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The unit of Stefan's constant is

Asked in CBSE AIPMT 2002 · Units and definitions

(1) watt m²K⁴
(2) watt m²/K⁴
(3) watt/m²K
(4) watt/m²K⁴

Answer: (4) watt/m²K⁴

Step-by-step solution

Idea: read the unit straight off the defining relation.

E=σ T⁴, where E is the power radiated per unit area.

σ=E/(T⁴)

E is measured in watt/m² and T⁴ in K⁴.

[σ]=watt/m²K⁴

In SI symbols that is W m⁻²K⁻⁴.

Why the other options are wrong

(1) comes from puts both the area and T⁴ on top; in E=σ T⁴ the emitted power is reckoned per unit area and T⁴ multiplies σ, so both belong underneath
(2) comes from keeps m² in the numerator; the radiated power is per unit area, so the area divides
(3) comes from has the form right but only the first power of the temperature; Stefan's law carries T⁴

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