Download Blackbody Radiation - Thermodynamics and Statistical Mechanics - Lecture Slides and more Slides Thermodynamics in PDF only on Docsity! Thermodynamics and Statistical Mechanics Blackbody Radiation Docsity.com Classical Energy Equipartition This image cannot currently be displayed. 321 321 321 321 321 lnlnln lnlnlnln εεεε βββ εεεε ++== ∂ ∂ − ∂ ∂ − ∂ ∂ −= ++= = ++= N U ZZZ N U ZZZZ ZZZZ VVV Docsity.com Quantum Harmonic Oscillator 1 1 exitations no. avg. exitation energy iewEinstein v-Bose 1 ere wh 1 energy excitation Average − ×= ×= = − == ωβ ωβ ωε ε βωε e kTeN U Docsity.com Energy of EM Waves in a Cavity •Calculate the number of standing wave states in the frequency range between ω and ω + dω. Then Bose-Einstein statistics is used to determine the number of photons in each state. With that information the energy can be calculated. Docsity.com Density of States (Lec 17) ωω π γωω ωω π γ d c Vdg c ddk c k dkkVdkkg 2 32 2 2 2 )( 2 )( = == = Docsity.com Photon Energy ( ) ( ) ( )1 8 1 Use, 1 3 33233 3 23 3 − = − = = − == εβεβ ωβ εεπ π εε εω π ωω e d chec ddu ec d V dUdu Docsity.com Graph Black Body Radiation 0 5E+17 1E+18 1.5E+18 2E+18 2.5E+18 3E+18 3.5E+18 4E+18 4.5E+18 0 1 2 3 4 5 Photon Energy (eV) En er gy D en si ty 5000 6000 7000 Docsity.com Total Energy Density ( ) ( ) 4-3-164 4 33 454 4 33 0 3 4 33 0 3 33 KmJ 1055.7 15 8 15 )(8 1 )(8 1 8 ⋅×== == − = − = − ∞∞ ∫∫ aaTu T ch kkT ch u e dxxkT che d ch u x πππ πεεπ εβ Docsity.com e
Relative sensitivity
@)
Human Eye
s
80
60
40
20
0
400 450 500 550 600 650 700
Wavelenguh (rim)
Peak at 555 nm
FIGURE 34-2 The relative sensitrrity of
the eye to electromagnetic waves at
different wavelengths. This portion of the
electromagnetic spectrum consists of
visible light.
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A Problem? •The graph of the energy density as a function of frequency, for a blackbody at a temperature of 5800 K, has a maximum at 1.41 eV. Photons of that energy have a wavelength of 879 nm, which is out of the visible spectrum, in the infrared. What is wrong? Docsity.com Solution •The energy density is plotted as a function of energy, while the eye’s sensitivity is plotted as a function of wavelength. If we plot the energy density as a function of wavelength, its peak does not occur at 879 nm. How can this be? Docsity.com Graph Black Body Radiation -500000 0 500000 1000000 1500000 2000000 2500000 3000000 3500000 0 2E-07 4E-07 6E-07 8E-07 1E-06 1E-06 Wavelength (m) En er gy D en si ty 5000 5800 7000 Docsity.com Agreement •The maximum of the graph for 5800 K, the temperature of the sun’s surface has a maximum at 500 nm, in reasonable agreement with the peak sensitivity of the human eye. Docsity.com Wien Displacement Law Km 1090.2 96.4 0 : find To .at occursPeak 3 max maxmax ⋅×== = − k hcT d dR λ λ λλ λ Docsity.com
