B.2.2—Emissivity

Emissivity

Emissivity, $$\varepsilon$$, compares the power radiated per unit area by a real surface with that radiated per unit area by an ideal black surface at the same absolute temperature:

$$\varepsilon=\frac{P/A}{\sigma T^4}$$

Use the radiation equation

For a surface of area A,

$$P=\varepsilon\sigma AT^4$$

Use T in kelvin. A black body has $$\varepsilon=1$$; real surfaces have emissivity less than or equal to 1 in this model.

What emissivity is not

Emissivity is not the fraction of incoming sunlight reflected; that is albedo. Emissivity concerns emission of thermal radiation by a surface at its temperature.

Worked example from the mapped local textbook

A planet has surface temperature $-63\,^{\circ}\mathrm{C}=210\,\mathrm{K}$, area $1.4\times10^{14}\,\mathrm{m^2}$ and luminosity $1.3\times10^{16}\,\mathrm{W}$.

$$\varepsilon=\frac{P/A}{\sigma T^4}=\frac{(1.3\times10^{16})/(1.4\times10^{14})}{(5.67\times10^{-8})(210)^4}=0.84$$

Emissivity is dimensionless, and the kelvin conversion is required by the fourth-power law.

Calculation boundary

Keep surface emission and atmospheric re-radiation as separate energy-flow terms. Do not subtract reflected solar power from the Stefan–Boltzmann emission formula.