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Stefan–Boltzmann law
Intermediate
Radiated power grows as the fourth power of temperature.
P = εσAT⁴The power radiated is P = εσAT⁴, with σ = 5.67×10⁻⁸ W/m²K⁴. Doubling T gives 16 times the power.
Sun's surface at 5800 K emits 64 MW/m².
Net radiation = σεA(T⁴ − T_s⁴).
In more detail
The Stefan-Boltzmann law gives the total power radiated per unit area by a blackbody, P = σT⁴. Doubling the temperature increases the radiated power sixteen times.
Real-world uses
- Estimating the surface temperature of stars from their luminosity.
- Designing thermal shields for spacecraft.
- Astronomers estimate the temperature of stars from their brightness and the Stefan–Boltzmann law.
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Frequently asked questions
What is the constant σ?
The Stefan-Boltzmann constant, about 5.67 × 10⁻⁸ W/(m² K⁴).
Does it apply only to blackbodies?
Real objects emit less, so an emissivity factor is included.
What does the fourth power mean in practice?
Doubling the absolute temperature increases the radiated power by a factor of sixteen.
Related topics in Heat & Thermodynamics
Thermal resistance · Convection · Radiation · Newton's law of cooling · Wien's displacement law · Blackbody radiation