The dimensions of Stefan's constant are - Vidyadip

MCQ

The dimensions of Stefan's constant are

A
$\left[ M ^0 L ^1 T ^{-3} K ^{-4}\right]$
B
$\left[ M ^1 L ^1 T ^{-3} K ^{-3}\right]$
C
$\left[ M ^1 L ^2 T ^{-3} K ^{-4}\right]$
✓
$\left[ M ^1 L ^0 T ^{-3} K ^{-4}\right]$

✓

Answer

Correct option: D.

$\left[ M ^1 L ^0 T ^{-3} K ^{-4}\right]$

(d) : According to Stefan's law, energy radiated per unit time by a black body is given by
$
\begin{aligned}
& u=\sigma A T^4 ; \sigma=\frac{u}{A T^4} \\
& {[\sigma]=\frac{[u]}{[A]\left[T^4\right]}=\frac{\left[ ML ^2 T ^{-2} / T \right]}{\left[ L ^2\right]\left[ K ^4\right]}=\frac{\left[ ML ^2 T ^{-3}\right]}{\left[ L ^2\right]\left[ K ^4\right]}}
\end{aligned}
$
$[\sigma]=\left[ M ^1 L ^0 T ^{-3} K ^{-4}\right]$

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