Stefan–Boltzmann law

The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan, who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically.

For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature,

T

{\displaystyle T}

:

M

∘

=

σ

T

4

.

{\displaystyle M^{\circ }=\sigma \,T^{4}.}

The constant of proportionality,

σ

{\displaystyle \sigma }

, is called the Stefan–Boltzmann constant. It has the value

In the general case, the Stefan–Boltzmann law for radiant exitance takes the form:

M

=

ε

M

∘

=

ε

σ

T

4

,

{\displaystyle M=\varepsilon \,M^{\circ }=\varepsilon \,\sigma \,T^{4},}

where

ε

{\displaystyle \varepsilon }

is the emissivity of the surface emitting the radiation. The emissivity is generally between zero and one. An emissivity of one corresponds to a black body.

Detailed explanation

The radiant exitance (previously called radiant emittance),

M

{\displaystyle M}

, has dimensions of energy flux (energy per unit time per unit area), and the SI units of measure are joules per second per square metre (J⋅s−1⋅m−2), or equivalently, watts per square metre (W⋅m−2). The SI unit for absolute temperature, T, is the kelvin (K).

To find the total power,

P

{\displaystyle P}

, radiated from an object, multiply the radiant exitance by the object's surface area,

A

{\displaystyle A}

:

P

=

A

⋅

M

=

A

ε

σ

T

4

.