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:

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

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

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

In US customary units the Stefan–Boltzmann constant is:

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

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:

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

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:

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

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:

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

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