Blackbody radiation is electromagnetic thermal radiation that radiates inside or surrounding a body that is in thermal equilibrium with its surroundings. Thermal equilibrium is a state in which two or more systems in thermal contact have reached a constant temperature and no heat is exchanged between them. In other words, in thermal equilibrium, the temperature of the systems is the same, and there is no net flow of heat between them.  The emitting body is an ideal thermal emitter, called a black body. The historical aspects of black body radiation date back to 1860, when Gustav Kirchhoff introduced the term "black body".

Black body is an idealized opaque, non-reflective body that absorbs all radiation incident upon it without passing on the energy. This property is applicable to all wavelengths and angle of incidence of radiation. Therefore, these bodies are perfect absorbers and emitters of electromagnetic radiation, with a specific intensity that is determined by their temperature.

Appearance of Black body

Black-body radiation (BBR) is interpreted only as a theory. The thermal radiation spontaneously emitted by real-world objects resembles black body radiation. A perfectly insulated container that is in thermal equilibrium internally contains black-body radiation and will radiate it via a hole in its wall if the opening is small enough to have no significant impact on the equilibrium.

At room temperature, a black body appears black because the majority of the energy it emits is in the infrared spectrum, which the human eye cannot see. It appears to be dull red when it gets a little hotter. Further raising the temperature causes it to turn yellow, white, and eventually blue-white.

Black-body radiation is used as a first approximation for the energy that planets and stars emit, despite the fact that they are neither perfect black bodies nor in thermal equilibrium with their surroundings. Black holes are almost ideal black bodies because they completely absorb all radiation that strikes them. It has been hypothesized that they emit black-body radiation, also called Hawking radiation, whose temperature varies with the black hole's mass.

The distinctive, continuous frequency spectrum of black-body radiation is solely dependent on body temperature and is called 'Planck's spectrum'. At room temperature, the majority of the emission occurs in the infrared area of the electromagnetic spectrum. Black bodies begin to generate a significant amount of visible light as the temperature rises over roughly 500 degrees celsius. The first dim illumination appears "ghostly" grey to the human eye when seen in the dark. Low-intensity light merely activates the eye's grey-level sensors, even if visible light is truly red.

In spite of the fact that a black body emits energy at all frequencies, its intensity quickly goes to zero at higher frequencies (short wavelengths).

Black Body Radiation Laws:

The characteristics of blackbody radiation can be described in terms of several laws: Kirchhoff's law, Planck’s law, Wien’s displacement law, and Stefan-Boltzmann law.

Kirchhoff's laws

It states that the ratio of the spectral emissive power e_λ to the spectral absorptivity a_λ for a particular wavelength λ is the same for all bodies at the same temperature and is equal to the emissive power of a perfectly black body at that temperature. 

where  is the emissive power of a perfectly black body and  is a universal function of λ and T.

Planck’s law

The german physicist Max Planck postulated that a black body's energy is delivered in discrete packets rather than constantly, known as quanta. 

Planck's law, which states that the energy density of a radiation is inversely proportional to the frequency of the radiation raised to the power of four, can be used to calculate the intensity of black body radiation at a specific temperature and wavelength. The spectrum has a particular peak frequency that changes to higher frequencies with increasing temperature, and the total energy emitted increases.

Bν(T) is the spectral radiance density of frequency ν radiation per unit frequency at thermal equilibrium at temperature T.

h is the planck’s constant

C is the speed of light in a vacuum

K is the boltzmann constant

ν is the frequency of EM radiation

T is the temperature of the body

Wien’s Displacement Law

Wien’s law states how the black-body radiation spectrum varies with temperature and how it relates the spectrum at any temperature to any other temperature spectrum. It is possible to express spectral intensity as a function of wavelength or frequency.

where b is the Wien’s displacement constant, which equals to 2.897771955 × 10⁻³ mK.

Stefan-Boltzmann Law

The emissive power which is the energy radiated per second by unit surface area of the black body is given as:

where  is σ, Stefan-Boltzmann constant, which is approximately 5.67 x 10^-8 W·m^-2·K^-4

If the radiation emitted normal to the surface and the energy density of radiation is , then emissive power of the surface is given as  

Applications

One of the most well-known uses of black body radiation is the study of cosmic microwave background radiation, a faint radiation that permeates the whole cosmos and is assumed to be a holdover from the hot, dense state of the universe at the Big Bang. The study of this radiation has provided significant knowledge about the development and composition of the universe. Astronomers use the concept to determine the temperature of stars and to study the cosmic microwave background radiation, which provides insights into the early universe.

The concept of BBR can be used in Infrared thermometers which measures the intensity of the radiation emitted by an object to determine its temperature.

BBR is also used in the design of heat exchangers, which convert heat from one medium to another. Engineers can design efficient and effective heat exchangers for a variety of everyday technologies, such as electric heaters and incandescent bulbs. These devices work by heating a filament to a high temperature, which causes it to produce black body radiation, which is then transformed into heat or visible light.

In the field of material science, engineers can use the concept to determine the thermal conductivity of materials, which is critical for the design of efficient heat exchangers and thermal management systems.

By understanding the radiation emitted by the sun and the behavior of black body radiation, engineers can design more efficient solar panels that can capture more energy from the sun.