Question

What is the value of absorptive power of a perfect black body?
A.) Zero
B.) Infinity
C.) One
D.) Constant

Answer 1

Hint: A perfectly black body is that which absorbs completely the radiations of all wavelengths incident on it.

Complete step by step answer:

Let us first understand what radiation is. Radiation is a process of transfer of heat from one place to another without heating the intervening medium. In simple words, radiation is transfer of heat without the need of a medium unlike conduction and convection. For example, the heat of the sun reaches us through space which is a vacuum (no medium). To be precise, radiation is electromagnetic energy transfer in the form of electromagnetic waves through any medium. That is why the heat of the sun reaches us on earth. These electromagnetic waves are called thermal radiation and they belong to infra-red region of the electromagnetic spectrum. Everybody whose temperature is above zero Kelvin emits thermal radiation.

Just like light waves, thermal radiation waves also follow the laws of reflections, and refraction. Being electromagnetic waves, when thermal radiations fall on a body they are partly reflected, partly absorbed and the rest are transmitted through the body. On this basis, we have somethings known as reflectance, absorbance, and transmittance.

Reflectance or reflecting power(r) is the ratio of the amount of thermal radiations reflected (Qr) by the body in a given time to the total amount of thermal radiations (Q) incident on the body in that given time.

Absorbance or absorbing power (a) is the ratio of the amount of thermal radiations absorbed (Qa) by the body in a given time to the total amount of thermal radiations (Q) incident on the body in that given time.

Transmittance or transmitting power (t) is the ratio of the amount of thermal radiations transmitted (Qt) by the body in a given time to the total amount of thermal radiations (Q) incident on the body in that given time.

Therefore, $r=\dfrac{{{Q}_{r}}}{Q}$ $a=\dfrac{{{Q}_{a}}}{Q}$ $t=\dfrac{{{Q}_{t}}}{Q}$
A perfect black body is that body which absorbs all the thermal radiation incident on it. It neither reflects nor transmits any radiation. So, in this case ${{Q}_{a}}=Q$.

Therefore, $a=\dfrac{{{Q}_{a}}}{Q}=\dfrac{Q}{Q}=1$.

This concludes that the absorbing power of a perfectly black body is 1. So, the correct option is (c) one.

Note: The reflectance, absorbance and transmittance of a body are always between 0 and 1 i.e. $0\le r,a,t\le 1$. But practically, none of the body is perfectly reflective, perfectly absorptive, or perfectly transmitting. So, 0 < r,a,t < 1.