Step 1: Understanding the Concept:
A perfectly black body is defined as an ideal physical body that absorbs all incident electromagnetic radiation, regardless of its frequency or angle of incidence.
The coefficient of emission (or emissivity), denoted by \(e\), is a measure of a material's ability to emit infrared energy compared to a black body.
Step 2: Key Formula or Approach:
According to Kirchhoff's law of thermal radiation, for an arbitrary body in thermal equilibrium with its surroundings, its emissivity (\(e\)) is equal to its absorptivity (\(a\)).
Mathematically, this is expressed as:
\[ e = a \]
Step 3: Detailed Explanation:
By definition, a perfectly black body is a perfect absorber of radiation.
This means it absorbs 100% of the radiation that falls on it.
Therefore, its coefficient of absorption (\(a\)) is exactly 1.
Using Kirchhoff's law (\(e = a\)), it directly follows that the coefficient of emission (\(e\)) for a perfectly black body must also be exactly 1.
A value of 1 is referred to as "unity".
Step 4: Final Answer:
The coefficient of emission for a perfectly black body is unity.