Convert 1 joule into erg using dimensional analysis
1 joule = 10⁷ erg. Energy is [M L² T⁻²], so only the powers of mass, length and time decide the factor.
joule = erg
Step by step
- The dimension of energyEnergy has the dimensions [M L² T⁻²]. Only the powers of M, L and T matter for the conversion.
- The conversion ruleA quantity with dimensions [Ma Lb Tc] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂] [L₁/L₂]² [T₁/T₂]⁻².
- The size of each base unitM: 1 kilogram (kg) is 1000 gram (g). L: 1 metre (m) is 100 centimetre (cm). T: 1 second (s) is the same in both systems.
- Put the numbers inn₂ = 1 [1 kg / 1 g] [1 m / 1 cm]² [1 s / 1 s]⁻²
- Work out each bracket[M₁/M₂] = 1000; [L₁/L₂]² = 100² = 10000; [T₁/T₂]⁻² = 1⁻² = 1
- Multiplyn₂ = 1 × 1000 × 10000 × 1 = 10⁷
- The answer1 joule = 10⁷ erg
Joule to erg: quick answers
How do you convert joule to erg?
Energy is [M L² T⁻²]. Multiply by the ratio of each base unit raised to its power in the dimension. That gives 1 joule = 10⁷ erg.
What is 1 joule in erg?
1 joule = 10⁷ erg.