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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&nbsp;g/mol by definition);
*''&alpha;'' 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

Template:Distinguish

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:

σ5.6704×105ergcm2s1K4.
σ11.7×108calcm2day1K4.

In US customary units the Stefan–Boltzmann constant is:[1]

σ=0.1714×108BTUhr1ft2R4.

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:

σ=2π5kB415h3c2=π2kB4603c2=5.670373(21)108Jm2s1K4

where:

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

σ=2π5R415h3c2NA4=32π5hR4R415Ar(e)4Mu4c6α8

where:

A related constant is the radiation constant (or radiation density constant) a which is given by:[2]

a=4σc=7.5657×1015ergcm3K4=7.5657×1016Jm3K4.

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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Template:Thermodynamics-stub

de:Stefan-Boltzmann-Gesetz

  1. Heat and Mass Transfer: a Practical Approach, 3rd Ed. Yunus A. Çengel, McGraw Hill, 2007
  2. Radiation constant from ScienceWorld