Joule

Joule
Unit systemSI derived unit
Unit ofEnergy
SymbolJ 
Named afterJames Prescott Joule
Conversions
1 J in ...... is equal to ...
   SI base units   1 kg·m2/s2
   CGS units   1×107 erg
   kWh   2.78×10−7 kW⋅h
   kcal   2.39×10−4 kcal
   BTU   9.48×10−4 BTU
   eV   6.24×1018 eV

The joule (symbol: J) (/ˈdʒaʊl/ or sometimes /ˈdʒuːl/) is a unit in the SI system named after English physicist James Prescott Joule.

Classical mechanics

Work done by pushing a block horizontally, with S being the displacement measured in m.
Work done by lifting a block against gravity. The work done in this case equals the gain in potential energy of the block.

1 J is defined as the amount of energy transferred to an object when a force of 1 newton (kg m s-2) is exerted on it over a distance of 1 metre (1 J = 1 N × 1 m), which is related to the W, a unit of power (P): One watt is defined as one joule per second of energy transfer. Algebraically, work done in classical mechanics (W) can be expressed as:

W = F • s

Electromagnetism

Electronics

1 J is defined as the work done for one ampere of electric current to pass through an electric circuit with external resistance equivalent to one ohm per second. It can be illustrated by the following equations:

E = C V — (1)
V = I R — (2)
P = V I — (3)
E = P t — (4)

Combining (2), (3) and (4),

E = I2 R t

where V is the voltage, E is the electrical energy, C is the charge, I is the current, R is the resistance, P is the power and t is the time of energy transfer.

Atomic physics

Arithmetically, 1 J ≈ 6.24 × 1012 MeV due to mass-energy equivalence. One unified atomic mass unit (u, amu or Da) is approximatey 931 MeV of energy (M = 106).

Derivation
1 amu ≈ 1.66 × 10-27 kg (¹⁄₁₂ mass of a carbon-12 isotope by definition). Speed of light (c) = 3.00 × 108 ms-1.

ΔE = Δmc2
ΔE = (1.66 × 10-27)(3.00 × 108)2
= 1.49 × 10-10 J

∵ 1 eV ≈ 1.60 × 10-19 J
1 MeV = 1.60 × 10-19 × 106 J
= 1.60 × 10-13 J

1.49 × 10-10 J = 1.49 × 10-10/1.60 × 10-13 MeV = 931 MeV (3 s.f.)

∴ 1 amu ≈ 931 MeV

References

  1. ↑ "Joule (unit) - Knowino". Radboud Universiteit. Retrieved December 1, 2024.
  2. ↑ "CGS and SI (MKS) unit systems". University of Southampton. Retrieved December 1, 2024.
  3. ↑ "What is a kilowatt hour and the cost of electricity per kWh". British Gas. June 24, 2024. Retrieved December 1, 2024.
  4. ↑ Levy, Sidney M. (2012). Kilocalories. Elsevier. ISBN 978-0-12-382243-7. Retrieved December 1, 2024.
  5. ↑ "British thermal unit (Btu)". The US Solar Institute. Archived from the original on December 8, 2024. Retrieved December 1, 2024.
  6. ↑ "Electron volt | energy, particles, force". Britannica. October 10, 2024. Retrieved December 1, 2024.
  7. ↑ "Work Equals Force Times Distance". NASA. Retrieved November 30, 2024.
  8. ↑ "Converted number: Conversion from eV to J". National Institute of Standards and Technology (NIST). 2022. Retrieved November 30, 2024.
  9. ↑ "Nuclear Binding Energy and the Mass Defect". Boston University. Retrieved November 30, 2024.
  10. ↑ "Speed of light | Definition, Equation, Constant, & Facts". Britannica. Retrieved October 29, 2024.