What Is Emissivity and How Is It Calculated?

Emissivity is the ratio of the power radiated per unit area by a real surface to the power radiated per unit area by an ideal black body at the same temperature. It is calculated by dividing the surface's emitted power per unit area by $\sigma T^4$.

The Reasoning and Calculation

An ideal black body is a perfect emitter with emissivity $e=1$. Real surfaces emit less thermal radiation, so $0\le e\le 1$ and emissivity has no unit. The comparison must use the same temperature because radiated power changes strongly with $T$.

The Stefan and Boltzmann law for a real surface is

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

where $P$ is radiated power in watts, $A$ is emitting area in $\text{m}^2$, $T$ is absolute temperature in kelvin, and $\sigma=5.67\times10^{-8}\,\text{W m}^{-2}\text{K}^{-4}$.

Rearranging gives

$$e=\frac{P}{\sigma AT^4}.$$

Equivalently, if emitted power per unit area (P/A) is given, use

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

For example, a surface at $300\,\text{K}$ emits $150\,\text{W m}^{-2}$. A black body at that temperature would emit

$$\sigma T^4=(5.67\times10^{-8})(300)^4=459\,\text{W m}^{-2}.$$

Thus, $e=150/459=0.327\approx0.33$. The result means the surface emits about 33% of the power emitted by an ideal black body under identical conditions.

Do not confuse emissivity with albedo:

The common misconception is that a shiny or highly reflective surface must have high emissivity. In fact, strong reflection corresponds to high albedo, while emissivity concerns emission; the quantities are not interchangeable.

IB Exam Technique

This is SL and HL content in B.2 Greenhouse effect. In a Calculate question, convert Celsius to kelvin, distinguish $P$ from (P/A), include area only when using total power, and report a dimensionless value between 0 and 1. For an Explain question, state that increasing emissivity increases radiated power when area and temperature remain constant.