A) universal gas constant
B) specific heat
C) Boltzmann constant
D) gravitational potential
E) None of the above
Correct Answer: C
Solution :
\[\text{Entropy}=\frac{\text{Heat}\,\text{absorbed}}{\text{Temperature}}\] \[\Rightarrow \] \[S=\frac{Q}{T}\] \[\Rightarrow \] \[[S]=[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}]\] Also, \[E=\frac{1}{2}{{k}_{B}}T\]where \[{{k}_{B}}\] is Boltzmann constant. \[\Rightarrow \] \[[{{k}_{B}}]=\frac{[E]}{[T]}=\frac{[M{{L}^{2}}{{T}^{-2}}]}{[K]}=[M{{L}^{2}}{{T}^{-2}}{{K}^{-1}}]\] Hence, dimensional formula of entropy is same as that of Boltzmann constant.
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