Question

The dimensional formula for Boltzmann's constant is

• A. $ [M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}] $
• B. $ [M{{L}^{2}}{{T}^{-2}}] $
• C. $ [M{{L}^{o}}{{T}^{-2}}{{\theta }^{-2}}] $
• D. $ [M{{L}^{-2}}{{T}^{-1}}{{\theta }^{-1}}] $

Answer 1

Answer: (A)

Boltzmann constant $(k)$ is the ratio of the universal gas constant $(R) $ to the Avogadro constant $\left(N_{A}\right)$.
It may be thought of therefore as the gas constant
$k=\frac{R}{N_{A}}=\left[M L^{2} T^{-2} \theta^{-2}\right]$
It is named after Ludwig Boltzmann.