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Q.
The dimensions of $\sigma b^{4}$ are (where $\sigma=$ Stefan's constant and $b=$ Wein's constant)
Physical World, Units and Measurements
Solution:
$\lambda_{m} T=b$ or $b^{4}=\lambda_{m}^{4} T^{4}$
and $\frac{\text { Energy }}{\text { Area } \times \text { Time }}=\sigma T^{4}$
or $\sigma=\frac{\text { Energy }}{(\text { Area } \times \text { Time }) T^{4}}$
or $\sigma b^{4}=\left(\frac{\text { Energy }}{\text { Area } \times \text { Time }}\right) \lambda_{m}^{4}$
$\therefore \quad\left[\sigma b^{4}\right]=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ L ^{2}\right][ T ]}\left[ L ^{4}\right]$
$=\left[ ML ^{4} T ^{-3}\right]$