The SI unit and dimensions of Stefan's constant σ in case of Stefan's law of radiation is (a) Jm³ s⁴, [M¹L⁰T⁻³K⁻⁴] (b) Jm² s⁴ K, [M¹L⁰T⁻³K³] (c) Jm³ s K⁴, [M¹L⁰T⁻³K⁴] (d) Jm² s K⁴, [M¹L⁰T⁻³K⁻⁴]

Answer: (d). E = σ T⁴ ⇒ σ = E/T⁴, with E in J m ⁻² s ⁻¹ Unit: (J)/(m² s K⁴) (W m ⁻² K ⁻⁴) Dimensions: [ML²T⁻²][L²][T][K⁴] = [M¹L⁰T⁻³K⁻⁴] So the answer is (d).

The SI unit and dimensions of Stefan's constant σ in case of Stefan's… | MHT CET 2019 (3 May, Shift 1)

Q98MHT CET 2019 · 3 MAY · SHIFT 1Easy

Thermal Radiation: Black Body, Stefan & Wien

The SI unit and dimensions of Stefan's constant $\sigma$ in case of Stefan's law of radiation is

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Answer: (d)

$E = \sigma T^4 \Rightarrow \sigma = \dfrac{E}{T^4}$ , with $E$ in J m $^{-2}$ s $^{-1}$
Unit: $\dfrac{\text{J}}{\text{m}^2\,\text{s}\,\text{K}^4}$ (W m $^{-2}$ K $^{-4}$ )
Dimensions: $\dfrac{[ML^2T^{-2}]}{[L^2][T][K^4]} = [M^1L^0T^{-3}K^{-4}]$
So the answer is (d).

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2019 (3 May, Shift 1)

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