Dimensional Formula of Boltzmann Constant
The dimensional formula of Boltzmann constant is given by,
[M1 L2 T-2 K-1]
- M = Mass
- K = Temperature
- L = Length
- T = Time
Boltzmann Constant (k) = Energy × [Temperature]-1 . . . (1)
Since, Energy = M × a × displacement = [M1 × M0 L1 T-2 × L1]
Therefore, the dimensions of energy = [M1 L2 T-2] . . . (2)
And, the dimensional formula of temperature = [M0 L0 T0 K1] . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Boltzmann Constant = Energy × [Temperature]-1
Or, k = [M1 L2 T-2] × [M0 L0 T0 K1]-1 = [M1 L2 T-2 K-1].
Therefore, the Boltzmann constant is dimensionally represented as [M1 L2 T-2 K-1].