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.

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, that 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. And in general, specific energy and energy density are at odds due to charge screening.

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

(Notes: 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. The symbol ** indicates the item is an energy carrier, not an energy source.)

storage type	energy density		recovery efficiency
	by mass	by volume	peak	practical
	MJ/kg	MJ/L	%	%
**mass-energy equivalence	89,876,000,000
**binding energy of helium nucleus	675,000,000	8.57x1024
nuclear fusion of hydrogen (energy from the sun)	300,000,000	423,000,000
nuclear fission (of U-235) (Used in Nuclear Power Plants)	77,000,000	1,500,000,000		30% 50%
**liquid hydrogen	143	10.1
**compressed gaseous hydrogen at 700 bar[1]	143	4.7
**hydrogen	143	0.01079
beryllium (toxic) (burned in air)	67.6	125.1
lithium borohydride (burned in air)	65.2	43.4
boron [2] (burned in air)	58.9	137.8
compressed natural gas at 200 bar	53.6[3]	10
gasoline[4]	46.9	34.6
diesel fuel/residential heating oil[5]	45.8	38.7
polyethylene plastic	46.3[6]	42.6
polypropylene plastic	46.3[7]	41.7
gasohol (10% ethanol 90% gasoline)	43.54	28.06
lithium (burned in air)	43.1	23.0
Jet A aviation fuel[8]	42.8	33
biodiesel oil (vegetable oil)	42.20	30.53
DMF (2,5-dimethylfuran)	42[9]	37.8
crude oil (according to the definition of ton of oil equivalent)	41.87	37[10]
polystyrene plastic	41.4[11]	43.5
body fat metabolism	38	35	22-26%[12]
butanol	36.6	29.2
LPG	34.39	22.16
**specific orbital energy of Low Earth orbit	33 (approx.)
graphite (burned in air)	32.7	72.9
anthracite coal	32.5	72.4		36%
silicon (burned in air)[13]	32.2	75.1
aluminum (burned in air)	31.0	83.8
ethanol	30	24
polyester plastic	26.0[14]	35.6
magnesium (burned in air)	24.7	43.0
bituminous coal [15]	24	20
PET pop bottle plastic	?23.5 impure	?
methanol	19.7	15.6
**hydrazine (toxic) combusted to N2+H2O	19.5	19.3
**liquid ammonia (combusted to N2+H2O)	18.6	11.5
PVC plastic (improper combustion toxic)	18.0[16]	25.2
sugars, carbohydrates & proteins metabolism	17	26.2(dextrose)	22-26% [17]
Cl2O7 + CH4 - computed	17.4
lignite coal	14-19
calcium (burned in air)	15.9	24.6
dry cowdung and cameldung	15.5[18]
wood	6–17[19]	1.8–3.2
**liquid hydrogen + oxygen (as oxidizer) (1:8 (w/w), 14.1:7.0 (v/v))	13.333	5.7
sodium (burned to wet sodium hydroxide)	13.3	12.8
Cl2O7 decomposition - computed	12.2
nitromethane	11.3	12.9
household waste	8-11[20][21]
sodium (burned to dry sodium oxide)	9.1	8.8
iron (burned to iron(III) oxide)	7.4	57.9
Octanitrocubane explosive - computed	7.4
ammonal (Al+NH4NO3 oxidizer)	6.9	12.7
Tetranitromethane + hydrazine explosive - computed	6.6
Hexanitrobenzene explosive - computed	6.5
zinc (burned in air)	5.3	38.0
Teflon plastic (combustion toxic, but flame retardant)	5.1	11.2
iron (burned to iron(II) oxide)	4.9	38.2
**TNT	4.184	6.92
Copper Thermite (Al + CuO as oxidizer)	4.13	20.9
Thermite (powder Al + Fe2O3 as oxidizer)	4.00 [22]	18.4
**compressed air at 300 bar	4	0.14	?
ANFO	3.88
hydrogen peroxide decomposition (as monopropellant)	2.7	3.8
Lithium Thionyl Chloride Battery	2.5
**hydrazine(toxic) decomposition (as monopropellant)	1.6	1.6
**ammonium nitrate decomposition (as monopropellant)	1.4	2.5
Molecular spring	~1
**sodium-sulfur battery	?	1.23[23]	?	85%[24]
**liquid nitrogen	0.77	0.62
**lithium ion battery	0.54–0.72	0.9–1.9		95%[25]
**lithium sulphur battery	0.54-1.44	?
kinetic energy penetrator	1.9-3.4	30-54
5.56 × 45 mm NATO bullet	0.4-0.8	3.2-6.4
**Zn-air batteries	0.40 to 0.72	?	?	?
**flywheel	0.5	?	?	81-94%[www.ccm.nl]
melting ice	0.335	0.335
**zinc-bromine flow battery	0.27–0.306[26]
**compressed air at 20 bar	0.27		?	64%[27]
**NiMH Battery	0.22[28]	0.36	?	60% [29]
**NiCd Battery	0.14-0.22	?	?	80% [30]
**lead acid battery	0.09–0.11[31]	0.14–0.17	?	75-85%[32]
**commercial lead acid battery pack	0.072-0.079[33]	?	?	?
**vanadium redox battery	.09[34]	.1188	?	70-75%
**vanadium bromide redox battery	.18[35]	.252	?	81%
**ultracapacitor	0.0206 [36]	?	?	?
**ultracapacitor by EEStor (claimed capacity)	1.0 [37]	?	?	?
**supercapacitor	0.01	?	98.5%	90%[38]
**capacitor	0.002 [39]	?	?	?
water at 100 m dam height	0.001	0.001	?	85-90%[40]
**spring power (clock spring), torsion spring	0.0003[41]	0.0006	?
zero point energy	0	0

Conclusion: the highest density sources of energy are fusion and fission. Fusion includes energy from the sun which will be available for billions of years (in the form of sunlight) but humans have not learned to make our own fusion power sources. Fission of U-235 in nuclear power plants will be available for thousands of years because of the vast supply of the element on earth. Coal and petroleum are the current primary energy sources in the U.S. 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 creates environmental impacts: for example, global warming, nuclear waste storage, and deforestation are a few of the consequences of supplying our growing energy demands from fossil fuels, nuclear fission, or biomass.

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, as explained by the laws of thermodynamics. No single energy storage method boasts the best in specific power, specific energy, and energy density. 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.

See also

• Figure of merit
• Energy content of biofuel
• Heat of combustion
• Heating value
• Specific impulse
• Vacuum energy

External references

Zero point energy

1. Eric Weisstein's world of physics: energy density [42]
2. Baez physics: Is there a nonzero cosmological constant? [43]; What's the Energy Density of the Vacuum?.
3. Introductory review of cosmic inflation [44]
4. An exposition to inflationary cosmology [45]

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
• table of batteries

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