Joseph Stefan

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:

$\sigma \approx 5.6704\times 10^{-5}\ {\textrm {erg}}\,{\textrm {cm}}^{-2}\,{\textrm {s}}^{-1}\,{\textrm {K}}^{-4}.$

$\sigma \approx 11.7\times 10^{-8}\ {\textrm {cal}}\,{\textrm {cm}}^{-2}\,{\textrm {day}}^{-1}\,{\textrm {K}}^{-4}.$

In US customary units the Stefan–Boltzmann constant is:

$\sigma =0.1714\times 10^{-8}\ {\textrm {BTU}}\,{\textrm {hr}}^{-1}\,{\textrm {ft}}^{-2}\,{\textrm {R}}^{-4}.$

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:

$\sigma ={\frac {2\pi ^{5}k_{\rm {B}}^{4}}{15h^{3}c^{2}}}={\frac {\pi ^{2}k_{\rm {B}}^{4}}{60\hbar ^{3}c^{2}}}=5.670373(21)\,\cdot 10^{-8}\ {\textrm {J}}\,{\textrm {m}}^{-2}\,{\textrm {s}}^{-1}\,{\textrm {K}}^{-4}$

where:

• k_B 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:

$\sigma ={\frac {2\pi ^{5}R^{4}}{15h^{3}c^{2}N_{\rm {A}}^{4}}}={\frac {32\pi ^{5}hR^{4}R_{\infty }^{4}}{15A_{\rm {r}}({\rm {e}})^{4}M_{\rm {u}}^{4}c^{6}\alpha ^{8}}}$

where:

• R is the Universal gas constant;
• N_A is the Avogadro constant;
• R_∞ is the Rydberg constant;
• A_r(e) is the "relative atomic mass" of the electron;
• M_u 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:

$a={\frac {4\sigma }{c}}=7.5657\times 10^{-15}{\textrm {erg}}\,{\textrm {cm}}^{-3}\,{\textrm {K}}^{-4}=7.5657\times 10^{-16}{\textrm {J}}\,{\textrm {m}}^{-3}\,{\textrm {K}}^{-4}.$

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

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.