Definition:Stefan-Boltzmann Constant

Definition

The Stefan-Boltzmann constant is the constant of proportion that defines the intensity of the thermal radiation emitted by a body in terms of that body's temperature:

$\sigma := \dfrac {2 \pi^5 k^4} {15 c^2 h^3}$

where:

$k$ is Boltzmann's constant

$c$ is the speed of light

$h$ is Planck's constant.

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Symbol

$\sigma$

The symbol for the Stefan-Boltzmann constant is $\sigma$.

Its $\LaTeX$ code is \sigma .

Dimension

The Stefan-Boltzmann constant has the dimension $\mathsf {M T^{-3} \Theta^{-4} }$.

Units

The SI unit for the Stefan-Boltzmann constant is given in watts per square metre per kelvin to the $4$th:

$\mathrm {W \, m^{-2} \, K^{-4} }$

Value

The value of the Stefan-Boltzmann constant is:

\(\ds \sigma\)

\(\approx\)

\(\ds 5 \cdotp 67037 \, 4419 \ldots \times 10^{-8}\)

$\mathrm {W \, m^{-2} \, K^{-4} }$

\(\quad\) in SI units

\(\ds \)

\(\approx\)

\(\ds 5 \cdotp 67037 \, 4419 \ldots \times 10^{-5}\)

$\mathrm {erg \, cm^{-2} \, s^{-1} \, K^{-4} }$

\(\quad\) in CGSunits

\(\ds \)

\(\approx\)

\(\ds 4 \cdotp 76 \times 10^{-13}\)

$\mathrm {btu \, ft^{-2} \, \rankine^{-4} }$

\(\quad\) in FPS units

Also see

• Stefan-Boltzmann Law

• Definition:Boltzmann's Constant: not to be confused with this

Source of Name

This entry was named for Josef Stefan and Ludwig Eduard Boltzmann.

Sources

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