Question

Dimensional formula for entropy is identical to that of

• A. universal gas constant
• B. specific heat
• C. Boltzmann constant
• D. gravitational potential

Answer 1

Answer: (C)

$\text{Entropy}=\frac{\text{Heat}\text{absorbed}}{\text{Temperature}}$ $\Rightarrow$ $S=\frac{Q}{T}$ $\Rightarrow$ $[S]=[M{L}^2{T}^{-2}{K}^{-1}]$ 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.