Black Body Radiation:
A black body
is one that absorbs all electromagnetic radiations falling on it.
It is a
perfect absorber & perfect emitter of radiation.
A black body
in thermal equilibrium means constant temperature emits electromagnetic
radiations. The radiation emitted by such a body is called black body radiation
or full radiation or temperature radiation. This radiation is emitted according
to Planck’s law & its spectrum is determined by the temperature alone, not
by the shape or configuration of the body.
Again according to Kirchhoff’s law the emissive power of a black body is
independent of its geometry, so universal in character.
A perfect
black body is an idealization, it doesn’t really exist. Lamp black or platinum
black is nearest approach to a perfectly black body. Lamp black can absorbs
about 96% of radiant energy & platinum black absorbs about 98%. However,
most glowing substances like a piece of red hot iron or the sun are good
approximations.
A hollow
closed cavity with blackened inner walls with a small opening serves as a very
good approximation of a black body.
The spectrum
of this radiation is not dependent on the chemical composition of the matter
but it's only determined by its absolute temperature T. It turns out that all
objects behave like black bodies, regardless if they are actually black or not.
A black body
radiates more when it is hot than when it is cold, hence the spectrum of a
hotter black body has its peak at higher frequency as compared to the cooler
one.
Since hot
bodies are very often used as light sources colour temperature is used to
describe the colour of the light. For example the sun, a filament light bulb, a
candle, and many other light sources can be considered as "black
body" radiators.
Colour Perception:
1'000 K
|
Red
|
|
1'500 K
|
Reddish orange
|
|
2'000 K
|
Yellowish orange
|
|
2'800 K
|
Yellow
|
|
3'500 K
|
Yellowish white
|
|
4'500 K
|
Warm white
|
|
5'500 K
|
White
|
|
1'500 K
|
Candlelight
|
|
2'700 K
|
Incandescent lamp
|
|
3'200 K
|
Sunrise / sunset
|
|
3'400 K
|
Halogen incandescent lamp
|
|
5'500 K
|
Sunny daylight around noon
|
|
6'000 K
|
Electronic photo flash
|
|
7'000 K
|
Overcast sky
|
|
10'000 K
|
Blue sky
|
Idealization/ Ferry’s black body:
- A widely used model of black body radiation which is a spherical cavity whose walls are opaque to radiations.
- The sphere contains a small hole ‘O’ with a conical projection ‘P’ opposite to hole ‘O’.
- The inner surface of the sphere is coated with lamp black. The space between the walls is evacuated to prevent loss of heat by conduction of convection.
- When the radiant energy enters the hole, suffers multiple reflections inside the cavity & ultimately absorbed.
- At each reflection about 96% of incident radiation energy is absorbed, hence after few reflections all the radiant energy is absorbed by the sphere.
- The function of the conical projection is to prevent direct reflection of the radiant energy from the surface opposite to hole.
- Till thermal equilibrium, radiation is absorbed & emitted by the walls of the cavity. The energy is distributed until the bunch of photon achieves Planck’s distribution.
- Thus sphere absorbs all radiant energy incidents on it. When the sphere is heated, blackbody radiations are emitted from the hole ‘O’.
- To sphere is heated to & maintained at different temperature, wavelength & energy distribution is studied.
- By an infrared spectrometer & Bolometer (instrument used to measure intensity), the intensities of different wavelengths are drawn.
Results:
- The distribution of energy in the spectrum of black body radiations is not uniform over a wide range of wavelength.
- As the temperature increases, E for every wavelength increases.
- At constant temperature as λ increases till it becomes maximum at a certain wavelength λmax & then with further increase of ˄, E decreases. At a higher temperature the wavelength λmax at which E maximum, shifts towards a shorter wavelength.
Theoretical laws of Blackbody radiation:
1 1.Kirchhoff’s
Law:
At
any particular temperature, the ratio of emissive power (Ee) of a
body in thermal equilibrium with its surroundings to its absorptive power (Ea)
is a constant equal to the emissivity (ε) of a perfectly black body at that
temperature.
Ε = Ee
/ Ea
2. Stefan-Boltzmann
Law:
This
law states that the total energy radiated in unit time per unit surface area of
a black body (I) is proportional to the fourth power of absolute temperature T
of the black body.
I= σT4
Where σ =5.67x10-8
W/m2K4 = Stefan-Boltzmann constant
3. Wien’s
Displacement Law:
This
law states that the wavelength corresponding to the maximum spectral intensity
is inversely proportional to the absolute temperature of the body emitting
radiation & expressed as
λmax=b/T
Where
b=2.898x10-3 mK= Wien’s displacement constant
4. Wien's
radiation formula:
According
to Wien, the energy density in the wavelength interval λ to λ+dλ, emitted by
a blackbody at a temperature T is expressed as
uλ dλ=A/λ^5
exp(-B/kT) dλ
1 5. Rayleigh-Jeans Law:
According to this law
uλ dλ = 8πkT/ λ^4 dλ
Watch the Video Series by BS
Numerical:
Problems on Black body Radiation |
Objectives
Blackbody Radiation:
1.
The emissivity
& absorptivity of a real surface are equal for radiation with identical
temperature & wavelength. This law is referred as
a)
Rayleigh Law
b)
Kirchhoff’s Law
c)
Planck’s Law
d)
Wien’s Law
2.
The energy radiated by a blackbody should not
vary in accordance with
a)
Wavelength
b)
Temperature
c)
Surface Characteristics
d) Time
3.
As the
wavelength of the radiation decreases, the intensity of the black body
radiations ____________
a) Increases
b) Decreases
c) First increases then decrease
d) First decreases then increase
a) Increases
b) Decreases
c) First increases then decrease
d) First decreases then increase
4.
The
radiations emitted by hot bodies are called as ________________
a) X-rays
b) Black-body radiation
c) Gamma radiations
d) Visible light
a) X-rays
b) Black-body radiation
c) Gamma radiations
d) Visible light
5. What relation between emissivity, e, and
Absorptive Power, a, is given by Kirchhoff’s law?
a) e < a
b) e > a
c) e = a
d) no specific relation
b) e > a
c) e = a
d) no specific relation
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