Let σ and b be Stefan's constant and Wien's constant respectively, then dimensions of σ b are (a) [L¹M⁻¹T⁻³K⁻³] (b) [L¹M¹T³K⁻³] (c) [L⁻¹M¹T⁻³K⁻³] (d) [L¹M¹T⁻³K⁻³]

Answer: (d). E = σ T⁴ (power per area): [σ] = [MT⁻³][K⁴] = [MT⁻³K⁻⁴] λm T = b: [b] = [LK] [σ b] = [L¹M¹T⁻³K⁻³] So the answer is (d).

Let σ and b be Stefan's constant and Wien's constant respectively… | MHT CET 2020 (19 Oct, Shift 2)

Q68MHT CET 2020 · 19 OCT · SHIFT 2Easy

Units & Dimensions

Let $\sigma$ and $b$ be Stefan's constant and Wien's constant respectively, then dimensions of $\sigma b$ are

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Answer: (d)

$E = \sigma T^4$ (power per area): $[\sigma] = \frac{[\mathrm{MT^{-3}}]}{[\mathrm{K^4}]} = [\mathrm{MT^{-3}K^{-4}}]$
$\lambda_m T = b$ : $[b] = [\mathrm{LK}]$
$[\sigma b] = [\mathrm{L^1M^1T^{-3}K^{-3}}]$
So the answer is (d).