Question

Sol. [Key Concept: Dimensional analysis of physical constants]

$\sigma_{s} = {MT}^{- 3}{\text{ }K}^{- 4}$

$$\begin{matrix} & k_{B} = M^{1}{\text{ }L}^{2}{\text{ }T}^{- 2}{\text{ }K}^{- 1} \\ & b = M^{0}{LT}^{0}\text{ }K \end{matrix}$$

$$\begin{matrix} & \sigma_{s}k_{B}^{- 1}b = \left\lbrack {MT}^{- 3}{\text{ }K}^{- 4} \right\rbrack\left\lbrack M^{- 1}{\text{ }L}^{- 2}{\text{ }T}^{2}\text{ }K \right\rbrack\left\lbrack M^{0}\text{ }L{\text{ }T}^{0}\text{ }K \right\rbrack \\ & \ = T^{- 1}{\text{ }K}^{- 2}{\text{ }L}^{- 1} \\ & \ = L^{- 1}{\text{ }T}^{- 1}{\text{ }K}^{- 2} \end{matrix}$$