Dimensional analysis for Stefan-Boltzmann constant

Steps:

• Power P has SI units kg m² s⁻³ (watt = joule/second, joule = kg m² s⁻²).
• Surface area A has units m².
• Temperature T has units K, so T⁴ has units K⁴.
• Rearrange equation: [σ] = [P] / ([A] [T]⁴) = (kg m² s⁻³) / (m² K⁴) = kg s⁻³ K⁻⁴.

Why none are correct:

• Correct units are kg s⁻³ K⁻⁴, matching the Stefan-Boltzmann law where σ radiates energy as power per unit area per temperature⁴.

Why the others are wrong:

• A omits m⁰ and uses s⁻¹ instead of s⁻³.
• B omits m⁰ and uses s² instead of s⁻³.
• C includes m⁻² and uses s⁻⁴ instead of s⁻³.
• D includes m² and uses s⁻² instead of s⁻³.

Final answer: None; kg s^{-3} K^{-4}