Question

What are the dimensions of Stefan’s constant?

• A. $M{L}^{-2}{T}^{-2}{K}^{-4}$
• B. $M{L}^{-1}{T}^{-2}{K}^{-4}$
• C. $ML{T}^{-3}{K}^{-4}$
• D. $M{L}^0{T}^{-3}{K}^{-4}$

Answer 1

The correct option is D

$M{L}^0{T}^{-3}{K}^{-4}$

The energy emitted per unit area per second by a black body in given by

$E=\sigma T^4$

Where is the Stefan’s constant and T is the absolute temperature

$\therefore \sigma =\frac{E}{T^4}$

$\therefore$ Dimensions of $\sigma =\frac{\text{dimensions of energy per unit area per second}}{\text{dimension of}{T}^4}$

$=\frac{M{L}^2{T}^{-2}\times L^{-2}\times T^{-1}}{K^4}=M{L}^0{T}^{-3}{K}^{-4}$

Hence the correct choice is (d).