Stefan-Boltzmann Constant

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Stefan%E2%80%93Boltzmann Constant

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The **Stefan-Boltzmann constant** (also **Stefan's constant**), a physical constant denoted by the Greek letter *?* (sigma), is the constant of proportionality in the Stefan-Boltzmann law: "the total intensity radiated over all wavelengths increases as the temperature increases", of a black body which is proportional to the fourth power of the thermodynamic temperature.^{[1]} The theory of thermal radiation lays down the theory of quantum mechanics, by using physics to relate to molecular, atomic and sub-atomic levels. Slovenian physicist Josef Stefan formulated the constant in 1879, and it was later derived in 1884 by Austrian physicist Ludwig Boltzmann.^{[2]} The equation can also be derived from Planck's law, by integrating over all wavelengths at a given temperature, which will represent a small flat black body box.^{[3]} "The amount of thermal radiation emitted increases rapidly and the principal frequency of the radiation becomes higher with increasing temperatures".^{[4]} The Stefan-Boltzmann constant can be used to measure the amount of heat that is emitted by a blackbody, which absorbs all of the radiant energy that hits it, and will emit all the radiant energy. Furthermore, the Stefan-Boltzmann constant allows for temperature (K) to be converted to units for intensity (W?m^{-2}), which is power per unit area.

The value of the Stefan-Boltzmann constant is given in SI units by

*?*= .^{[5]}

In cgs units the Stefan-Boltzmann constant is:

*?*? .

In thermochemistry the Stefan-Boltzmann constant is often expressed in cal?cm^{-2}?day^{-1}?K^{-4}:

*?*? .

In US customary units the Stefan-Boltzmann constant is:^{[6]}

*?*? .

The value of the Stefan-Boltzmann constant is derivable as well as experimentally determinable; see Stefan-Boltzmann law for details. It can be defined in terms of the Boltzmann constant as

where:

*k*_{B}is the Boltzmann constant*h*is the Planck constant*?*is the reduced Planck constant*c*is the speed of light in vacuum.

The CODATA recommended value [ref?] prior to 20 May 2019 (2018 CODATA) was calculated from the measured value of the gas constant:

where:

*R*is the universal gas constant*N*_{A}is the Avogadro constant*R*_{?}is the Rydberg constant*A*_{r}(e) is the "relative atomic mass" of the electron*M*_{u}is the molar mass constant (1 g/mol by definition)*?*is the fine-structure constant.

Dimensional formula: M^{1}T^{-3}?^{-4}

A related constant is the **radiation constant** (or **radiation density constant**) *a* which is given by:^{[7]}

**^**Krane, Kenneth (2012).*Modern Physics*. John Wiley & Sons. p. 81.**^**"Stefan-Boltzmann Law".*Encyclopædia Britannica*.**^**Halliday & Resnick (2014).*Fundamentals of Physics (10th Ed)*. John Wiley and Sons. p. 1166.**^**Eisberg, Resnick, Robert, Robert (1985).*Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd Ed)*(PDF). John Wiley & Sons. Archived from the original (PDF) on 2014-02-26.**^**"2018 CODATA Value: Stefan-Boltzmann constant".*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved .**^**Heat and Mass Transfer: a Practical Approach, 3rd Ed. Yunus A. Çengel, McGraw Hill, 2007**^**Radiation constant from ScienceWorld

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