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{{distinguish|Boltzmann constant}} | |||
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]]. | |||
The value of the Stefan–Boltzmann constant is given in [[International System of Units|SI units]] by | |||
:{{math|{{physconst|sigma|symbol=yes|after=.}}}} | |||
In [[Centimeter gram second system of units|cgs units]] the Stefan–Boltzmann constant is: | |||
:<math>\sigma \approx 5.6704 \times 10^{-5}\ \textrm{erg}\,\textrm{cm}^{-2}\,\textrm{s}^{-1}\,\textrm{K}^{-4}.</math> | |||
:<math>\sigma \approx 11.7 \times 10^{-8}\ \textrm{cal}\,\textrm{cm}^{-2}\,\textrm{day}^{-1}\,\textrm{K}^{-4}.</math> | |||
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> | |||
:<math>\sigma = 0.1714 \times 10^{-8}\ \textrm{BTU}\,\textrm{hr}^{-1}\,\textrm{ft}^{-2}\,\textrm{R}^{-4}.</math> | |||
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: | |||
:<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> | |||
where: | |||
*''k''<sub>B</sub> 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]]: | |||
:<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> | |||
where: | |||
*''R'' is the [[Universal gas constant]]; | |||
*''N''<sub>A</sub> is the [[Avogadro constant]]; | |||
*''R''<sub>∞</sub> is the [[Rydberg constant]]; | |||
*''A''<sub>r</sub>(e) is the "[[relative atomic mass]]" of the [[electron]]; | |||
*''M''<sub>u</sub> is the [[molar mass constant]] (1 g/mol by definition); | |||
*''α'' is the [[fine structure constant]]. | |||
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> | |||
:<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> | |||
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. | |||
== References == | |||
{{reflist}} | |||
{{thermodynamics-stub}} | |||
{{DEFAULTSORT:Stefan-Boltzmann constant}} | |||
[[Category:Physical constants]] | |||
[[Category:Thermodynamics]] | |||
[[de:Stefan-Boltzmann-Gesetz]] |
Revision as of 22:51, 29 December 2013
The Stefan–Boltzmann constant (also Stefan's constant), a physical constant denoted by the 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.
The value of the Stefan–Boltzmann constant is given in SI units by
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In cgs units the Stefan–Boltzmann constant is:
In US customary units the Stefan–Boltzmann constant is:[1]
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:
- kB 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:
where:
- R is the Universal gas constant;
- NA is the Avogadro constant;
- R∞ is the Rydberg constant;
- Ar(e) is the "relative atomic mass" of the electron;
- Mu is the molar mass constant (1 g/mol by definition);
- α is the fine structure constant.
A related constant is the radiation constant (or radiation density constant) a which is given by:[2]
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.
References
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- ↑ Heat and Mass Transfer: a Practical Approach, 3rd Ed. Yunus A. Çengel, McGraw Hill, 2007
- ↑ Radiation constant from ScienceWorld