chapter 1 blackbody radiation

BlackbodyBlackbody

radiationradiation

ChaPtER 1 :

SCOPE OF STUDYSCOPE OF STUDY

SUB TOPICS

Stefan’s Law, energy

spectrum

Wien’s displacement

law

Concept of black body

introductionintroduction

The black body notion is important in studying thermal radiation and

electromagnetic radiation energy transfer in all wavelength bands.

Black body as an ideal radiation absorber and it is used as a standard

for comparison with the radiation of real physical bodies.

This notion and its characteristics are sometimes are used in

describing and studying artificial, quasi deterministic electromagnetic

radiation (in radio and TV- broadcasting and communication).

Concept of black bodyConcept of black body

Black BodyBlack Body

An ideal body which absorbs all the electromagnetic

radiation that strikes it so that all incident radiation is

completely absorbed.


Why black body??

Because those bodies that absorb incident visible light well seem

black to the human eye.

Example: We can hardly characterize our sun which is indeed

almost a black body within a very wide band of electromagnetic

radiation wavelength as a black physical object in optics. It is namely

bright-white sunlight which represents the equilibrium black body

radiation.


Application :

Optical band (surfaces approach an ideal black body in their

ability to absorb radiation) such as soot, silicon carbide, platinum and

golden niellos.

Earth surfaces (water surfaces, ice, land) absorb infrared radiation

well and in thermal IR band, these physical objects are ideal black

bodies.


Black body radiation /

Cavity radiation

Black body radiation /

Cavity radiation

The electromagnetic radiation that would be

radiated from an ideal black body


Where are the black body radiation comes from??

Sources of black body radiation :

Cosmic microwave background (CMB) of the universe –

fluctuation electromagnetic radiation that fills the part of the universe.

the radiation possesses nearly isotropic spatial-angular field with an

intensity that can be characterized by the radio brightness temperature of

2.73K.

to determine accuracy, direction and velocity of motion of the

solar system.

as a re-reflected radiation to investigate the emissive characteristics

of terrestrial surfaces.


The Sun

the presence of thermal black body radiation with a brightness

temperature of 5800K at the Sun.

along with a black body radiation, there exist powerful,

non-stationary quasi-noise radiation (flares, storms).

The Earth

possesses radiation close to black body radiation with a

thermodynamic temperature of 287K.


Figure : The characteristic graph of the thermal radiation emitted by

a hot object

Figure : The characteristic graph of the thermal radiation emitted by

a hot object

Blackbody radiation is emitted as a broad spectrum of wavelengths

Energy spectrumEnergy spectrum

EM Radiation : A kind of radiation including visible light, radio

waves, gamma rays, and X-rays, in which electric and magnetic fields

vary simultaneously.

Energy spectrum based on the EM spectrum.

EM Spectrum : The distribution of electromagnetic radiation

according to energy (or equivalently, by virtue of the relations in the

previous section, according to frequency or wavelength).

Energy spectrumEnergy spectrum

Energy spectrumEnergy spectrumSpectrum of Electromagnetic Radiation

Region Wavelength(Angstroms)

Wavelength(centimeters)

Frequency(Hz)

Energy(eV)

Radio > 109 > 10 < 3 x 109 < 10-5

Microwave 109 - 106 10 - 0.01 3 x 109 - 3 x 1012 10-5 - 0.01

Infrared 106 - 7000 0.01 - 7 x 10-5 3 x 1012 - 4.3 x 1014 0.01 - 2

Visible 7000 - 4000 7 x 10-5 - 4 x 10-5 4.3 x 1014 - 7.5 x 1014 2 - 3

Ultraviolet 4000 - 10 4 x 10-5 - 10-7 7.5 x 1014 - 3 x 1017 3 - 103

X-Rays 10 - 0.1 10-7 - 10-9 3 x 1017 - 3 x 1019 103 - 105

Gamma Rays < 0.1 < 10-9 > 3 x 1019 > 105

black body RADIATION LAWSblack body RADIATION LAWS

Laws

Stefan’s Law

Wein’s Displacement

Law

Stefan’s lawStefan’s law

Stefan’s Law or Stefan’s Boltzmann’s LawStefan’s Law or Stefan’s Boltzmann’s Law

The energy radiated by a blackbody radiator per second

per unit area is proportional to the fourth power of

the absolute temperature.


Formula

where P = Energy/ time = Power

A = Area

T = Temperature

σ = Stefan-Boltzmann constant


Stefan’s Law (1879, 1884)

Josef Stefan deduced the rule in 1879 and Ludwig Boltzmann

provided a formal derivation in 1884.

Classical physics

Explain the growth in the height of the curve as the

temperature increase.

Energy emitted increase rapidly with an increase in

temperature which is proportional to the temperature raised to the

fourth power.

Stefan’s lawStefan’s law For hot objects other than ideal radiators, the law is expressed in the form:

where e is the emissivity of the object (e = 1 for ideal radiator).

e = characteristic of the surface of the radiating material ( 0 < e < 1)

black surface such as charcoal, e close to 1, shinny metal surfaces have e

close to 0 (emit less radiation and absorb little radiation that falls upon them).

e depends on the temperature of material.

Black and very dark object is good emitter and good absorber.

Example : The light-colored clothing is preferable to dark clothing on a hot

day.


If the hot object is radiating energy to its cooler surroundings at

temperature Tc, the net radiation loss rate takes the form

The above equation is valid for T = T1 = temperature of the surface area of

the object and Tc = T2 = Temperature of surrounding

wein’s displacement lawwein’s displacement law

The wavelength distribution peaks at a

value that is inversely proportional to the

temperature.

The wavelength distribution peaks at a

value that is inversely proportional to the

temperature.

Wein’s Displacement Law,

1893

Wein’s Displacement Law,

1893


Formula Formula

Unit constant, c : meter per Kelvin (m/K)

The ratio of the maximum wavelengths for two temperatures, T and T',

λmax = c = 2.898x10-3

T

λmax = c = 2.898x10-3

TT


Wien's Law tells us that objects of different temperature emit spectra

that peak at different wavelengths.

Hotter objects emit most of their radiation at shorter wavelengths,

hence they will appear to be bluer .

Cooler objects emit most of their radiation at longer wavelengths,

hence they will appear to be redder.

Furthermore, at any wavelength, a hotter object radiates more (is

more luminous) than a cooler one.


Temperature , T ( ), Radiated energy, E ( ), Wavelength, λ ( )


Black body thermal emission intensity as a function of wavelength

for various (absolute) temperatures.


Examples:

•Light from the Sun and Moon. The surface temperature (or more correctly, the

effective temperature) of the Sun is 5778 K. Using Wien's law, this temperature

corresponds to a peak emission at a wavelength of 2.90 × 106 nm-K / 5778 K = 502

nm = about 5000 Å. This wavelength is (not incidentally) fairly in the middle of the

most sensitive part of land animal visual spectrum acuity.

•Light from incandescent bulbs and fires. A lightbulb has a glowing wire with a

somewhat lower temperature, resulting in yellow light, and something that is "red

hot" is again a little less hot. It is easy to calculate that a wood fire at 1500 K puts

out peak radiation at 2.90 × 106 nm-K / 1500 K = 1900 nm = 19,000 Å. This is far

more energy in the infrared than in the visible band, which ends about 7500 Å.

wein’s displacement lawwein’s displacement law•Radiation from mammals and the living human body. Mammals at roughly 300 K

emit peak radiation at 2900 μm-K / 300 K ~ 10 μm, in the far infrared. This is,

therefore, the range of infrared wavelengths that pit viper snakes and passive IR

cameras must sense.

•The wavelength of radiation from the Big Bang. A typical application of Wien's

law would also be to the blackbody radiation resulting from the Big Bang.

Remembering that Wien's displacement constant is about 3 mm-K, and the

temperature of the Big Bang background radiation is about 3 K (actually 2.7 K), it is

apparent that the microwave background of the sky peaks in power at 2.9 mm-K / 2.7

K = just over 1 mm wavelength in the microwave spectrum. This provides a

convenient rule of thumb for why microwave equipment must be sensitive on both

sides of this frequency band, in order to do effective research on the cosmic

microwave background.

~ ~The end~ ~~ ~The end~ ~

“If you really want to do

something, you will find a

way. If you don't, you will

find an excuse.“

-Jim Rohn-