Question

Dimensional formula of Stefan's constant is

• A. $\left[M{T}^{-3}{K}^{-4}\right]$
• B. $\left[M{L}^2{T}^{{}^{-2}}{K}^{-4}\right]$
• C. $\left[M{L}^2{T}^{-2}\right]$
• D. $\left[M{L}^{-2}{T}^0\right]$
• E. $\left[M{T}^{-4}{L}^0\right]$

Answer 1

The correct option is A

$\left[M{T}^{-3}{K}^{-4}\right]$

Definition of the Stefan's Law

According to the Stefan's Law, the energy or power $P$ radiated per second is given as,

$P=\sigma A{T}^4$, Where, $\sigma$ is Stefan's constant

$T$ is Temperature

$A$ is area

$\sigma =\frac{P}{A{T}^4}$

Finding the Dimensional formula of the Stefan's constant

$\left[\sigma \right]=\frac{\left[M{L}^2{T}^{-3}\right]}{\left[L^2\right]\left[K^4\right]}$

$\left[\sigma \right]=\left[M{T}^{-3}{K}^{-4}\right]$

Hence, the correct option is $\left[A\right]$.