Energies per unit mass

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This article gives constants of proportionality for cases where energy is proportional to mass.

• Kinetic energy: <math>\begin{matrix} \frac{1}{2} \end{matrix} v^2 </math> J/kg, where v is the speed in m/s.
• Potential energy with respect to gravity, close to earth: ca. 9.8 h J/kg, with h the height in m.
• Heat: specific heat capacity times temperature difference, specific melting heat, specific heat of vaporization
• Chemical energy: The fuel value or relative energy density is the quantity of potential energy in fuel, food or other substance.

nature	energy density (MJ.kg-1)	equivalent to...
mass-energy equivalence	89,876,000,000	21.48 Mt TNT per kg 149.3 pJ/u 931.5 MeV/u
binding energy of helium	675,000,000	28.3 MeV/atom
nuclear fusion (D-T)	300,000,000	70 kt TNT per kg
nuclear fission (of U-235)	90,000,000	22 kt TNT per kg 210 MeV/atom
hydrogen	120
gasoline	44 [1]
oil (according to the definition of ton of oil equivalent)	41.87
fat	38
specific orbital energy of Low Earth orbit	(roughly) 33
coal	23 to 29
sugar	17
wood	15
TNT	4.184
Lithium ion battery	0.540 to 0.720
melting ice	0.335
water at 100 m dam height	0.001

For rocket fuel a more relevant quantity is the energy per unit mass including oxidizer. For example, to burn 1 kg of hydrogen, 8 kg of oxygen is needed, so that the high fuel value reduces to 13.3 MJ per kg propellant.

Also relevant is the density: for liquid hydrogen this is only 70.8 kg/m³ (at 20 K), so the energy per unit volume is 8 MJ/L, which is much less than e.g. that of gasoline. Thus a large and therefore heavy tank is needed. See also density and hydrogen storage.

For projectiles, compare the value for TNT with the energy of a kinetic kill vehicle with a closing speed of e.g. 10 km/s, which is 50 MJ/kg.

The available energy from commercial explosives depends on their composition. The energy yield for ANFO is about 927 kcal/kg (3.88 MJ/kg) depending on the heating value of fuel oil. Aluminised ones will yield as high as 1470 kcal/kg (6.15 MJ/kg) (Brady et al, 1985).

NH₄NO₃ + 2/3 Al = 2H₂O + 1/3Al₂O₃ + N₂ + 1975 kcal/kg

NH₄NO₃ + 1/3 CH₂ = 7/3 H₂O + 1/3 CO₂ + N₂ + 986 kcal/kg

Contents 1 Relation with specific fuel consumption 2 Conversions 3 See also 4 External links

Relation with specific fuel consumption

Specific fuel consumption is the amount of fuel needed to do a given amount of work, e.g. a typical value for gasoline engines is 0.5 lb/(hp·h) = 0.3 kg/(kW·h), i.e. 1 kg per 12 MJ. The efficiency of the engine is the ratio of this 12 MJ/kg and the 44 MJ/kg mentioned above, about 27%. In particular, part of the energy goes into heat.

Conversions

• 1 eV/u = 160.2177 zJ/u = 96.4853 MJ/kg, using:
  • 1 eV = 160.2177 zJ
  • 1 u = 1.66054 yg (or 1 kg = 602.2142 Yu)
• Absorbed dose of radiation:
  • 1 gray = 1 J/kg
• with application of a dimensionless "quality factor":
  • 1 sievert = 1 J/kg
  • 1 rad = 0.01 J/kg

See also

• Binding energy
• Conversion of units for energy
• Energy density
• Energy value of coal
• Heating value
• Food energy
• Related units of measure: megaton and gigaton (often "of TNT"), barrel of oil equivalent, ton of oil equivalent, GTOE, conversion of units (includes the ones listed here and others such as cubic foot of natural gas, ton of coal equivalent)
• Nuclear weapon yield
• Orders of magnitude (energy)
• Power-to-weight ratio
• Specific heat capacity
• Specific heat of vaporization
• Specific kinetic energy
• Specific melting heat
• Specific orbital energy

External links

• Energy density of gasoline (reference: The Physics Factbook).