Radiation: Definition, Properties, Blackbody, Prevost Theory

Every hot surface emits energy. The energy emitted by a hot body in the form of electromagnetic waves, by virtue of its temperature, is called thermal radiation. Solar energy is vital for our survival on earth. In fact, it is our planet’s position in this solar system that allows life to exist on our planet. However, how does heat from the sun reach us? How does the heat energy travel such a long-distance? It is because of the process of heat transfer called Radiation.

Thermal radiation is the process of heat transfer by the emission of electromagnetic waves. These waves carry energy from the body emitting thermal radiation. The transfer of heat by the process of radiation can take place through a vacuum or transparent medium.

What is Radiation?

There are three modes of transmission of heat energy. They are conduction, convection, and radiation.

Radiation is the transmission mode from a hot body to a cold body or surroundings with the help of electromagnetic waves and all bodies continuously radiate energy in the form of electromagnetic waves. Radiation does not require a material medium. The speed of radiation is equal to the speed of light in that medium.  Electromagnetic waves from the sun, for example, travel through the void of space during their journey to earth. Even an ice cube radiates energy, although so little of it is in the form of visible light that an ice cube cannot be seen in the dark.

The electromagnetic radiation emitted by a body due to its temperature, like the radiation by a red hot iron or light from a filament lamp, is called thermal radiation. The surface of an object plays an important role in determining how much radiant energy the object will emit or absorb.

Properties of Thermal Radiation

1. The radiation process does not need any material medium for heat transfer.
2. The term radiation refers to the continuous emission of energy from the surface of all bodies, and this energy is called radiant energy.
3. Radiant energy is in the form of Electromagnetic waves.
4. Radiant energy emitted by a surface depends on the temperature and nature of the surface.

5. All bodies, whether they are solid, liquid, or gas, emit radiant energy.
6. Electromagnetic radiations emitted by a body by the increased temperature of a body are called thermal radiation.
7. Thermal radiation falling on a body can partly be absorbed and partly be reflected by the body. This absorption and reflection of radiation depend on the colour of the body.
8. Thermal radiation travels through a vacuum on a straight line and with the velocity of light.
9. Thermal radiations can be reflected and refracted.

Black Body

A body that completely absorbs thermal radiations of all wavelengths falling upon it is called a black body. When such a body is heated, it emits radiations of all possible wavelengths. The radiations emitted by a black body are called black body radiations. A black body is also called an ideal radiator.

There is no ideal black body, but the Ferry cavity can be considered a perfectly black body. The best practical blackbody is a small hole in a box with a blackened interior because practically none of the radiation entering such a hole could escape again, and it would be absorbed inside.

Prevost Theory of Exchange

We know that all objects emit heat radiations at all finite temperatures (except at absolute zero, i.e., \(0\,{\rm{K}}\)) and absorb radiations from the surroundings. A body at a high temperature radiates more heat to the surroundings than it receives from it. Similarly, a body at a lower temperature receives more heat from the surroundings than it loses to it.

Prevost applied the idea of ‘thermal equilibrium’ to radiation. He suggested that all bodies radiate energy, but hot bodies radiate more heat than cooler bodies. At one point in time, the exchange rate of heat from both the bodies will become the same. Now the bodies are said to be in ‘thermal equilibrium.

Only at absolute zero temperature, a body will stop emitting. Therefore, Prevost theory states that all bodies emit thermal radiation at all temperatures above absolute zero, irrespective of the nature of the surroundings.

Terms Related to Black Body Radiation

1. Total Emissive Power \((e)\): The total emissive power of a body at a particular temperature is defined as the total amount of radiant energy emitted per second per unit area of the body’s surface. The symbol \((e)\) represents it. The symbol \(E\) represents the total emissive power of a black body. Its SI unit is \({\rm{J}}\,{{\rm{m}}^{{\rm{ – 2}}}}\,{{\rm{s}}^{{\rm{ – 1}}}}\).
2. Emissivity \((\varepsilon )\): The emissivity of a body is the ratio of the total emissive power of the body to the total emissive power of a black body. The symbol \((\varepsilon )\) represents it.
   It means that \(\varepsilon {\mkern 1mu} = {\mkern 1mu} e/E\) or \(e{\mkern 1mu} = {\mkern 1mu} \varepsilon E\)
   For a black body, \(\varepsilon \, = \,1\).
3. Total Absorptive Power \((a)\). The total absorptive power of a body is defined as the ratio of the total radiant energy absorbed by the body in a certain interval of time to the total energy that falls upon it in the same interval of time. It is represented by the symbol \((a)\). The total absorptive power of a black body is represented by the symbol \((A)\) By definition, \(A\, = \,1\).

Kirchhoff’s Law

Kirchoff’s law states that for a given temperature, at a particular wavelength, the ratio of the emissive power to the absorptive power of a body is a constant for all bodies and is equal to the emissive power of a perfectly black body. An object at some non-zero temperature radiates electromagnetic energy, and if it is a perfect black body, it will radiate energy according to the blackbody radiation formula. At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity.

If \({e_\lambda }\) and \({a_\lambda }\) be the emissive and absorptive powers of a body for wavelength \(\lambda \), and \({E_\lambda }\) be the emissive power of a black body for wavelength \({\lambda }\), then,
\(\frac{{{e_\lambda }}}{{{a_\lambda }}} = {\text{Constant}} = {E_\lambda }\)

According to this law, good emitters are good absorbers, and poor emitters are poor absorbers.

Stefan’s Law

According to Stefan’s law, the total amount of radiant energy emitted by the unit area of a perfectly black body in one second is directly proportional to the fourth power of its absolute temperature.

If \(E\) be the amount of radiant energy emitted by unit area in one second and \(T\) be the absolute temperature of the body, then

\(\frac{E}{A} = \sigma {T^4}\)

where \(\sigma \) is Stefan’s constant and \(\sigma \, = \,5.67 \times {10^{ – 8}}\,{\rm{W}}{{\rm{m}}^{{\rm{ – 2}}}}{{\rm{K}}^{\rm{4}}}\)

A body that is not black absorbs and hence emits less radiation,

For such a body, \(E\, = \,e\sigma \,A{T^4}\)

\(e = \) emissivity (which is equal to absorptive power), which lies between \(0\) and \(1\).

With the surroundings of temperature \({T_0}\) net energy radiated by an area \(A\) per unit time.

\(\Delta E\, = \,E – {E_0} = e\sigma A[{T^4} – {T_0}^4]\)

Stefan Boltzmann Law relates the temperature of the blackbody to the amount of power it emits per unit area.

Wien’s Displacement Law

Wien’s displacement law states that the wavelength \(({\lambda _m})\) corresponding to which the maximum energy emitted by a black body is inversely proportional to its absolute temperature \((T)\).

\(({\lambda _m}) \propto \frac{1}{T}\)

or \(({\lambda _m})T = b\)

Where \(b = 2.9 \times {10^{ – 3}}\,{\rm{mK}}\) is Wien’s constant.

Summary

Radiation is the transmission mode from a hot body to a cold body or surroundings with the help of electromagnetic waves and doesn’t need any help from a material medium. All bodies continuously radiate energy in the form of electromagnetic waves.
The electromagnetic radiation emitted by a body due to its temperature, like the radiation by a red hot iron or light from a filament lamp, is called thermal radiation.

Black body Radiation: A body that completely absorbs thermal radiations of all wavelengths falling upon it is called a black body. When such a body is heated, it emits radiations of all possible wavelengths. The radiations emitted by a black body are called black body radiations.

Prevost theory: Prevost applied the idea of ‘thermal equilibrium’ to radiation. He suggested that all bodies radiate energy, but hot bodies radiate more heat than cooler bodies. At one point in time, the exchange rate of heat from both the bodies will become the same. Now the bodies are said to be in ‘thermal equilibrium’.

Kirchoff’s law of Radiation: Kirchoff’s law states that for a given temperature, at a particular wavelength, the ratio of the emissive power to the absorptive power of a body is a constant for all bodies and is equal to the emissive power of a perfectly black body.

Stefan’s Law: According to Stefan’s law, the total amount of radiant energy emitted by the unit area of a perfectly black body in one second is directly proportional to the fourth power of its absolute temperature, i.e. \(E = e\sigma A {T^4}\).

Wein’s Law: Wien’s displacement law states that the wavelength \(({\lambda _m})\) corresponding to which the maximum energy emitted by a black body is inversely proportional to its absolute temperature \((T)\).

FAQs on Radiation

Q.1. What are the modes of heat transfer?
Ans: There are three modes of heat transfer: Conduction, Convection, and Radiation.

Q.2. State Kirchoff’s radiation law.
Ans: The law states that for a given temperature, the ratio of the emissive power to the absorptive power of a body at a particular wavelength is a constant for all bodies.
This ratio is equal to the emissive power of a perfectly black body.

Q.3. What is an ideal black body?
Ans: A blackbody is defined as an ideal body that allows all incident radiation to pass into it (zero reflectance) and absorbs all the incident radiation (zero transmittance) internally.

Q.4. State Stefan’s law.
Ans: This law states that the total heat energy emitted by a perfect black body per second per unit area is directly proportional to the fourth power of the absolute temperature of its surface. 

Q.5. Which modes of transfer can be useful to transfer heat through the vacuum?
Ans: Heat transfer through radiation can occur through the vacuum, while conduction and convection require a material medium for heat transfer.

Q.6. How is heat radiation different from light?
Ans: Heat radiation and light are electromagnetic waves, the only difference between the two lies in their wavelength or frequency.

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