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The total emission capacity <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s087/s087580/s0875801.png" /> of an absolutely-black body is proportional to the fourth power of its absolute temperature <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s087/s087580/s0875802.png" />:
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where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s087/s087580/s0875804.png" /> (the Stefan–Boltzmann constant). This law was obtained empirically from analysis of experimental data by J. Stefan (1879), and was proposed in thermodynamic terms by L. Boltzmann (1884).
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The total emission capacity  $  u $
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of an absolutely-black body is proportional to the fourth power of its absolute temperature  $  T $:
  
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$$
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u  =  \sigma T  ^ {4} ,
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$$
  
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where  $  \sigma = ( 5.67032 \pm  0.00071) \cdot 10  ^ {-} 1 Bt/m  ^ {2} \cdot K  ^ {4} $(
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the Stefan–Boltzmann constant). This law was obtained empirically from analysis of experimental data by J. Stefan (1879), and was proposed in thermodynamic terms by L. Boltzmann (1884).
  
 
====Comments====
 
====Comments====
 
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Born,  "Atomic physics" , Blackie &amp; Son  (1958)</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M. Born,  "Atomic physics" , Blackie &amp; Son  (1958)</TD></TR></table>

Revision as of 08:23, 6 June 2020


The total emission capacity $ u $ of an absolutely-black body is proportional to the fourth power of its absolute temperature $ T $:

$$ u = \sigma T ^ {4} , $$

where $ \sigma = ( 5.67032 \pm 0.00071) \cdot 10 ^ {-} 1 Bt/m ^ {2} \cdot K ^ {4} $( the Stefan–Boltzmann constant). This law was obtained empirically from analysis of experimental data by J. Stefan (1879), and was proposed in thermodynamic terms by L. Boltzmann (1884).

Comments

References

[a1] M. Born, "Atomic physics" , Blackie & Son (1958)
How to Cite This Entry:
Stefan-Boltzmann law. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Stefan-Boltzmann_law&oldid=23043
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article