1Which of these has the same dimensions as Boltzmann constant?
Boltzmann constant and heat capacity both have the dimensions [M L² T⁻² K⁻¹].
Fundamental constantsClass 11, Kinetic Theory
Dimensional formula of Boltzmann constant
[M L2 T-2 K-1]
Energy per molecule per kelvin. It is the gas constant divided by the Avogadro number.
How to get the dimensional formula of Boltzmann constant
- Start from the definition: Boltzmann constant = energy / temperature.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
- Put in the dimension of each part: [M L2 T-2] / [K].
- Add the powers of each base quantity: [M L2 T-2 K-1].
Quantities with the dimensions [M L² T⁻² K⁻¹]
Equal dimensions do not make them the same quantity. Compare Boltzmann constant with the others in the full grid.
Three questions on Boltzmann constant
2What is the SI unit of Boltzmann constant?
The SI unit of Boltzmann constant is the joule per kelvin (J/K).
3Which one has different dimensions from the others?
Faraday constant is [T A mol⁻¹]. The other three are all [M L² T⁻² K⁻¹].
Boltzmann constant: quick answers
What is the dimensional formula of Boltzmann constant?
The dimensional formula of Boltzmann constant is [M L² T⁻² K⁻¹]. It comes from Boltzmann constant = energy / temperature.
What is the SI unit of Boltzmann constant?
The SI unit of Boltzmann constant is the joule per kelvin (J/K).
Which quantities have the same dimensions as Boltzmann constant?
Boltzmann constant shares [M L² T⁻² K⁻¹] with heat capacity, entropy. Equal dimensions do not make them the same quantity.