Blackbody radiation.pdf

7/28/2019 Blackbody radiation.pdf

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BLACKBODY RADIATION


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THERMAL RADIATION

Thermal radiationEmitted by a body as a result of its temperature

Examples

How color of emitted radiation changes with temperature

1000 K 2500 K 5000 K 6500 K 9000 K


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ELECTROMAGNETIC SPECTRUM


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ELECTROMAGNETIC SPECTRUM


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SPECTRAL RADIANCY

DefinitionEnergy emitted by a unit area in unit time as radiation of

given frequency (power emitted by a unit area)


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BLACKBODY

BlackbodyAbsorbs all incoming radiation, does not reflectAll emitted radiation is produced by the blackbody

A cavity hole is a nice blackbody.


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WHY BLACKBODY?

Universal characterEvery blackbody has the same spectral radiancyThe radiancy depends only on wavelength and temperature

Kirchhoffs law of thermal radiationAt thermal equilibrium good absorbers are good emitters

Rreal

T()

() =RT

(

)

absorption coefficient(absorbed fraction of incident power)

spectral radiancyof a real body

(emitted power)

spectral radiancy of blackbody


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OUR SUN IS ALMOST A BLACKBODY


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HUMAN EYE EVOLUTION

Adapted to the sunAlmost the greatest part of its radiation lies within visible rangeMost sensitive to wavelengths radiated most intensively


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COSMIC MICROWAVE BACKGROUND RADIATION


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NIGHT VISION & INFRARED THERMOMETERS

HumansThermal radiation mainly in infrared


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HISTORY OF SCIENCE

Nobel prizes related to blackbody radiation

Wilhelm Wien (1911)for his discoveries regarding the laws governing the radiation of heat

Max Planck (1918)

in recognition of the services he rendered to the advancement ofPhysics by his discovery of energy quanta

John Mather & George Smoot (2006)for their discovery of the blackbody form and anisotropy ofthe cosmic microwave background radiation

Arno Penzias & Robert Wilson (1978)for their discovery of cosmic microwave background radiation


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PROPERTIES OF BLACKBODY RADIATION

Stefan-Boltzmann lawPower radiated per unit surface area is proportional to T4


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Stefan-Boltzmann lawArea under the spectral radiancy curve

Z1

0

RT()d = T4

= 5.67 108W

m2K4


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Wiens displacement lawPeak wavelength is inversely proportional to T

maxT = 2.898 103m K

peak wavelength of spectral radiancy

temperature

Wiens displacement constant


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THEORIST POINT OF VIEW: ENERGY DENSITY

Spectral radiancyDirectly experimentally accessible, emitted power

Spectral energy density

Energy in a unit volume inside the cavity

T() RT() T() =4

c

RT()


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ULTRAVIOLET CATASTROPHE

The catastropheClassically, energy density diverges for higher frequencies


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PLANCK THEORY

AimCalculate the energy density assuming quantization of energy

Steps as in the Rayleigh-Jeans theory

The average total energy of each standing wave is now different

T()d=82

c3h

exp(h/kT) 1d

T()d =8hc5

1exp(hc/kT) 1

d


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PERFECT AGREEMENT OF PLANCK THEORY WITH EXPERIMENT

Stefan-Boltzmann lawIntegrate over all frequencies

Wiens displacement lawCalculate derivate and set it to zero

Classical limitRayleigh-Jeans result for long wavelengths

Matches the shape of spectral radiancy


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PLANCK CONSTANT

Tiny in macroscopic units

h = 6.626 1034J s

Planck constant

Eq = h


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SUMMARY

Allowed energies are multiples of the energy quantum

Total energy of harmonic motion is quantized

Eq = h

h = 6.626

10

34

J s

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