Let σ_s, k_B and b represent the Stefan–Boltzmann constant, Boltzmann constant and Wien's displacement-law constant respectively. The dimension of σ_s k_B⁻¹ b is:
- A.[L⁻¹T⁻¹K⁻²]✓
- B.[L⁻¹K⁻²]
- C.[L⁻¹T⁻¹K⁻³]
- D.[L⁻¹T⁻¹K⁻⁴]
Correct Answer
(A) [L⁻¹T⁻¹K⁻²]
Solution & Explanation
Write each constant's dimensions, then combine. Stefan–Boltzmann constant σ_s: from E = σ_s T⁴ (energy flux = power per area), so σ_s = [M T⁻³ K⁻⁴]. Boltzmann constant k_B: from energy E = k_B T, so k_B = [M L² T⁻² K⁻¹]. Wien's constant b: from λ_m T = b, so b = [L K]. Now form σ_s k_B⁻¹ b: = [M T⁻³ K⁻⁴] × [M L² T⁻² K⁻¹]⁻¹ × [L K] = [M T⁻³ K⁻⁴] × [M⁻¹ L⁻² T² K] × [L K] Mass: M·M⁻¹ = M⁰. Length: L⁻²·L = L⁻¹. Time: T⁻³·T² = T⁻¹. Temperature: K⁻⁴·K·K = K⁻². Result: [L⁻¹ T⁻¹ K⁻²], matching option A.
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