Question

The emissive power of a gray body is:
A) less than the emissive power of the black body
B) greater than the emissive power of the black body
C) equal to the emissive power of the black body
D) cannot say

Answer 1

Hint : The emissive power of a body is the energy radiated by the body due to its temperature. We will use Kirchhoff’s law of thermal radiation law to relate the power radiated by a gray body as compared to a black body.

Complete step by step answer:
Kirchhoff’s law of thermal radiation states that for a body of any material emitting and absorbing thermal energy in the form of electromagnetic radiation, the ratio of its emissive power to its absorption power is equal to the uniform feature of radiative wavelength and temperature only and is constant for a body.
For a black body, this ratio is 1 which means the blackbody emits all the energy it receives. While for a grey body, this ratio is less than 1 which means that it will not emit all the energy it receives. This means that the emissive power of a grey body will be less than that of a black body since it won’t be able to emit all the energy it receives.
Hence option (A) is correct.

Note:
The colour of a black body and a grey body are the typical colours of very good and mediocre radiating bodies respectively at room temperature. However, for higher temperatures than room temperatures, blackbodies can have colours in the visible wavelengths too. So, an object like stars are often considered as blackbodies since they emit much more radiation than they absorb and they do it at visible wavelengths too due to their higher temperatures. In reality, there is no perfect blackbody and all objects are grey bodies.