Question

Emissive and absorptive power of a material at 2000 K is 8 and 10 respectively. Calculate the emissivity of IBB (Ideal black body) :
a) 0.2
b) 0.4
c) 0.6
d) 0.8

Answer 1

Hint: The emissivity of a material is the energy of radiation it can emit and is defined with respect to the energy radiated by a blackbody. The emissivity of a material is defined at a fixed temperature and frequency of radiation.

Detailed step by step solution:
A black body can be defined as an ideal body which has the ability to absorb and also emit the electromagnetic radiations of all wavelengths or frequencies without any dependence on the angle of incidence of the incoming radiation.
An ideal black body does not exist but we can compare the radiation behaviour of day-to-day materials with that of an ideal blackbody. The amount of electromagnetic radiation emitted by a material compared to that of a blackbody is called the emissivity of that material. Mathematically, it is given as
Emissivity $= \dfrac{{{\text{Radiant energy of a material}}}}{{{\text{Radiant energy of IBB}}}}$
The ratio of emissive power of a body to its absorptive power is equal to the emissivity of the black body and is the same for all materials at a given temperature.
We are given that for a material at 2000K the emissive power is 8 while its absorptive power is 10. The ratio of these quantities which is the emissivity of the material is the same for all materials at the same temperature.
$\therefore {\text{Emissivity of IBB}} = \dfrac{8}{{10}} = 0.8$
Hence, the correct answer is option D.

Note: A black body is called so because in ideal cases, it can absorb all kinds of radiation which means it cannot reflect any radiation and in order to see something, light needs to be reflected from it. Due to this reason, an ideal blackbody is considered black.