What is Dimensional Formula of Boltzmann Constant?

Dimensional Formula of Boltzmann constant is [M¹L²T^-2K^-1]

Derivation of Dimensional Formula of Boltzmann constant

We derive a dimensional formula of Boltzmann constant. For this we already need to know the dimensions of Avogadro number and gas constant

As, Boltzmann Constant = Gas Constant(R)/Avogadro Number(N_A)

Thus, Dimensional formula of k = dimensional formula of (R/N_A) . . . (1)

Now we calculate the dimensional formula of each quantity individually

Dimensional formula of R= [M¹L²T^-2K^-1] From(PV=nRT)

Dimensional formula of N_A= [M⁰L⁰T⁰] (It is 1/mol)

Putting all the above three-dimensional formulas in Equation (1) we get

Dimensional Formula of k = [M¹L²T^-2K^-1] / [M⁰L⁰N⁰]

⇒ Dimensional Formula of k = [M¹L²K^-1T^-2]

Hence, the dimensional formula of Charge is [ML²T^-2K^-1]

Dimensional Formula of the Boltzmann constant is [M¹L²T^-2K^-1]. As we know, a dimensional formula is a way of representing a physical quantity in terms of its dimensions.

Boltzmann constant is a physical constant of great significance in physics, especially when discussing the Kinetic Theory of gases. Now let’s learn about the Boltzmann constant and its dimensional formula.