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| {{distinguish|Boltzmann constant}}
| | Telecommunications Field Engineer Woodrow Massar from Houston, usually spends time with hobbies and interests for example table tennis, health and fitness and stamp collecting. Discovers the charm in visiting destinations all over the entire world, recently just coming back from Rock-Hewn Churches.<br><br>Also visit my website ... [http://www.discountat.net/author/mi30x/ best Weight Gainer available in market] |
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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:
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| *''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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Telecommunications Field Engineer Woodrow Massar from Houston, usually spends time with hobbies and interests for example table tennis, health and fitness and stamp collecting. Discovers the charm in visiting destinations all over the entire world, recently just coming back from Rock-Hewn Churches.
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