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Stefan–Boltzmann's law

Every body with a temperature above absolute zero radiates energy as electromagnetic waves, and this is the only form of heat transport that works in a vacuum. The power radiated grows with the fourth power of the absolute temperature, so even a small temperature rise gives a large increase in radiative loss.

\dot Q_{out} = \varepsilon\sigma AT^4

power radiated from a gray surface,

\sigma = 5.67\cdot 10^{-8}

W/(m²K⁴)

\dot Q = \varepsilon\sigma A(T^4 - T_{surr}^4)

net radiative loss to the surroundings

Symbols

$\varepsilon$	emissivity (0–1)
$\sigma$	Stefan–Boltzmann constant	W/(m²K⁴)
$T$	absolute temperature	K

Example

A surface with $\varepsilon = 0.8$ , $A = 0.5$ m² is at $T = 500$ K in surroundings at $T_{surr} = 300$ K. $\dot Q = 0.8\cdot 5.67\cdot 10^{-8}\cdot 0.5\cdot(500^4-300^4) \approx 1090$ W.

Always use

T

in kelvin in Stefan–Boltzmann's law –

T^4

is very sensitive to a wrong unit.

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Part of Heat Transfer: Radiation and transient heat.