Question

The dimensions of σb⁴ (σ = Stefan's constant and b = Wein's constant) are –

• A. $\lbrack M^{0}L^{0}T^{0}\rbrack$
• B. $\lbrack\text{M}\text{L}^{4}T^{\text{-3}}\rbrack$
• C. $\lbrack\text{M}\text{L}^{\text{-2}}T\rbrack$
• D. $\lbrack\text{ML6}\text{T}^{\text{-3}}\rbrack$

Answer 1

Answer: (B)

$\lbrack\text{M}\text{L}^{4}T^{\text{-3}}\rbrack$

Answer 2

$\mathbf{\lambda}_{\mathbf{m}}\mathbf{T = b}$or $b^{4} = \lambda_{m}^{4}T^{4}$ and $\frac{energy}{area - time} = \sigma T^{4}$

or $\sigma = \frac{energy}{(area - time)T^{4}}$

∴ $\sigma b^{4} = \left( \frac{energy}{area - time} \right)\lambda_{m}^{4}$

or =$\left\lbrack \sigma b^{4} \right\rbrack\frac{\lbrack ML^{2}T^{- 2}\rbrack}{\lbrack L^{2}\rbrack\lbrack T\rbrack}\lbrack L^{4}\rbrack\ = \ \lbrack\text{M}\text{L}^{4}T^{\text{-3}}\rbrack$