Energy density: Difference between revisions

Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored.^[1] Quantified energy is energy that has some sort of, as the name suggests, quantified magnitude with related units.

For fuels, the energy per unit volume is sometimes a useful parameter. Comparing, for example, the effectiveness of hydrogen fuel to gasoline, hydrogen has a higher specific energy than gasoline does, but, even in liquid form, a much lower energy density.

Energy 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 compressed gas a little more may be determined by multiplying the difference between the gas pressure and the pressure outside by the change in volume. In short, pressure is a measure of volumetric enthalpy of a system. A pressure gradient has a potential to perform work on the surroundings by converting enthalpy until equilibrium is reached.

In energy storage applications the energy density relates the mass of an energy store to the volume of the storage facility, e.g. the fuel tank. The higher the energy density of the fuel, the more energy may be stored or transported for the same amount of volume. The energy density of a fuel per unit mass is called the specific energy of that fuel. In general an engine using that fuel will generate less kinetic energy due to inefficiencies and thermodynamic considerations—hence the specific fuel consumption of an engine will always be greater than its rate of production of the kinetic energy of motion.

The greatest energy source by far consists of mass itself. This energy, E = mc², where m = ρV, ρ is the mass per unit volume, V is the volume of the mass itself and c is the speed of light. This energy, however, can be released only by the processes of nuclear fission, nuclear fusion, or the annihilation of some or all of the matter in the volume V by matter-antimatter collisions. Nuclear reactions cannot be realized by chemical reactions such as combustion. Although greater matter densities can be achieved, the density of a neutron star would approximate the most dense system capable of matter-antimatter annihilation possible. A black hole, although denser than a neutron star, doesn't have an equivalent anti-particle form.

If we thus consider the volume of the sphere around a proton defined by the extent of its electric field, we can get an approximate energy density for the proton, as seen in the table below.

The highest density sources of energy outside of antimatter are fusion and fission. Fusion includes energy from the sun which will be available for billions of years (in the form of sunlight) but so far (2011), sustained fusion power production continues to be elusive. Fission of U-235 in nuclear power plants will be available for some decades even though the vast supply of the element on earth is being depleted (peak uranium) - it might, however be possible at some future time to extract uranium from seawater.^[2][3] Coal, gas, and petroleum are the current primary energy sources in the U.S.^[4] but have a much lower energy density. Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide.

Energy density (how much energy you can carry) does not tell you about energy conversion efficiency (net output per input) or embodied energy (what the energy output costs to provide, as harvesting, refining, distributing, and dealing with pollution all use energy). Like any process occurring on a large scale, intensive energy use impacts the world. For example, climate change, nuclear waste storage, and deforestation may be some of the consequences of supplying our growing energy demands from fossil fuels, nuclear fission, or biomass.

No single energy storage method boasts the best in specific power, specific energy, and energy density. Peukert's Law describes how the amount of useful energy that can be obtained (for a lead-acid cell) depends on how quickly we pull it out. To maximize both specific energy and energy density, one can compute the specific energy density of a substance by multiplying the two values together, where the higher the number, the better the substance is at storing energy efficiently.

Gravimetric and volumetric energy density of some fuels and storage technologies (modified from the Gasoline article):

Note: Some values may not be precise because of isomers or other irregularities. See Heating value for a comprehensive table of specific energies of important fuels.

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It has been suggested that List of energy densities be merged into this section. (Discuss) Proposed since June 2010.

This table gives the energy density of a complete system, including all required external components, such as oxidisers or heat sources. 1 MJ ≈ 0.28 kWh ≈ 0.37 HPh.

This table lists energy densities of systems that require external components, such as oxidisers or a heat sink or source. These figures do not take into account the mass and volume of the required components as they are assumed to be freely available and present in the atmosphere. Such systems cannot be compared with self-contained systems.

Divide Joule meter⁻³ with 10⁹ to get MJ L⁻¹.

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

${\displaystyle U={\frac {\varepsilon _{0}}{2}}\mathbf {E} ^{2}+{\frac {1}{2\mu _{0}}}\mathbf {B} ^{2}}$

where E is the electric field and B is the magnetic field. 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

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

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

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.

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).

• Power density and specifically
  • Power-to-weight ratio
• Figure of merit
• Energy content of biofuel
• Heat of combustion
• Heating value
• Rechargeable battery
• Specific impulse
• Vacuum energy

1. Eric Weisstein's world of physics: energy density^[25]
2. Baez physics: Is there a nonzero cosmological constant?^[26]
3. Introductory review of cosmic inflation^[27]
4. An exposition to inflationary cosmology^[28]

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

• “Fuels of the Future for Cars and Trucks” - Dr. James J. Eberhardt - Energy Efficiency and Renewable Energy, U.S. Department of Energy - 2002 Diesel Engine Emissions Reduction (DEER) Workshop San Diego, California - August 25–29, 2002

• energy fundamentals

• 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