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Sayfa 1
Department of Engineering Physics
University of Gaziantep
June 2014
Topic X
BLACKBODY RADIATION
EP324 Applied Optics
Sayfa 2
Introduction
If you turn on an electric stove, the stove plate heats up until it becomes red or orange hot.
The red glow that you see consists of photons with energies in the visible red range.
When the stove plate was cold, it also emitted photons, but those were of too low energy to be seen by our eyes.
Sayfa 3
All objects radiate energy continuously in the form of electromagnetic waves produced by thermal vibrations of the molecules.
The characteristics of this radiation depend on the temperature and properties of the object’s surface.
Every second, approximately 1370 J of electromagnetic radiation from the Sun passes perpendicularly through each 1 m2 at the top of the Earth’s atmosphere.
Sayfa 4
Stefan’s Law
The rate at which an object radiates energy is proportional to the fourth power of its absolute temperature:
P = power in watts of electromagnetic waves radiated
from the surface.
σ = 5.6696 x 10–8 W/m2 . K4
A = surface area
T = surface temperature in kelvins.
e = emissivity or absorptivity (0<e<1).
for perfect mirror e = 0
for black body e = 1
4AeTP
Sayfa 5
EXAMPLE
Two lightbulbs have cylindrical filaments much greater in
length than in diameter. The evacuated lightbulbs are identical
except that one operates at a filament temperature of
2 100°C and the other operates at 2 000°C. Find the
ratio of the power emitted by the hotter lightbulb to that
emitted by the cooler lightbulb.
Sayfa 6
An object radiates energy:
It also absorbs electromagnetic
radiation from the surroundings:
Net rate of energy gained or lost:
4AeTP
40AeTP
)( 40
4 TTAeP
Sayfa 7
Black Body Radiation
From a classical viewpoint,
thermal radiation originates
from accelerated charged particles
in the atoms near the surface
of the object;
Black body is an ideal system
that absorbs all radiation incident
on it.
The electromagnetic
radiation emitted by the black body
is called blackbody radiation.
Sayfa 8
Cavity
A good approximation of a
black body is a small hole
leading to the inside
of a hollow object.
Sayfa 10
Black Body Spectrum
Intensity of blackbody radiation
versus wavelength at three
temperatures.
The amount of radiation emitted
(the area under a curve) increases
with increasing temperature.
Sayfa 11
Black Body Spectrum
u(λ) spectral distibution function
Rule 1:
Rule 2 (Wein’s displacement law):
The peak of the wavelength
distribution shifts to shorter
wavelengths as the temperature
increases.
0
4)( Tdu
Km 0029.0max T
Sayfa 12
See lecture notes for details.
1)/exp(
18)(
5
Tkhc
hcu
B
http://en.wikipedia.org/wiki/Thermal_radiation
Plank’s Formula
Sayfa 13
EXAMPLE
Using Plank’s formula for a black-body radiator,
derive Wein law:
or
Hint: Plank formula is given by:
use dimensionless variable:
and solve
2014.0max TkB
Km 0029.0max T
1)/exp(
18)(
5
Tkhc
hcu
B
Tkhc
xB
0dx
du
http://en.wikipedia.org/wiki/Thermal_radiation
Sayfa 15
This thermometer is very sensitive
because temperature
is raised to the fourth power in
Stefan’s law.
Ear Thermometer
Sayfa 16
Blackbody radiation is the radiation emitted by a black surface that is in thermal equilibrium.
Planck’s blackbody spectrum determines how much is radiated at each frequency.
Surfaces that are not black emit radiation that is less by a factor called the emissivity.
Emissivity equals absorptivity for the same frequency and direction of radiation.
Key Points