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Department of Engineering Physics

University of Gaziantep

June 2014

Topic X

BLACKBODY RADIATION

EP324 Applied Optics

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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.

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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.

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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

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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.

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An object radiates energy:

It also absorbs electromagnetic

radiation from the surroundings:

Net rate of energy gained or lost:

4AeTP

40AeTP

)( 40

4 TTAeP

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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.

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Cavity

A good approximation of a

black body is a small hole

leading to the inside

of a hollow object.

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Black Body Spectrum

When a black body heated

a distribution of wavelength

is observed.

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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.

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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

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See lecture notes for details.

1)/exp(

18)(

5

Tkhc

hcu

B

http://en.wikipedia.org/wiki/Thermal_radiation

Plank’s Formula

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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

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Quiz

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This thermometer is very sensitive

because temperature

is raised to the fourth power in

Stefan’s law.

Ear Thermometer

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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

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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)