Physics - Unit & Dimension Question with Solution | TestHub

According to Stefan’s law, energy emitted by a body per unit area per second is proportional to fourth power of the absolute temperature.
$E=\sigma T^4$
where, E = energy emitted/areas/second,
T = absolute temperature in kelvin
And$\sigma$= Stefan’s constant$\Rightarrow \sigma =\frac{E}{T^4}$
Unit of Stefan’s constant
$\Rightarrow \frac{\frac{J}{m^{2}s}}{K^4}=\frac{J}{m^{2}s{K}^4}$
Dimensions of Stefan’s constant,
$\sigma \frac{\left[Energy\right]}{\left[Area\right]\times \left[Time\right]\times {\left[Temperature\right]}^4}$
$=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^{2}T\times K^4\right]}=\left[M^1{L}^0{T}^{-3}{K}^{-4}\right]$