Blackbody in chemistry

8/6/2019 Blackbody in chemistry

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Sadam AlSadam Al--HazaimayHazaimay

M.Sc Environmental Physics (PEP)M.Sc Environmental Physics (PEP)

ProPro--seminar Techniques WS 07/08seminar Techniques WS 07/08

Bremen UniversityBremen University

19/12/200719/12/2007


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ContentsContents

MotivationMotivation Definition of a BlackDefinition of a Black--BodyBody BlackBlack--Body Radation LawsBody Radation Laws

11-- The Planck LawThe Planck Law

22-- The Wien Displacement LawThe Wien Displacement Law33-- The StefanThe Stefan--Boltzmann LawBoltzmann Law44-- The RayleighThe Rayleigh--Jeans LawJeans Law

Application for Black BodyApplication for Black Body

ConclusionConclusion SummarySummary


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MotivationMotivation

The black body is importance in thermalThe black body is importance in thermalradiation theory and practice.radiation theory and practice.

The ideal black body notion is importanceThe ideal black body notion is importancein studying thermal radiation andin studying thermal radiation andelectromagnetic radiation transfer in allelectromagnetic radiation transfer in allwavelength bands.wavelength bands.

The black body is used as a standard withThe black body is used as a standard withwhich the absorption of real bodies iswhich the absorption of real bodies iscompared.compared.


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Definition of a black bodyDefinition of a black body

A black body is an ideal bodywhich allows the whole of theincident radiation to pass intoitself ( without reflecting the

energy ) and absorbs within itselfthis whole incident radiation(without passing on the energy).This propety is valid for radiationcorresponding to all wavelengths

and to all angels of incidence.Therefore, the black body is anideal absorber of incidentradaition.

Univ. of Oregon web site


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BlackBlack--Body Radiation Laws (1)Body Radiation Laws (1)

11-- The RayleighThe Rayleigh--Jeans Law.Jeans Law.* It agrees with experimental* It agrees with experimentalmeasurements for longmeasurements for longwavelengths.wavelengths.

* It predicts an energy output that* It predicts an energy output thatdiverges towards infinity asdiverges towards infinity aswavelengths grow smaller.wavelengths grow smaller.

* The failure has become known* The failure has become knownas the ultraviolet catastrophe.as the ultraviolet catastrophe.

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http://www.egglescliffe.org.uk/physics/astronomy/blackbody/Image22c.gif


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This formula also had aThis formula also had aproblem. The problem wasproblem. The problem wasthe term in thethe term in thedenominator.denominator.

For large wavelengths itFor large wavelengths itfitted the experimental datafitted the experimental data

but it had major problems atbut it had major problems atshorter wavelengths.shorter wavelengths.

Ultraviolet CatastropheUltraviolet Catastrophe

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http://theory.uwinnipeg.ca/users/gabor/foundations/quantum/images/slide5.gif


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22-- Planck LawPlanck Law

-- We have two forms. As a functionWe have two forms. As a functionof wavelength.of wavelength.

And as a function of frequencyAnd as a function of frequency

The Planck Law gives a distribution thatThe Planck Law gives a distribution thatpeaks at a certain wavelength, the peakpeaks at a certain wavelength, the peak

shifts to shorter wavelengths for highershifts to shorter wavelengths for highertemperatures, and the area under thetemperatures, and the area under thecurve grows rapidly with increasingcurve grows rapidly with increasingtemperature.temperature.


http://scienceworld.wolfram.com/physics/PlanckLaw.html

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Comparison between Classical andComparison between Classical andQuantum viewpointQuantum viewpoint

http://upload.wikimedia.org/wikipedia/commons/a/a1/Blackbody-lg.png

There is a good fit at long wavelengths, but at short wavlengths there is amajor disagreement. Rayleigh-Jeans , but Black-body 0.


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33-- Wein Displacement LawWein Displacement Law-- It tells us as we heat an object up, itsIt tells us as we heat an object up, its

color changes from red to orange tocolor changes from red to orange towhite hotwhite hot..

-- You can use this to calculate theYou can use this to calculate the

temperature of stars.temperature of stars.The surface temperature of the Sun isThe surface temperature of the Sun is

5778 K, this temperature5778 K, this temperaturecorresponds to a peak emission =corresponds to a peak emission =502 nm = about 5000 .502 nm = about 5000 .

-- b is a constant of proportionality,b is a constant of proportionality,called Wien's displacement constantcalled Wien's displacement constantand equals 2.8977685(51)and equals 2.8977685(51) 101033 mmK = 2.8977685(51)K = 2.8977685(51) 101066 nmnm K.K.


http://www.rumford.com/radiant/images/Wiengraph.gif

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44-- The StefanThe Stefan--Boltzmann LawBoltzmann Law* Gives the total energy being* Gives the total energy being

emitted at all wavelengths byemitted at all wavelengths bythe blackbody (which is thethe blackbody (which is thearea under the Planck Lawarea under the Planck Law

curve).curve).* Explains the growth in the* Explains the growth in the

height of the curve as theheight of the curve as thetemperature increases. Noticetemperature increases. Noticethat this growth is very abrupt.that this growth is very abrupt.

** Sigma = 5.67 * 10Sigma = 5.67 * 10--88 J sJ s--11 mm--22 KK--44,,Known as the StefanKnown as the Stefan--Boltzmann constant.Boltzmann constant.

BlackBlack--Body Radiation Laws (4)Body Radiation Laws (4)4

Tj W

http://ceos.cnes.fr:8100/cdrom-98/ceos1/science/dg/fig10.gif


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http://en.wikipedia.org/wiki/Image:RWP-comparison.svg

Comparison of Rayleigh-Jeans law with Wien'slaw and Planck's law, for a body of8 mK

temperature.


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Application for Black BodyApplication for Black Body-- The area of Earth's disk as viewed from spaceThe area of Earth's disk as viewed from space

is, Area = ris, Area = r22..

-- The total energy incident on Earth is, IncidentThe total energy incident on Earth is, Incidentenergy = (renergy = (r22)S)Soo..

-- The energy absorbed by the Earth/atmosphereThe energy absorbed by the Earth/atmospheresystem, as viewed from space issystem, as viewed from space is

Absorbed energy = (rAbsorbed energy = (r22)S)Soo(1(1 -- A). As we knowA). As we knowthat bodies must be in radiative equilibrium.that bodies must be in radiative equilibrium.The solar energy striking Earth's disk asThe solar energy striking Earth's disk as

viewed from space is reviewed from space is re--emitted as thermalemitted as thermalradiation by the surface of the entire globe,radiation by the surface of the entire globe,as described by the Stefanas described by the Stefan--Boltzmann Law,Boltzmann Law,Emitted energy = (4rEmitted energy = (4r22)T)T44..

-- Set the absorbed energy equal to the emittedSet the absorbed energy equal to the emittedenergy:energy:

(r(r

22

)S)Soo(1(1 -- A) = (4rA) = (4r

22

)T)TEE44

, Solving for T yields:, Solving for T yields:TTEE = [S= [Soo(1(1 -- A)/(4)]A)/(4)](1/4)(1/4)

= [1370(1= [1370(1--0.3)/(45.67x100.3)/(45.67x10--88)])](1/4)(1/4) = 255 K.= 255 K.

http://soer.justice.tas.gov.au/2003/image/378/atm_structure/o_atm_Radn_Balance-m.jpg


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ConclusionConclusion As the temperatureAs the temperature

increases, the peakincreases, the peakwavelength emitted by thewavelength emitted by theblack body decreases.black body decreases.

As temperature increases,As temperature increases,the total energy emittedthe total energy emitted

increases, because theincreases, because thetotal area under the curvetotal area under the curveincreases.increases.

The curve gets infinitelyThe curve gets infinitelyclose to the xclose to the x--axis butaxis but

never touches it.never touches it.

http://www.astro.ufl.edu/~oliver/ast3722/lectures/BasicDetectors/BlackBody.gif


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SummarySummary

-- A black body is a theoretical object that absorbs 100% of theA black body is a theoretical object that absorbs 100% of theradiation that hits it. Therefore it reflects no radiation andradiation that hits it. Therefore it reflects no radiation andappears perfectly black.appears perfectly black.

-- Roughly we can say that the stars radiate like blackbodyRoughly we can say that the stars radiate like blackbodyradiators. This is important because it means that we can useradiators. This is important because it means that we can use

the theory for blackbody radiators to infer things about stars.the theory for blackbody radiators to infer things about stars.-- At a particular temperature the black body would emit theAt a particular temperature the black body would emit the

maximum amount of energy possible for that temperature.maximum amount of energy possible for that temperature.

-- Blackbody radiation does not depend on the type of objectBlackbody radiation does not depend on the type of object

emitting it. Entire spectrum of blackbody radiation depends onemitting it. Entire spectrum of blackbody radiation depends ononly one parameter, the temperature, T.only one parameter, the temperature, T.


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Thanks for your attentionThanks for your attention

Any suggestions or questions areAny suggestions or questions are

welcome.welcome.

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Blackbody in chemistry