Question

The dimensions of Stefan's constant are

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

Answer 1

The correct option is D $\left[M{L}^0{T}^{-3}{K}^{-4}\right]$

Rate of heat radiated is given by, $R=\sigma Ae{T}^4$

where, $\sigma$ is the Stefan's constant, $A$ is the area and $T$ is the temperature

$e$ is the emissivity of the body

$⟹\sigma =\frac{R}{Ae{T}^4}$

Dimension of power, $R=\frac{Energy}{Time}=\left[M{L}^2{T}^{-3}\right]$

Emissivity is dimensionless.

Dimension of area, $A=\left[M^0{L}^2{T}^0\right]$

Dimension of temperature, $T=\left[K\right]$

$\therefore$ Dimension of, $\sigma =\frac{\left[M{L}^2{T}^{-3}\right]}{\left[M^0{L}^2{T}^0\right]\times \left[K^4\right]}$

$⟹$ Dimension of Stefan's constant $\sigma =\left[M{L}^0{T}^{-3}{K}^{-4}\right]$