Question

How is black body radiation calculated?

Answer 1

Hint: When solving questions like the one given to us above, it is important to keep in mind all the concepts regarding black body radiation like what causes it, what factors affect it, if it can be increased or decreased and if yes then how. Keep in mind that the total power in a black body radiation can be calculated.

Complete step by step answer:
In simple terms black body is an object which is capable of absorbing all the radiation that reaches it without reflecting back anything. The intensity of the radiation emitted by the said black body can vary with the wavelength according to a characteristic curve that maximum depends on body temperature.
When a body is heated, it will emit radiation. The nature of the radiation depends on the temperature, if it is low then the body emits long wavelength radiation in the infrared region which is invisible. If the temperature is high, then the shorter wavelengths increase more than the long wavelengths.
A black body will be both an ideal absorber and an ideal radiator, because it has the property of absorbing all the radiation entering it.
The radiation of black body can be calculated by calculating the power emitted by the black body radiation. When the temperature of a black body increases, as discussed before, the radiated energy too increases. It is this power radiated by the blackbody which can be calculated by the Stefan-Boltzmann equation, which states that the thermal energy radiated by a black body radiator per second and unit area is proportional to the fourth power of the absolute temperature and this equation is given by;
\[ \Rightarrow \]\[\dfrac{P}{A} = \sigma {T^4}j{m^{ - 2}}{s^{ - 1}}\]
Here \[\sigma \] is known as the Stefan Boltzmann constant.
\[P\]is the power of the radiating black body which is to be calculated
\[A\]is the radiating area
And \[T\]is the temperature of the radiator or also called the absolute temperature.
Hence, we can say that the radiation of a black body can be calculated by using the Stefan-Boltzmann equation.

Note:
Another term to be noted is heat radiation. Heat or thermal radiation is basically energy transfer by the emission of electromagnetic waves which carry the energy away from the emitting object. For temperatures lower than red hot temperature, the radiation is in the infrared region which is invisible.