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 ( ) 
8hc
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:
kBTmax  0.2014
or
maxT  0.0029 m  K
Hint: Plank formula is given by:
u ( ) 
8hc
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