stefanboltzmann

Stefan-Boltzmann law, named for Josef Stefan and Ludwig Boltzmann, describes the power radiated by a blackbody. It states that the total energy emitted per unit area across all wavelengths is proportional to the fourth power of the body's absolute temperature. The radiative flux is given by E = σ T^4, where T is temperature in kelvin and σ is the Stefan-Boltzmann constant.

The Stefan-Boltzmann constant has a CODATA recommended value of σ = 5.670374419 × 10^-8 W m^-2 K^-4. For real materials, emissivity ε (0 ≤ ε ≤ 1) reduces the flux to E = ε σ T^4, so a non-ideal surface emits less than a perfect blackbody.

Historically, Stefan derived the T^4 law from experimental data in 1879, and Boltzmann provided a theoretical justification in the following years. Planck's law later explained the full spectral distribution and confirmed the T^4 dependence of total emission for blackbodies.

Applications of the law include estimating radiative heat transfer in engineering, determining effective temperatures and luminosities of stars in astrophysics, and modeling planetary and atmospheric radiation balance. The rule is a foundational result in thermodynamics and heat transfer, underpinning more detailed models of radiation and energy exchange in both natural and engineered systems.

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