Transcript Document
EP324 Applied Optics
Topic X
BLACKBODY
RADIATION
Department of
Engineering Physics
University of Gaziantep
June 2014
Sayfa 1
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 2
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 3
Stefan’s Law
The rate at which an object radiates energy is proportional to
the fourth power of its absolute temperature:
P AeT
P
σ
A
T
e
4
= power in watts of electromagnetic waves radiated
from the surface.
= 5.6696 x 10–8 W/m2 . K4
= surface area
= surface temperature in kelvins.
= emissivity or absorptivity (0<e<1).
for perfect mirror e = 0
for black body e = 1
Sayfa 4
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 5
An object radiates energy:
P AeT
4
It also absorbs electromagnetic
radiation from the surroundings:
P AeT0
4
Net rate of energy gained or lost:
P Ae(T T0 )
4
4
Sayfa 6
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 7
Cavity
A good approximation of a
black body is a small hole
leading to the inside
of a hollow object.
Sayfa 8
Black Body Spectrum
When a black body heated
a distribution of wavelength
is observed.
Sayfa 9
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 10
Black Body Spectrum
u(λ) spectral distibution function
Rule 1:
4
u
(
)
d
T
0
Rule 2 (Wein’s displacement law):
The peak of the wavelength
distribution shifts to shorter
wavelengths as the temperature
increases.
maxT 0.0029 m K
Sayfa 11
Plank’s Formula
u ( )
8hc
5
1
exp(hc / k BT ) 1
See lecture notes for details.
http://en.wikipedia.org/wiki/Thermal_radiation
Sayfa 12
EXAMPLE
Using Plank’s formula for a black-body radiator,
derive Wein law:
kBTmax 0.2014
or
maxT 0.0029 m K
Hint: Plank formula is given by:
u ( )
8hc
5
1
exp(hc / k BT ) 1
use dimensionless variable: x
and solve
hc
k BT
du
0
dx
http://en.wikipedia.org/wiki/Thermal_radiation
Sayfa 13
Quiz
Sayfa 14
Ear Thermometer
This thermometer is very sensitive
because temperature
is raised to the fourth power in
Stefan’s law.
Sayfa 15
Key Points
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.
Sayfa 16
References
[1]. http://www.mathworks.com/products/matlab
[2]. Numerical Methods in Engineering with MATLAB,
J. Kiusalaas, Cambridge University Press (2005)
[3]. Numerical Methods for Engineers, 6th Ed.
S.C. Chapra, Mc Graw Hill (2010)
Sayfa 17