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  4. The dimensions of σb4 (σ = Stefan’s constant and b = Wein’s constant) are

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Q. The dimensions of $σb^4$ ($σ =$ Stefan’s constant and b = Wein’s constant) are

Physical World, Units and Measurements

Solution:

Wein’s displacement law
$λ_{m}T = b$ or $b^{4} = λ_{m} ^{4} T^{4}\quad...\left(i\right)$
From Stefan’s law,
$\sigma = \frac{E}{AtT^{4}}\quad...\left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$,
$\sigma b^{4} = \frac{Eλ_{m} ^{4} T^{4}}{AtT^{4}}$
$\left[\sigma b^{4} \right] = \frac{\left[ML^{2}T^{-2}\right]\left[L\right]^{4}}{\left[L^{2}\right]\left[T\right]}$
$ = \left[ML^{4}T^{-3}\right]$