Energy density

Energy density is the amount of energy stored in a given system or region of space per unit volume. Colloquially it may also be used for energy per unit mass, though the accurate term for this is specific energy. Often only the useful or extractable energy is measured, which is to say that inaccessible energy (such as rest mass energy) is ignored.[1] In cosmological and other general relativistic contexts, however, the energy densities considered are those that correspond to the elements of the stress–energy tensor and therefore do include mass energy as well as energy densities associated with the pressures described in the next paragraph.

Energy per unit volume has the same physical units as pressure, and in many circumstances is a synonym: for example, the energy density of a 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 external pressure by the change in volume. In short, pressure is a measure of the enthalpy per unit volume of a system. A pressure gradient has the potential to perform work on the surroundings by converting enthalpy to work until equilibrium is reached.

Energy density
SI unitJ/m3
In SI base unitskg·m−1s−2
Derivations from
other quantities
U = E/V

Introduction to energy density

There are different types of energy stored in materials, and it takes a particular type of reaction to release each type of energy. In order of the typical magnitude of the energy released, these types of reactions are: nuclear, chemical, electrochemical, and electrical.

Nuclear reactions take place in stars and nuclear power plants, both of which derive energy from the binding energy of nuclei. Chemical reactions are used by animals to derive energy from food, and by automobiles to derive energy from gasoline. Liquid hydrocarbons (fuels such as gasoline, diesel and kerozene) are today the most dense way known to economically store and transport chemical energy at a very large scale (1 kg of diesel fuel burns with the oxygen contained in ~15 kg of air). Electrochemical reactions are used by most mobile devices such as laptop computers and mobile phones to release the energy from batteries.

Types of energy content

There are several different types of energy content. One is the theoretical total amount of thermodynamic work that can be derived from a system, with a given temperature and pressure for the surroundings. This is called exergy. Another is the theoretical amount of work that can be derived from reactants that are initially at room temperature and atmospheric pressure. This is given by the change in standard Gibbs free energy. But as a source of heat or for use in a heat engine, the relevant quantity is the change in standard enthalpy or the heat of combustion.

There are two kinds of heat of combustion:

  • The higher value (HHV), or gross heat of combustion, includes all the heat released as the products cool to room temperature and whatever water vapor is present condenses.
  • The lower value (LHV), or net heat of combustion, does not include the heat which could be released by condensing water vapor, and may not include the heat released on cooling all the way down to room temperature.

A convenient table of HHV and LHV of some fuels can be found in the references.[2].

Energy density in energy storage and in fuel

Energy density
Selected energy densities plot[3][4][5][6][7][8][9][10]

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.

Broad implications

Energy density differs from energy conversion efficiency (net output per input) or embodied energy (the energy output costs to provide, as harvesting, refining, distributing, and dealing with pollution all use energy). Large scale, intensive energy use impacts and is impacted by climate, waste storage, and environmental consequences.

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.

Alternative options are discussed for energy storage to increase energy density and decrease charging time.[11][12][13][14]

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.
Note: Also it is important to realise that generally the density values for chemical fuels do not include the weight of oxygen required for combustion. This is typically two oxygen atoms per carbon atom, and one per two hydrogen atoms. The atomic weight of carbon and oxygen are similar, while hydrogen is much lighter than oxygen. Figures are presented this way for those fuels where in practice air would only be drawn in locally to the burner. This explains the apparently lower energy density of materials that already include their own oxidiser (such as gunpowder and TNT), where the mass of the oxidiser in effect adds dead weight, and absorbs some of the energy of combustion to dissociate and liberate oxygen to continue the reaction. This also explains some apparent anomalies, such as the energy density of a sandwich appearing to be higher than that of a stick of dynamite.

Table of energy content

Unless otherwise stated, the values in the following table are supposed to be lower heating values. The following unit conversions may be helpful when considering the data in the table: 3.6 MJ = 1 kWh ≈ 1.34 HPh.

Energy densities of energy media
Storage type Specific energy
Energy density
Specific energy
Energy density
Uses and comments
Antimatter 89,875,517,874 Depends on the density of the antimatter's form 24,965,421,631,578 Depends on the density of the antimatter's form
Deuterium (in Fusion reactor)
87,900,000[15] 15,822[16] Experimental
Plutonium-239 83,610,000 (thermal energy)

31,000,000 (electrical energy)

Depends on crystallographic phase 23,222,915,000 (thermal energy)

8,700,000,000 (electrical energy)

Depends on crystallographic phase
Uranium (in breeder) 80,620,000[17] 1,539,842,000 Electric power plants (Nuclear fission)
Thorium (in breeder) 79,420,000[17] 929,214,000 Experimental (Nuclear fission)
Plutonium 238 2,239,000 43,277,631 RTGs
Hydrogen, liquid[18] 141.86 (HHV)
119.93 (LHV)
10.044 (HHV)
8.491 (LHV)
39,405.6 (HHV)
33,313.9 (LHV)
2,790.0 (HHV)
2,358.6 (LHV)
Rocket engines, Fuel Cells, H2 Storage/Transport.
Energy figures apply after reheating to 60°F
Hydrogen, at 690 bar and 60°F[18] 141.86 (HHV)
119.93 (LHV)
5.323 (HHV)
4.500 (LHV)
39,405.6 (HHV)
33,313.9 (LHV)
1,478.6 (HHV)
1,250.0 (LHV)
Fuel Cells, Natural Gas Heating Supplement
Hydrogen, gas, 1 atm, 60°F[18] 141.86 (HHV)
119.93 (LHV)
0.01188 (HHV)
0.01005 (LHV)
39,405.6 (HHV)
33,313.9 (LHV)
3.3 (HHV)
2.8 (LHV)
Diborane[19] 78.2 21,722.2
Beryllium 67.6 125.1 18,777.8 34,750.0
Lithium borohydride 65.2 43.4 18,111.1 12,055.6
Boron[20] 58.9 137.8 16,361.1 38,277.8
Methane (1.013 bar, 15 °C) 55.6 0.0378 15,444.5 10.5
Natural gas 53.6[21] 0.0364 14,888.9 10.1
LNG (NG at −160 °C) 53.6[21] 22.2 14,888.9 6,166.7
CNG (NG compressed to 250 bar/~3,600 psi) 53.6[21] 9 14,888.9 2,500.0
LPG propane[22] 49.6 25.3 13,777.8 7,027.8
LPG butane[22] 49.1 27.7 13,638.9 7,694.5
Gasoline (petrol)[22] 46.4 34.2 12,888.9 9,500.0
Polypropylene plastic 46.4[23] 41.7 12,888.9 11,583.3
Polyethylene plastic 46.3[23] 42.6 12,861.1 11,833.3
Crude oil (according to the definition of tonne of oil equivalent) 41.868 37[21] 11,630 10,278
Residential heating oil[22] 46.2 37.3 12,833.3 10,361.1
Diesel fuel[22] 45.6 38.6 12,666.7 10,722.2
100LL Avgas 44.0[24] 31.59 12,222.2 8,775.0
Jet fuel 43[25][26][27] 35 Aircraft engines
Gasohol E10 (10% ethanol 90% gasoline by volume) 43.54 33.18 12,094.5 9,216.7
Lithium 43.1 23.0 11,972.2 6,388.9
Biodiesel oil (vegetable oil) 42.20 33 11,722.2 9,166.7
DME[28][29] 31.7 (HHV)
28.4 (LHV)
21.24 (HHV)
19.03 (LHV)
8,805.6 (HHV)
7,888.9 (LHV)
5,900.0 (HHV)
5,286.1 (LHV)
Clean Diesel fuel
DMF (2,5-dimethylfuran) 42[30] 37.8 11,666.7 10,500.0
Polystyrene plastic 41.4[23] 43.5 11,500.0 12,083.3
Body fat metabolism 38 35 10,555.6 9,722.2 Efficiency 22%[31]
Butanol 36.6 29.2 10,166.7 8,111.1
Gasohol E85 (85% ethanol 15% gasoline by volume) 33.1 25.65 9,194.5 7,125.0
Graphite 32.7 72.9 9,083.3 20,250.0
Coal, anthracite[32] 26–33 34–43 7,222.2–9,166.7 9,444.5–11,944.5 Efficiency of conversion to electricity ~36%
Silicon[33] 32.2 75.1 8,944.5 20,861.1
Aluminum 31.0 83.8 8,611.1 23,277.8
Ethanol 30 24 8,333.3 6,666.7
Polyester plastic 26.0[23] 35.6 7,222.2 9,888.9
Magnesium 24.7 43.0 6,861.1 11,944.5
Coal, bituminous[32] 24–35 26–49 6,666.7–9,722.2 7,222.2–13,611.1
PET plastic 23.5 (impure)[34] 6,527.8
Methanol 19.7 15.6 5,472.2 4,333.3
Hydrazine (combusted to N2+H2O) 19.5 19.3 5,416.7 5,361.1
Liquid ammonia (combusted to N2+H2O) 18.6 11.5 5,166.7 3,194.5
PVC plastic (improper combustion toxic) 18.0[23] 25.2 5,000.0 7,000.0
Wood[35] 18.0 5,000.0
Peat briquette[36] 17.7 4,916.7
Sugars, carbohydrates, and protein metabolism 17 26.2 (dextrose) 4,722.2 7,277.8 Efficiency 22%[37]
Calcium 15.9 24.6 4,416.7 6,833.3
Glucose 15.55 23.9 4,319.5 6,638.9
Dry cow dung and camel dung 15.5[38] 4,305.6
Coal, lignite 10–20 2,777.8–5,555.6
Sodium (burned to wet sodium hydroxide) 13.3 12.8 3,694.5 3,555.6
Peat 12.8 3,555.6
Nitromethane 11.3 3,138.9
Sulfur (burned to sulfur dioxide)[39] 9.23 19.11 2,563.9 5,308.3
Sodium (burned to dry sodium oxide) 9.1 8.8 2,527.8 2,444.5
Battery, lithium-air rechargeable 9.0[40] 2,500.0
Household waste 8.0[41] 2,222.2
Zinc 5.3 38.0 1,472.2 10,555.6
Iron (burned to iron(III) oxide) 5.2 40.68 1,444.5 11,300.0
Teflon plastic (combustion toxic, but flame retardant) 5.1 11.2 1,416.7 3,111.1
Iron (burned to iron(II) oxide) 4.9 38.2 1,361.1 10,611.1
Gunpowder 4.7–11.3[42] 5.9-12.9 Explosives, Ammunition
TNT 4.184 6.92 Explosives
ANFO 3.7 1,027.8
Battery, zinc-air[43] 1.59 6.02 441.7 1,672.2
Liquid nitrogen 0.77[44] 0.62 213.9 172.2
Compressed air at 300 bar (potential energy) 0.5 0.2 138.9 55.6
Latent heat of fusion of ice (thermal) 0.335 0.335 93.1 93.1
Water at 100 m dam height (potential energy) 0.001 0.001 0.278 0.278 Practical efficiency 85–90%[45][46]
Lithium metal battery 1.8 4.32 Portable electronic devices
Lithium-ion battery 0.36–0.875[49] 0.9–2.63 Automotive motors, portable electronic devices, RC vehicles
Flywheel 0.36–0.5 5.3 Power plants, Gyrobusses
Alkaline battery 0.48[50] 1.3[51] Portable electronic devices, flashlights
Nickel-metal hydride battery 0.41[52] 0.504–1.46[52] Portable electronic devices, flashlights
Lead-acid battery 0.17 0.56 Automotive engine ignition
Supercapacitor (EDLC) 0.01–0.036[59] 0.05–0.06[60] Electronic circuits
Electrolytic capacitor 0.00001–0.0002[61] 0.00001–0.001[64] Electronic circuits
Storage type Energy density by mass (MJ/kg) Energy density by volume (MJ/L) Specific energy (Wh/kg) Energy density (Wh/L) Uses and comments

Divide joule/m3 by 109 to get MJ/L. Divide MJ/L by 3.6 to get kWh/L.

Table on energy content of batteries:

Energy capacities
Storage device Energy content
Energy type Typical mass
Typical volume
(width × height × depth in mm)
Alkaline AA battery[65] 9,360 Electrochemical 24 14.2 × 50
Alkaline C battery[65] 34,416 Electrochemical 65 26 × 46
NiMH AA battery 9,072 Electrochemical 26 14.2 × 50
NiMH C battery 19,440 Electrochemical 82 26 × 46
Lithium-ion 18650 battery 28,800–46,800 Electrochemical 44–49[66] 18 × 65

Nuclear energy sources

The greatest energy source by far is 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 (0.1%), nuclear fusion (1%), or the annihilation of some or all of the matter in the volume V by matter-antimatter collisions (100%). 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, does not have an equivalent anti-particle form, but would offer the same 100% conversion rate of mass to energy in the form of Hawking radiation. In the case of relatively small black holes (smaller than astronomical objects) the power output would be tremendous.

The highest density sources of energy aside from 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 (2018), sustained fusion power production continues to be elusive.

Power from fission of uranium and thorium in nuclear power plants will be available for many decades or even centuries because of the plentiful supply of the elements on earth,[67] though the full potential of this source can only be realised through breeder reactors, which are, apart from the BN-600 reactor, not yet used commercially.[68] Coal, gas, and petroleum are the current primary energy sources in the U.S.[69] but have a much lower energy density. Burning local biomass fuels supplies household energy needs (cooking fires, oil lamps, etc.) worldwide.

Thermal power of nuclear fission reactors

The density of thermal energy contained in the core of a light water reactor (PWR or BWR) of typically 1 GWe (1 000 MW electrical corresponding to ~3 000 MW thermal) is in the range of 10 to 100 MW of thermal energy per cubic meter of cooling water depending on the location considered in the system (the core itself (~30 m3), the reactor pressure vessel (~50 m3), or the whole primary circuit (~300 m3)). This represents a considerable density of energy which requires under all circumstances a continuous water flow at high velocity in order to be able to remove the heat from the core, even after an emergency shutdown of the reactor. The incapacity to cool the cores of three boiling water reactors (BWR) at Fukushima in 2011 after the tsunami and the resulting loss of the external electrical power and of the cold source was the cause of the meltdown of the three cores in only a few hours, even though the three reactors were correctly shut down just after the Tōhoku earthquake. This extremely high power density distinguishes nuclear power plants (NPP's) from any thermal power plants (burning coal, fuel or gas) or any chemical plants and explains the large redundancy required to permanently control the neutron reactivity and to remove the residual heat from the core of NPP's.

Energy density of electric and magnetic fields

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

where E is the electric field and B is the magnetic field. The solution will be (in SI units) in Joules per cubic metre. 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 and nondispersive) substances, the energy density (in SI units) is

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

In the case of absence of magnetic fields, by exploting Fröhlich's relationships it is also possible to extend these equations to anisotropy and nonlinearity dielectrics, as well as to calculate the correlated Helmholtz free energy and entropy densities.[70]

See also


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Further reading

  • 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

External links

Alcubierre drive

The Alcubierre drive or Alcubierre warp drive (or Alcubierre metric, referring to metric tensor) is a speculative idea based on a solution of Einstein's field equations in general relativity as proposed by Mexican theoretical physicist Miguel Alcubierre, by which a spacecraft could achieve apparent faster-than-light travel if a configurable energy-density field lower than that of vacuum (that is, negative mass) could be created.

Rather than exceeding the speed of light within a local reference frame, a spacecraft would traverse distances by contracting space in front of it and expanding space behind it, resulting in effective faster-than-light travel. Objects cannot accelerate to the speed of light within normal spacetime; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination faster than light would in normal space without breaking any physical laws.Although the metric proposed by Alcubierre is consistent with the Einstein field equations, it may not be physically meaningful, in which case a drive will not be possible. Even if it is physically meaningful, its possibility would not necessarily mean that a drive can be constructed. The proposed mechanism of the Alcubierre drive implies a negative energy density and therefore requires exotic matter. So if exotic matter with the correct properties cannot exist, then the drive could not be constructed. However, at the close of his original article Alcubierre argued (following an argument developed by physicists analyzing traversable wormholes) that the Casimir vacuum between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive.

Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate quantum mechanics. Some physicists have presented arguments to suggest that a theory of quantum gravity (which would incorporate both theories) would eliminate those solutions in general relativity that allow for backwards time travel (see the chronology protection conjecture) and thus make the Alcubierre drive invalid.

Cosmological constant

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the energy density of space, or vacuum energy, that arises in Albert Einstein's field equations of general relativity. It is closely associated to the concepts of dark energy and quintessence.Einstein originally introduced the concept in 1917 to counterbalance the effects of gravity and achieve a static universe, a notion which was the accepted view at the time. Einstein abandoned the concept in 1931 after Hubble's discovery of the expanding universe. From the 1930s until the late 1990s, most physicists assumed the cosmological constant to be equal to zero. That changed with the surprising discovery in 1998 that the expansion of the universe is accelerating, implying the possibility of a positive nonzero value for the cosmological constant.Since the 1990s, studies have shown that around 68% of the mass–energy density of the universe can be attributed to so-called dark energy. The cosmological constant Λ is the simplest possible explanation for dark energy, and is used in the current standard model of cosmology known as the ΛCDM model. While dark energy is poorly understood at a fundamental level, the main required properties of dark energy are that it functions as a type of anti-gravity, it dilutes much more slowly than matter as the universe expands, and it clusters much more weakly than matter, or perhaps not at all.According to quantum field theory (QFT) which underlies modern particle physics, empty space is defined by the vacuum state which is a collection of quantum fields. All these quantum fields exhibit fluctuations in their ground state (lowest energy density) arising from the zero-point energy present everywhere in space. These zero-point fluctuations should act as a contribution to the cosmological constant Λ, but when calculations are performed these fluctuations give rise to an enormous vacuum energy. The discrepancy between theorized vacuum energy from QFT and observed vacuum energy from cosmology is a source of major contention, with the values predicted exceeding observation by some 120 orders of magnitude, a discrepancy that has been called "the worst theoretical prediction in the history of physics!". This issue is called the cosmological constant problem and it is one of the greatest unsolved mysteries in science with many physicists believing that "the vacuum holds the key to a full understanding of nature".

Dark energy

In physical cosmology and astronomy, dark energy is an unknown form of energy which is hypothesized to permeate all of space, tending to accelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate.Assuming that the standard model of cosmology is correct, the best current measurements indicate that dark energy contributes 68% of the total energy in the present-day observable universe. The mass–energy of dark matter and ordinary (baryonic) matter contribute 27% and 5%, respectively, and other components such as neutrinos and photons contribute a very small amount. The density of dark energy is very low (~ 7 × 10−30 g/cm3) much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the mass–energy of the universe because it is uniform across space.Two proposed forms for dark energy are the cosmological constant, representing a constant energy density filling space homogeneously, and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space. Contributions from scalar fields that are constant in space are usually also included in the cosmological constant. The cosmological constant can be formulated to be equivalent to the zero-point radiation of space i.e. the vacuum energy. Scalar fields that change in space can be difficult to distinguish from a cosmological constant because the change may be extremely slow.

Energy content of biofuel

The Energy content of biofuel is a description of the chemical energy contained in a given biofuel, measured per unit mass of that fuel, as specific energy, or per unit of volume of the fuel, as energy density.

A biofuel is a fuel, produced from living organisms. Biofuels include bioethanol, an alcohol made by fermentation—often used as a gasoline additive, and biodiesel, which is usually used as a diesel additive. Specific energy is energy per unit mass, which is used to describe the energy content of a fuel, expressed in SI units as joule per kilogram (J/kg) or equivalent units. Energy density is the amount of energy stored in a fuel per unit volume, expressed in SI units as joule per litre (J/L) or equivalent units.


A flywheel is a mechanical device specifically designed to efficiently store rotational energy. Flywheels resist changes in rotational speed by their moment of inertia. The amount of energy stored in a flywheel is proportional to the square of its rotational speed. The way to change a flywheel's stored energy is by increasing or decreasing its rotational speed by applying a torque aligned with its axis of symmetry. Since flywheels act as mechanical energy storage devices, they are the kinetic-energy-storage analogue to electrical capacitors, for example, which are a type of accumulator. Like other types of accumulators, flywheels smooth the ripple in power output, providing surges of high power output as required, absorbing surges of high power input (system-generated power) as required, and in this way act as low-pass filters on the mechanical velocity (angular, or otherwise) of the system.

Common uses of a flywheel include:

Smoothing the power output of an energy source. For example, flywheels are used in reciprocating engines because the active torque from the individual pistons is intermittent.

Energy storage systems

Delivering energy at rates beyond the ability of an energy source. This is achieved by collecting energy in a flywheel over time and then releasing it quickly, at rates that exceed the abilities of the energy source.

Controlling the orientation of a mechanical system, gyroscope and reaction wheelFlywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a maximum revolution rate of a few thousand RPM. High energy density flywheels can be made of carbon fiber composites and employ magnetic bearings, enabling them to revolve at speeds up to 60,000 RPM (1 kHz).Carbon-composite flywheel batteries have recently been manufactured and are proving to be viable in real-world tests on mainstream cars. Additionally, their disposal is more eco-friendly than traditional lithium ion batteries.

Intensity (physics)

In physics, intensity is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy. In the SI system, it has units watts per square metre (W/m2). It is used most frequently with waves ( Example - sound or light), in which case the average power transfer over one period of the wave is used. Intensity can be applied to other circumstances where energy is transferred. For example, one could calculate the intensity of the kinetic energy carried by drops of water from a garden sprinkler.

The word "intensity" as used here is not synonymous with "strength", "amplitude", "magnitude", or "level", as it sometimes is in colloquial speech.

Intensity can be found by taking the energy density (energy per unit volume) at a point in space and multiplying it by the velocity at which the energy is moving. The resulting vector has the units of power divided by area (i.e., surface power density).

Lambda-CDM model

The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parametrization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) and associated with dark energy; second, the postulated cold dark matter (abbreviated CDM); and third, ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

the existence and structure of the cosmic microwave background

the large-scale structure in the distribution of galaxies

the abundances of hydrogen (including deuterium), helium, and lithium

the accelerating expansion of the universe observed in the light from distant galaxies and supernovaeThe model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

The ΛCDM model can be extended by adding cosmological inflation, quintessence and other elements that are current areas of speculation and research in cosmology.

Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, entropic gravity, modified gravity, theories of large-scale variations in the matter density of the universe, bimetric gravity, and scale invariance of empty space.

Lithium-ion battery

A lithium-ion battery or Li-ion battery (abbreviated as LIB) is a type of rechargeable battery, first proposed by chemist M Stanley Whittingham at Exxon in the 1970s. Lithium-ion batteries are commonly used for portable electronics and electric vehicles and are growing in popularity for military and aerospace applications.In the batteries lithium ions move from the negative electrode to the positive electrode during discharge and back when charging. Li-ion batteries use an intercalated lithium compound as one electrode material, compared to the metallic lithium used in a non-rechargeable lithium battery. The batteries have a high energy density, no memory effect (other than LFP cells) and low self-discharge. They can however be a safety hazard since they contain a flammable electrolyte, and if damaged or incorrectly charged can lead to explosions and fires. Samsung were forced to recall Galaxy Note 7 handsets following lithium-ion fires, and there have been several incidents involving batteries on Boeing 787s.

Chemistry, performance, cost and safety characteristics vary across LIB types. Handheld electronics mostly use LIBs based on lithium cobalt oxide (LiCoO2), which offers high energy density but presents safety risks, especially when damaged. Lithium iron phosphate (LiFePO4), lithium ion manganese oxide battery (LiMn2O4, Li2MnO3, or LMO), and lithium nickel manganese cobalt oxide (LiNiMnCoO2 or NMC) offer lower energy density but longer lives and less likelihood of fire or explosion. Such batteries are widely used for electric tools, medical equipment, and other roles. NMC in particular is a leading contender for automotive applications.

Research areas for lithium-ion batteries include life extension, energy density, safety, cost reduction, and charging speed, among others. Research has also been under way for aqueous lithium-ion batteries, which have demonstrated fewer potential safety hazards due to their use of non-flammable electrolytes.

Lithium iron phosphate battery

The lithium iron phosphate (LiFePO4) battery, also called LFP battery (with "LFP" standing for "lithium ferrophosphate"), is a type of rechargeable battery, specifically a lithium-ion battery, using LiFePO4 as the cathode material, and a graphitic carbon electrode with a metallic backing as the anode. The specific capacity of LiFePO4 is higher than that of the related lithium cobalt oxide (LiCoO2) chemistry, but its energy density is less due to its lower operating voltage. The main drawback of LiFePO4 is its low electrical conductivity. Therefore, all the LiFePO4 cathodes under consideration are actually LiFePO4/C. Because of low cost, low toxicity, well-defined performance, long-term stability, etc. LiFePO4 is finding a number of roles in vehicle use, utility scale stationary applications, and backup power.

Magnetic field

A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. Magnetic fields are observed in a wide range of size scales, from subatomic particles to galaxies. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location. As such, it is an example of a vector field.

The term 'magnetic field' is used for two distinct but closely related fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter. B, magnetic flux density, is measured in tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, B and H are the same aside from units; but in a magnetized material, B/ and H differ by the magnetization M of the material at that point in the material.

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.

Magnetic fields are widely used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

Milne model

The Milne model was a special-relativistic cosmological model proposed by Edward Arthur Milne in 1935. It is mathematically equivalent to a special case of the FLRW model in the limit of zero energy density (in other words, an empty universe) and it obeys the cosmological principle. The Milne model is also similar to Rindler space, a simple re-parameterization of flat Minkowski space.

Since it features both zero energy density and maximally negative spatial curvature, the Milne model is inconsistent with cosmological observations. Cosmologists actually observe the universe's density parameter to be consistent with unity and its curvature to be consistent with flatness.

Planck star

In loop quantum gravity theory, a Planck star is a hypothetical astronomical object that is created when the energy density of a collapsing star reaches the Planck energy density. Under these conditions, assuming gravity and spacetime are quantized, there arises a repulsive 'force' derived from Heisenberg's uncertainty principle. The accumulation of mass-energy inside the Planck star cannot collapse beyond this limit because it violates the uncertainty principle for spacetime itself.The key feature of this theoretical object is that this repulsion arises from the energy density, not the Planck length, and starts taking effect far earlier than might be expected. This repulsive 'force' is strong enough to stop the collapse of the star well before a singularity is formed, and indeed, well before the Planck scale for distance. Since a Planck star is calculated to be considerably larger than the Planck scale, this means there is adequate room for all the information captured inside of a black hole to be encoded in the star, thus avoiding information loss.While it might be expected that such a repulsion would act very quickly to reverse the collapse of a star, it turns out that the relativistic effects of the extreme gravity such an object generates slow down time for the Planck star to a similarly extreme degree. Seen from outside the star's Schwartzschild radius, the rebound from a Planck star takes approximately fourteen billion years, such that even primordial black holes are only now starting to rebound from an outside perspective.

Furthermore, the emission of Hawking radiation can be calculated to correspond to the timescale of gravitational effects on time, such that the event horizon that 'forms' a black hole evaporates as the rebound proceeds.The existence of Planck stars was first proposed by Carlo Rovelli and Francesca Vidotto, who theorized in 2014 that Planck stars form inside black holes as a solution to the black hole firewall and black hole information paradox. Confirmation of emissions from rebounding black holes could possibly provide evidence for loop quantum gravity. Recent work demonstrates that Planck stars may exist inside of black holes as part of a cycle between black hole to white hole.

Research in lithium-ion batteries

Research in lithium-ion batteries has produced many proposed refinements of lithium-ion batteries. Areas on research interest have focused on improving energy density, safety, rate capability, cycle durability, flexibility, and cost.

Sound energy density

Sound energy density or sound density is the sound energy per unit volume. The SI unit of sound energy density is the pascal (Pa), that is the joule per cubic metre (J/m3) in SI based units.

Specific energy

Energy density has tables of specific energies of devices and materials.Specific energy is energy per unit mass. (It is also sometimes called "energy density," though "energy density" more precisely means energy per unit volume.) It is used to quantify, for example, stored heat and other thermodynamic properties of substances such as specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. It may also be used for the kinetic energy or potential energy of a body. Specific energy is an intensive property, whereas energy and mass are extensive properties.

The SI unit for specific energy is the joule per kilogram (J/kg). Other units still in use in some contexts are the kilocalorie per gram (Cal/g or kcal/g), mostly in food-related topics, watt hours per kilogram in the field of batteries, and the Imperial unit BTU per pound (BTU/lb), in some engineering and applied technical fields.The concept of specific energy is related to but distinct from the chemical notion of molar energy, that is energy per mole of a substance, which uses units of energy per mole, such as J/mol, kJ/mol, or the older (but still widely used) kcal/mol.

Spectral density

The power spectrum of a time series describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum.

When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over all time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would be found per unit time, since the total energy of such a signal over all time would generally be infinite. Summation or integration of the spectral components yields the total power (for a physical process) or variance (in a statistical process), identical to what would be obtained by integrating over the time domain, as dictated by Parseval's theorem.

The spectrum of a physical process often contains essential information about the nature of . For instance, the pitch and timbre of a musical instrument are immediately determined from a spectral analysis. The color of a light source is determined by the spectrum of the electromagnetic wave's electric field as it fluctuates at an extremely high frequency. Obtaining a spectrum from time series such as these involves the Fourier transform, and generalizations based on Fourier analysis. In many cases the time domain is not specifically employed in practice, such as when a dispersive prism is used to obtain a spectrum of light in a spectrograph, or when a sound is perceived through its effect on the auditory receptors of the inner ear, each of which is sensitive to a particular frequency.

However this article concentrates on situations in which the time series is known (at least in a statistical sense) or directly measured (such as by a microphone sampled by a computer). The power spectrum is important in statistical signal processing and in the statistical study of stochastic processes, as well as in many other branches of physics and engineering. Typically the process is a function of time, but one can similarly discuss data in the spatial domain being decomposed in terms of spatial frequency.

Stefan–Boltzmann law

The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (also known as the black-body radiant emittance) is directly proportional to the fourth power of the black body's thermodynamic temperature T:

The constant of proportionality σ, called the Stefan–Boltzmann constant, is derived from other known physical constants. The value of the constant is

where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum. The radiance (watts per square metre per steradian) is given by

A body that does not absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by an emissivity, :

The radiant emittance has dimensions of energy flux (energy per time per area), and the SI units of measure are joules per second per square metre, or equivalently, watts per square metre. The SI unit for absolute temperature T is the kelvin. is the emissivity of the grey body; if it is a perfect blackbody, . In the still more general (and realistic) case, the emissivity depends on the wavelength, .

To find the total power radiated from an object, multiply by its surface area, :

Wavelength- and subwavelength-scale particles, metamaterials, and other nanostructures are not subject to ray-optical limits and may be designed to exceed the Stefan–Boltzmann law.

Sugar battery

A sugar battery is an enzymatic biofuel cell that uses a maltodextrin solution as a fuel to directly generate electricity. An advantage of this type of biofuel technology is that it can provide constant energy density since it is derived from compounds. A sugar fuel cell can have a complete conversion of glucose and maltodextrin to carbon dioxide if there is a total of 13 enzymes and 2 co-factors in the anode compartment.In 2014, researchers at Virginia Tech published their research on a new kind of glucose fueled fuel cell that improves efficiency over previous cells, resulting in a total energy density closely competing with lithium-ion batteries. The new cell have a potential energy density of 596 Ah kg−1, which is higher than lithium-ion batteries. If these fuel cells are proven, they could be used as soon as three years from now. These fuel cells can be used to power a cell phone for ten days, unlike the current lithium-ion batteries that can only be used for one day.Sony was also able to successfully develop a sugar-based biofuel cell that does not require mixing or convection of the glucose solution or air movement. This was achieved through a passive-type cell that works by simply supplying sugar solution to the battery.

Wave shoaling

In fluid dynamics, wave shoaling is the effect by which surface waves entering shallower water change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth. Under stationary conditions, a decrease in transport speed must be compensated by an increase in energy density in order to maintain a constant energy flux. Shoaling waves will also exhibit a reduction in wavelength while the frequency remains constant.

In shallow water and parallel depth contours, non-breaking waves will increase in wave height as the wave packet enters shallower water. This is particularly evident for tsunamis as they wax in height when approaching a coastline, with devastating results.

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