Question

What is the emissivity of a black body?

Answer 1

1. The emissivity of a material can be defined as the ratio of the energy radiated from its surface at a given temperature to the energy radiated from the surface of a perfect black body at the same temperature.
2. The expression for emissivity is, $\text{Emissivity}\left(\epsilon \right)=\frac{\text{Radiant energy of an object at a given temperature}}{\text{Radiant energy of a blackbody at the same temperature}}$.
3. A black body is a perfect emitter, which means that it emits all energy absorbed as radiation.
4. Using the expression above, the emissivity of a black body can be calculated.

$\begin{array}{rcl}\text{Emissivity}\left(\epsilon \right)& =& \frac{\text{Radiant energy of an object at a given temperature}}{\text{Radiant energy of a blackbody at the same temperature}}\\ & =& \frac{\text{Radiant energy of a blackbody at a given temperature}}{\text{Radiant energy of a blackbody at the same temperature}}\\ & =& 1\end{array}$

Hence, the emissivity of a black body is $1$.