The Inflationary Universe: The Quest for a New Theory of Cosmic Origins by Alan H. Guth (1998) ISBN 0-201-32840-2
• Cosmological Inflation and Large-Scale Structure by Andrew R. Liddle, David H. Lyth (2000) ISBN 0-521-57598-2
• Richard Becker, "Electromagnetic Fields and Interactions", Dover Publications Inc., 1964

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