Let σₛ be the Stefan–Boltzmann constant, kᵦ the Boltzmann constant and b Wien's displacement constant. Find the dimensions of σₛ kᵦ⁻¹ b.
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Question

Let σₛ be the Stefan–Boltzmann constant, kᵦ the Boltzmann constant and b Wien's displacement constant. Find the dimensions of σₛ kᵦ⁻¹ b.

G1 Physics · Accepted Answer

Step 1: From radiant power per area = σₛT⁴, [σₛ] = [M T⁻³ K⁻⁴]. Step 2: Boltzmann constant has units energy/temperature: [kᵦ] = [M L² T⁻² K⁻¹]. Step 3: Wien constant b = λ_max T, so [b] = [L K]. Step 4: Combine: [σₛ kᵦ⁻¹ b] = [M T⁻³ K⁻⁴] × [M⁻¹ L⁻² T² K] × [L K]. Step 5: Cancel powers of M, L, T and K to obtain [L⁻¹ T⁻¹ K⁻²]. Final answer: [L⁻¹T⁻¹K⁻²] (Option A).