Unit check for the Stefan–Boltzmann constant σ Select the correct SI unit for σ used in thermal radiation calculations.

Introduction / Context:The Stefan–Boltzmann constant σ appears in the blackbody relation E_b = σ * T^4. Knowing σ’s units ensures dimensional consistency in radiation problems.

Given Data / Assumptions:

• Blackbody emissive power E_b has units W/m^2.
• Temperature is absolute (kelvin), denoted K.

Concept / Approach:Because E_b = σ * T^4 and E_b has units W/m^2, σ must carry units that when multiplied by K^4 yield W/m^2.

Step-by-Step Solution:Start with E_b units: W/m^2.T^4 units: K^4.Solve for σ units: (W/m^2) / K^4 = W/m^2·K^−4 = W/m^2·K^4 in denominator form.

Verification / Alternative check:Numerically, σ ≈ 5.6704 × 10^−8 W/m^2·K^4, consistent with standard references.

Why Other Options Are Wrong:

• W/m·K, W/m·K^2, W/m^2·K^2, J/m^2·K do not satisfy E_b = σ * T^4 dimensional balance.

Common Pitfalls:Mixing σ with convection coefficient h (W/m^2·K) or conduction constant k (W/m·K).

Final Answer:W/m^2·K^4