Joule

For the physicist, see James Prescott Joule.

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

Joule
Unit system	SI derived unit
Unit of	Energy
Symbol	J
Named after	James Prescott Joule
Conversions
1 J in ...	... is equal to ...
SI base units[1]	1 kg·m2/s2
CGS units[2]	1×107 erg
kWh[3]	2.78×10−7 kW⋅h
kcal[4]	2.39×10−4 kcal
BTU[5]	9.48×10−4 BTU
eV[6]	6.24×1018 eV

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),^[7] 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.^[8] One unified atomic mass unit (u, amu or Da) is approximatey 931 MeV of energy (M = 10⁶).^[9]

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.^[10]

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

Related pages

• Gravity
• Kinematics
• John Dalton
• Issac Newton
• Kinetic energy
• Aerodynamics
• Particle physics
• Nuclear physics
• Potential energy
• Quantum physics
• Thermodynamics
• Nuclear binding energy