# Stefan-Boltzmann Constant

In Physics, Stefan-Boltzmann Constant, also known as Stefan’s constant, is a physical constant. It is the constant of proportionality in Stefan-Boltzmann law of Blackbody radiation. Stefan Boltzmann Constant is denoted by the Greek letter σ. This physical constant was formulated by Josef Stefan in 1879 and derived by Ludwig Boltzmann in 1884.

## Stefan Boltzmann Constant Value

The value of Stefan Boltzmann constant is universally accepted and given in SI units as

Stefan Boltzmann Constant σ = 5.670367(13) × 10-8 W⋅m-2.K-4

It can also be expressed in other units as well. Stefan-Boltzmann Constant in the CGS unit is 5.6704Γ10-5
erg.cm2.s1.K4.

### Stefan Boltzmann Constant Formula

The Stefan Boltzmann constant value can be derived or determined experimentally. Classically it is derived from Boltzmann constant as –

 $$\begin{array}{l}\sigma =\frac{2\pi ^{5}k_{B}^{4}}{15h^{3}c^{2}} = 5.670367(13)\times 10^{-8}J.m^{-2}.s^{-1}.K^{-4}\end{array}$$

Where,

• kB is the Boltzmann constant.
• h is the Planck constant.
• c is the speed of light.
• σ is the Stefan Boltzmann constant.

CODATA is an association which works on assigning the values for physical constants. It has recommended value for this physical constant using the Gas constant as –

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

Where,

• σ is the Stefan Boltzmann constant.
• NA is the Avogadro constant.
• R is the Universal gas constant.
• R is the Rydberg constant.
• Ar(e) is the relative atomic mass of the electron.
• α is the fine structure constant.
• Mu is the molar mass constant (defined as 1g/mol).

## Applications

In Physics, the applications of the Stefan Boltzmann constant are many. Some of them are listed below-

• It measures the amount of heat radiated from the black body.
• It can be used to convert temperature(K) to units for intensity (W.m-2) that is basically Power per unit area.

Hope you have understood about Stefan Boltzmann constant, Dimensional formula, Stefan Boltzmann constant value, formula along with terms and units and its applications in physics.

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#### Comments

1. The applications of Stefan Boltzmann’s constant are very interesting, especially when it comes to measuring the amount of heat radiated from the black body.