ثابت شتفان-بولتسمان

يجب ألا يـُخلـَط بينها وبين ثابت بولتسمان.

Log–log graphs of peak emission wavelength and radiant exitance vs. black-body temperature – red arrows show that 5780 K black bodies have 501 nm peak and 63.3 MW/m² radiant exitance

ثابت ستيفان-بولتزمان (إنگليزية: Stefan–Boltzmann constant) هو ثابت فيزيائي وهو ثابت التناسب في قانون ستيفان - بولتزمان.

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

σ = 5.670373(21)×10⁻⁸ W m⁻² K⁻⁴.

In cgs units the Stefan–Boltzmann constant is:

${\displaystyle{\displaystyle\sigma\approx 5.6704\times 10^{-5}\ {\textrm{erg}}\,\,{\textrm{cm}}^{-2}\,{\textrm{s}}^{-1}\,{\textrm{K}}^{-4}.}}$

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

${\displaystyle{\displaystyle\sigma\approx 11.7\times 10^{-8}\ {\textrm{cal}}\,\,{\textrm{cm}}^{-2}\,{\textrm{day}}^{-1}\,{\textrm{K}}^{-4}.}}$

In US customary units the Stefan–Boltzmann constant is:

${\displaystyle{\displaystyle\sigma=0.1714\times 10^{-8}\ {\textrm{BTU}}\,{\textrm{hr}}^{-1}\,{\textrm{ft}}^{-2}\,{\textrm{R}}^{-4}.}}$

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:

${\displaystyle{\displaystyle\sigma={\frac{2\pi^{5}k_{\rm{B}}^{4}}{15h^{3}c^{2}}}={\frac{\pi^{2}k_{\rm{B}}^{4}}{60\hbar^{3}c^{2}}}=5.670373(21)\,\cdot 10^{-8}\ {\textrm{J}}\,{\textrm{m}}^{-2}\,{\textrm{s}}^{-1}\,{\textrm{K}}^{-4}}}$

where:

• k_B is the Boltzmann constant;
• h is the Planck constant;
• ħ is the reduced Planck constant;
• c is the speed of light in vacuum.

The CODATA recommended value is calculated from the measured value of the gas constant:

${\displaystyle{\displaystyle\sigma={\frac{2\pi^{5}R^{4}}{15h^{3}c^{2}N_{\rm{A}}^{4}}}={\frac{32\pi^{5}hR^{4}R_{\infty}^{4}}{15A_{\rm{r}}({\rm{e}})^{4}M_{\rm{u}}^{4}c^{6}\alpha^{8}}}}}$

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);
• α is the fine structure constant.

.. الصيغة ذات الأبعاد : [ M 1 L 0 T -3 K -4]

A related constant is the radiation constant (or radiation density constant) a which is given by:

${\displaystyle{\displaystyle a={\frac{4\sigma}{c}}=7.5657\times 10^{-15}{\textrm{erg}}\,{\textrm{cm}}^{-3}\,{\textrm{K}}^{-4}=7.5657\times 10^{-16}{\textrm{J}}\,{\textrm{m}}^{-3}\,{\textrm{K}}^{-4}.}}$