# 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 Greek letter σ. This physical constant was formulated by Josef Stefan during 1879 and derived by Ludwig Boltzmann during 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

The dimensional formula is [M]1 [T]-3[Θ]-4

It can also be expressed in other units as well. Refer the table given below for Stefan Boltzmann constant value and corresponding units.

 Types of units Stefan Boltzmann constant value Units CGS units σ ≈ 5.6704×105 erg.cm2.s1.K4 Thermochemistry σ ≈ 11.7×108 cal.cm2.day1.K4 US Customary units σ ≈ 1.714×109 BTU.hr1.ft2.°R4.

### Stefan Boltzmann Constant Formula

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

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

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

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

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 Stefan Boltzmann constant are many. Some of them are listed below-

• It is used to measure 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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