Radiation

Table of Content

What is Radiation?

The process of the transfer of heat from one place to another place without heating the intervening medium is called radiation. The term radiation used here is another word for electromagnetic waves. These waves are formed due to the superposition of electric and magnetic fields perpendicular to each other and carry energy.

Properties of Radiation

(a) All objects emit radiations simply because their temperature is above alsolute zero, and all objects absorb some of the radiation that falls on them from other objects.

(b) Maxwell on the basis of his electromagnetic theory proved that all radiations are electromagnetic waves and their sources are vibrations of charged particles in atoms and molecules.

(c) More radiations are emitted at higher temperature of a body and lesser at lower temperature.

(d) The wavelength corresponding to maximum emission of radiations shifts from longer wavelength to shorter wavelength as the temperature increases. Due to this the colour of a body appears to be changing. Radiations from a body at NTP has predominantly infrared waves.

(e) Thermal radiations travels with the speed of light and move in a straight line.

(f) Radiations are electromagnetic waves and can also travel through vacuum.

(g) Similar to light, thermal radiations can be reflected, refracted, diffracted and polarized.

(h) Radiation from a point source obeys inverse square law (intensity a \(\frac{1}{r^{2}}\)).

Prevost Theory of Exchange

According to this theory, all bodies radiate thermal radiation at all temperatures. The amount of thermal radiation radiated per unit time depends on the nature of the emitting surface, its area and its temperature. The rate is faster at higher temperatures. Besides, a body also absorbs part of the thermal radiation emitted by the surrounding bodies when this radiation falls on it. If a body radiates more then what it absorbs, its temperature falls. If a body radiates less than what it absorbs, its temperature rises. And if the temperature of a body is equal to the temperature of its surroundings it radiates at the same rate as it absorbs.

Black Body Radiation

(Fery’s black body)

Perfectly black body

A perfectly black body is one which absorbs all the heat radiations of whatever wavelength, incident on it. It neither reflects nor transmits any of the incident radiation and therefore appears

black whatever be the colour of the incident radiation.

In actual practice, no natural object possesses strictly the properties of a perfectly black body. But the lamp-black and platinum black are good approximation of black body. They absorb about 99 % of the incident radiation. The most simple and commonly used black body was designed by Fery. It consists of an enclosure with a small opening which is painted black from inside. The opeining acts as a perfect black body. Any radiation that falls on the opening goes inside and has very little chance of escaping the enclosure before getting absorbed through multiple reflections. The cone opposite to the opening ensures that no radiation is reflected back directly.

Absorption, Reflection, and Emission of Radiations

Q = Qr + Qt + Qa

\(1 = \frac{Q_r}{Q}+\frac{Q_1}{Q}+\frac{Q_2}{Q}\)

1 = r + t + a

where r = reflecting power , a = absorptive power
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and t = transmission power.

(i) r = 0, t = 0, a = 1, perfect black body

(ii) r = 1, t = 0, a = 0, perfect reflector

(iii) r = 0, t = 1, a = 0, perfect transmitter

Absorptive power

In particular the absorptive power of a body can be defined as the fraction of incident radiation that is absorbed by the body.

\(a = \frac{Enerdy\; absorbes}{Energy \;incident}\)

As all the raditions incident on a black body are absorbed, a = 1 for a black body.

Emissive power

Energy radiated per unit time per unit area along the normal to the area is known as emissive power.

\(E = \frac{Q}{\Delta A\Delta t}\)

(Notice that unlike absorptive power, emissive power is not a dimensionless quantity).

Spectral Emissive power (El)

Emissive power per unit wavelength range at wavelength l is known as spectral emissive power, El. If E is the total emissive power and El is spectral emissive power, they are related as follows,

\(E = \int_{0}^{\infty }E_\lambda d_\lambda\;\; and\;\; \frac{dE}{d\lambda} = E_\lambda\)

Emissivity

\(e= \frac{Emissive \; power\;of\;a\;body\;at\;temperature\; T}{Emissive power \;of\; a\;black\; at \; same\;temperature\;T}= \frac{E}{E_o}\).

Kirchoff’s Law

The ratio of the emissive power to the absorptive power for the radiation of a given wavelength is same for all substances at the same temperature and is equal to the emissive power of a perfectly black body for the same wavelength and temperature.

\(\frac{E(body)}{a(body)}-E(black \;body)\)

Hence we can conclude that good emitters are also good absorbers.

Wien’s Displacement Law – Nature of thermal radiations

From the energy distribution curve of black body radiation, the following conclusions can be drawn :

(a) The higher the temperature of a body, the higher is the area under the curve i.e. more amount of energy is emitted by the body at higher temperature.

(b) The energy emitted by the body at different temperatures is not uniform. For both long and short wavelengths, the energy emitted is very small.

(c) For a given temperature, there is a particular wavelength (lm) for which the energy emitted (El) is maximum.

(d) With an increase in the temperature of the black body, the maxima of the curves shift towards shorter wavelengths.

From the study of the energy distribution of black body radiation discussed as above, it was established experimentally that the wavelength (lm) corresponding to the maximum intensity of emission decreases inversely with the increase in the temperature of the black body. i.e.

lm µ
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or lm T = b

This is called Wien’s displacement law.

Here b = 0.282 cm-K, is the Wien’s constant.

 

Ex: Solar radiation is found to have an intensity maximum near the wavelength range of 470 nm. Assuming the surface of sun to be perfectly absorbing (a = 1), calculate the temperature of solar surface.

Sol. Since a =1, sun can be assumed to be emitting as a black body

from Wien’s law for a black body

lm . T = b

Þ \(T=\frac{b}{\lambda_m} = \frac{0.282(cm-K)}{(470\times10^{-7}cm)}\)

~ 6125 K. Ans.

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