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| {{distinguish|Boltzmann constant}}
| | Wilber Berryhill is the title his mothers and fathers gave him and he totally digs that name. To climb is something I really appreciate doing. Ohio is where my home is but my husband desires us to move. Office supervising is exactly where my primary income comes from but I've always wanted my own business.<br><br>Here is my blog post ... live psychic reading ([http://Stan.gs/users/ZPotter linked web-site Stan.gs]) |
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| The '''Stefan–Boltzmann constant''' (also '''Stefan's constant'''), a [[physical constant]] denoted by the [[Sigma|Greek letter ''σ'']], is the [[constant of proportionality]] in the [[Stefan–Boltzmann law]]: the total [[energy]] radiated per unit surface area of a [[black body]] in unit time is proportional to the fourth power of the [[thermodynamic temperature]].
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| The value of the Stefan–Boltzmann constant is given in [[International System of Units|SI units]] by
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| :{{math|{{physconst|sigma|symbol=yes|after=.}}}}
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| In [[Centimeter gram second system of units|cgs units]] the Stefan–Boltzmann constant is:
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| :<math>\sigma \approx 5.6704 \times 10^{-5}\ \textrm{erg}\,\textrm{cm}^{-2}\,\textrm{s}^{-1}\,\textrm{K}^{-4}.</math>
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| :<math>\sigma \approx 11.7 \times 10^{-8}\ \textrm{cal}\,\textrm{cm}^{-2}\,\textrm{day}^{-1}\,\textrm{K}^{-4}.</math>
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| In [[United States customary units|US customary]] units the Stefan–Boltzmann constant is:<ref>Heat and Mass Transfer: a Practical Approach, 3rd Ed. Yunus A. Çengel, McGraw Hill, 2007</ref>
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| :<math>\sigma = 0.1714 \times 10^{-8}\ \textrm{BTU}\,\textrm{hr}^{-1}\,\textrm{ft}^{-2}\,\textrm{R}^{-4}.</math>
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| 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:
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| :<math>\sigma = \frac{2\pi^5k_{\rm B}^4}{15h^3c^2} = \frac{\pi^2k_{\rm B}^4}{60\hbar^3c^2} = 5.670373(21) \, \cdot 10^{-8}\ \textrm{J}\,\textrm{m}^{-2}\,\textrm{s}^{-1}\,\textrm{K}^{-4} </math>
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| where: | |
| *''k''<sub>B</sub> is the [[Boltzmann constant]];
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| *''h'' is the [[Planck constant]];
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| *''ħ'' is the reduced Planck constant;
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| *''c'' is the [[speed of light]] in vacuum.
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| The [[CODATA]] recommended value is calculated from the measured value of the [[gas constant]]:
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| :<math>\sigma = \frac{2 \pi^5 R^4}{15 h^3 c^2 N_{\rm A}^4} = \frac{32 \pi^5 h R^4 R_{\infty}^4}{15 A_{\rm r}({\rm e})^4 M_{\rm u}^4 c^6 \alpha^8}</math>
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| where:
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| *''R'' is the [[Universal gas constant]];
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| *''N''<sub>A</sub> is the [[Avogadro constant]];
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| *''R''<sub>∞</sub> is the [[Rydberg constant]];
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| *''A''<sub>r</sub>(e) is the "[[relative atomic mass]]" of the [[electron]];
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| *''M''<sub>u</sub> is the [[molar mass constant]] (1 g/mol by definition);
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| *''α'' is the [[fine structure constant]].
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| A related constant is the '''radiation constant''' (or '''radiation density constant''') ''a'' which is given by:<ref>[http://scienceworld.wolfram.com/physics/RadiationConstant.html Radiation constant] from ScienceWorld</ref>
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| :<math>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}.</math>
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| A simple rule to remember the Stefan–Boltzmann constant is to think "5-6-7-8;" and try not to forget the negative sign before the final eight.
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| == References ==
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| {{reflist}}
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| {{thermodynamics-stub}}
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| {{DEFAULTSORT:Stefan-Boltzmann constant}}
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| [[Category:Physical constants]]
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| [[Category:Thermodynamics]]
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| [[de:Stefan-Boltzmann-Gesetz]]
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Wilber Berryhill is the title his mothers and fathers gave him and he totally digs that name. To climb is something I really appreciate doing. Ohio is where my home is but my husband desires us to move. Office supervising is exactly where my primary income comes from but I've always wanted my own business.
Here is my blog post ... live psychic reading (linked web-site Stan.gs)