Question

Ratio of emissive power of a body to the emissive power of a perfectly black body, is known

• A. Emissivity
• B. Absorptivity
• C. Transmissivity
• D. Reflectivity

Hint:

Emissivity (\( \epsilon \)) measures how well a body emits radiation compared to a perfect black body (\( \epsilon = 1 \)).

Answer 1

The Correct Option is A

Step 1: Understand the concept of emissive power and a black body.
Emissive power of a body is the energy radiated per unit area per unit time at a given temperature and wavelength.
A perfectly black body absorbs all incident radiation and emits the maximum possible radiation at a given temperature, as described by the Stefan-Boltzmann law (\( E_b = \sigma T^4 \), where \( \sigma \) is the Stefan-Boltzmann constant, and \( T \) is temperature).
Step 2: Define the ratio in the question.
The ratio of the emissive power of a body (\( E \)) to the emissive power of a perfectly black body (\( E_b \)) at the same temperature is: \[ \frac{E}{E_b}. \] This ratio is a property of the body and is called the emissivity (\( \epsilon \)): \[ \epsilon = \frac{E}{E_b}. \] Emissivity (\( \epsilon \)) ranges from 0 to 1:
\( \epsilon = 1 \) for a perfect black body.
\( \epsilon<1 \) for real bodies (gray bodies).
Step 3: Evaluate the options.
(1) Emissivity: Correct, as emissivity is defined as the ratio of the emissive power of a body to that of a black body at the same temperature. Correct.
(2) Absorptivity: Incorrect, as absorptivity (\( \alpha \)) is the fraction of incident radiation absorbed by a body, not the ratio of emissive powers. Incorrect.
(3) Transmissivity: Incorrect, as transmissivity (\( \tau \)) is the fraction of incident radiation that passes through a body, not related to emissive power. Incorrect.
(4) Reflectivity: Incorrect, as reflectivity (\( \rho \)) is the fraction of incident radiation reflected by a body, not related to emissive power. Incorrect. Step 4: Select the correct answer.
The ratio of the emissive power of a body to the emissive power of a perfectly black body is known as emissivity, matching option (1).