A) \[[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]\]
B) \[[M{{L}^{2}}{{T}^{-2}}]\]
C) \[[M{{L}^{o}}{{T}^{-2}}{{\theta }^{-2}}]\]
D) \[[M{{L}^{-2}}{{T}^{-1}}{{\theta }^{-1}}]\]
Correct Answer: A
Solution :
Boltzmann constant (k) is the ratio of the universal gas constant (R) to the Avogadro constant\[({{N}_{A}})\]. It may be thought of therefore as the gas constant\[k=\frac{R}{{{N}_{A}}}=[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-2}}]\] It is named after Ludwig Boltzmann.
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