Question

For a perfectly black body, coefficient of emission is

• A. zero
• B. infinity
• C. unity
• D. less than one (non-zero)

Hint:

The coefficients of absorption, reflection, transmission, and emission are all normalized ratios bounded between 0 and 1. An ideal, perfect system always takes a value of exactly 1 (unity) for its primary defining characteristic.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the value of the coefficient of emission ($e$) for an ideal, perfectly black body.

Step 2: Key Formula or Approach:
1. An ideal black body is defined as a surface that absorbs 100% of all incident electromagnetic radiation falling upon it, meaning its coefficient of absorption ($a$) is exactly equal to 1.
2. According to Kirchhoff's Law of Thermal Radiation, at any given temperature, the coefficient of emission ($e$) of a body is always equal to its coefficient of absorption ($a$):
$$e = a$$

Step 3: Detailed Explanation:
Let's look at the definitions of these thermal properties:
The coefficient of absorption ($a$) is the ratio of radiant energy absorbed to the total incident energy. For a perfectly black body, absorption is total, so $a = 1$.
According to Kirchhoff's law, good absorbers are equally effective emitters under thermal equilibrium conditions.
Substituting the absorption value ($a=1$) into Kirchhoff's relation gives:
$$e = a = 1$$ A coefficient value of 1 is referred to as "unity" in mathematical terms, which matches option (C).

Step 4: Final Answer:
The coefficient of emission for a perfectly black body is unity, which corresponds to option (C).