The SI unit and dimension of Stefan's constan | vedclass

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(D) According to Stefan's law,the energy emitted by a body per unit area per unit time is proportional to the fourth power of its absolute temperature

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$\frac{J}{m^2 s K^4}, [M^1 L^0 T^{-3} K^{-4}]$

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(D) According to Stefan's law,the energy emitted by a body per unit area per unit time is proportional to the fourth power of its absolute temperature.$E = \sigma T^4$Where $E$ is the energy emitted per unit area per unit time,$T$ is the absolute temperature in Kelvin,and $\sigma$ is Stefan's constant.Rearranging for $\sigma$: $\sigma = \frac{E}{T^4}$.The unit of $E$ is $\frac{J}{m^2 s}$.Therefore,the unit of $\sigma$ is $\frac{J}{m^2 s K^4}$.The dimensions of energy are $[M L^2 T^{-2}]$,area is $[L^2]$,time is $[T]$,and temperature is $[K]$.$\sigma = \frac{[M L^2 T^{-2}]}{[L^2] [T] [K^4]} = [M^1 L^0 T^{-3} K^{-4}]$.

The $SI$ unit and dimension of Stefan's constant $\sigma$ in the case of Stefan's law of radiation are

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