Black Body Radiation: Definition, Characteristics, and Applications

A black body is defined as an idealized object that absorbs all electromagnetic radiation that falls on it and emits radiation with a continuous spectrum that depends only on its temperature. Black body radiation is the thermal radiation emitted by a black body in thermodynamic equilibrium with its surroundings. Black body radiation has many applications in physics, astronomy, engineering, and other fields.

What is a Black Body?

A black body is a theoretical concept that represents an ideal absorber and emitter of radiation.

No real object is a perfect black body, but some objects can approximate it under certain conditions. For example, a cavity with a small hole can act as a black body, because any radiation that enters the hole is trapped inside and reflected many times until it is absorbed by the cavity walls. The radiation emitted by the hole is then characteristic of a black body.

A black body does not reflect or transmit any radiation; it only absorbs and emits radiation. Therefore, a black body appears black when it is cold and emits no visible light. However, as the temperature of a black body increases, it emits more radiation and its spectrum shifts to shorter wavelengths. At high temperatures, a black body can emit visible light and appear red, orange, yellow, white, or blue depending on its temperature.

Characteristics of Black Body Radiation

The spectrum of black body radiation is continuous and depends only on the temperature of the black body. The spectrum can be described by two important laws: Wien’s displacement law and Stefan-Boltzmann law.

Wien’s Displacement Law

Wien’s displacement law states that the wavelength at which the intensity of black body radiation is maximum is inversely proportional to the temperature of the black body. Mathematically, this can be expressed as:

where λmax is the peak wavelength, T is the absolute temperature of the black body, and b is a constant known as Wien’s displacement constant, which has a value of 2.898×10−3 m K.

Wien’s displacement law explains why the color of a black body changes with temperature.

As the temperature increases, the peak wavelength decreases, and the spectrum shifts to shorter wavelengths. For example, at room temperature (about 300 K), a black body emits mostly infrared radiation with a peak wavelength of about 10 $\mu$m. At 1000 K, a black body emits mostly red light with a peak wavelength of about 3 $\mu$m. At 6000 K, a black body emits mostly white light with a peak wavelength of about 0.5 $\mu$m.

Stefan-Boltzmann Law

Stefan-Boltzmann law states that the total power emitted per unit area by a black body is proportional to the fourth power of its absolute temperature.

Mathematically, this can be expressed as:

where Me is the total power per unit area (also known as emissive power or radiant exitance), T is the absolute temperature of the black body, and σ is a constant known as Stefan-Boltzmann constant, which has a value of 5.670×10−8 W m$^{-2}K^{-4}$.

Stefan-Boltzmann’s law explains why a black body emits more radiation as its temperature increases. For example, if the temperature of a black body doubles, its emissive power increases by 16 times.

Applications of Black Body Radiation

Black body radiation has many applications in various fields of science and technology. Some examples are:

• In astronomy, stars can be approximated as black bodies, and their temperatures can be estimated from their spectra using Wien’s displacement law.

   

• The sun, for instance, has an effective surface temperature of about 5800 K and emits mostly visible light with a peak wavelength of about 0.5 $\mu$m.

• In engineering, thermal imaging devices use infrared cameras to detect the heat emitted by objects based on their temperatures using the Stefan-Boltzmann law.

   

• Thermal imaging can be used for security, surveillance, firefighting, medical diagnosis, and other purposes.

• In physics, black body radiation was one of the phenomena that led to the development of quantum theory in the early 20th century.

   

• Classical physics could not explain why the spectrum of black body radiation deviated from the Rayleigh-Jeans law at high frequencies and produced an infinite energy known as the ultraviolet catastrophe. Max Planck proposed that energy was quantized and emitted in discrete units called quanta or photons to solve this problem. Planck’s law describes the spectrum of black body radiation using quantum theory.

Summary

• A black body is an idealized object that absorbs all incident radiation and emits radiation with a continuous spectrum that depends only on its temperature.

• Black body radiation is the thermal radiation emitted by a black body in thermodynamic equilibrium with its surroundings.

• Wien’s displacement law states that the peak wavelength of black body radiation is inversely proportional to its temperature.

• Stefan-Boltzmann law states that the total power emitted per unit area by a black body is proportional to the fourth power of its temperature.

• Black body radiation has many applications in physics, astronomy, engineering, and other fields.

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