Blackbody

# Blackbody - Department of Physics, Indiana University (HOM...

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BB - 1 Department of Physics, Indiana University (HOM 2/1/00) [Rev. MRS: 10/4/11] Black-Body Radiation Goal: Test Planck’s law and the Stephan-Boltzmann law Equipment: Tungsten lamp with power supply, Ocean Optics spectrometer, pyrometer 1. Introduction The Planck distribution law states that a “black” body at temperature T emits radiation with a spectral distribution f( λ ) given by ) , ( 1 8 ) ( 5 T e c h f T k c h λ ε π = . (1) where λ is the wavelength, T the temperature in K, h =6.626•10 -34 Js is Planck’s constant, k =1.381•10 –23 J/K is the Boltzmann constant, c =2.998•10 8 m/s, and ε ( λ ,T) <1, called the emissivity, is a correction function that takes into account that ideal black bodies (for which ε =1) do not exist in reality. For visible light, the exponential term in eq.1 is much larger that 1, so we can replace the denominator of eq.1 by exp(–hc/ λ kT). We will use a commercial spectrometer and a computer to measure f( λ ). The intensity I measured by the spectrometer is given by I ( , T ) = b ( ) ( , T ) 8 hc 5 e hc kT , (2) where b ( λ ) is a function, ideally unity, that accounts for absorption of light between the filament and spectrometer. When one integrates the Planck distribution to get the total power radiated, P R , one obtains the law of Stephan-Boltzmann, 4 T A P eff R = σ , (3) where σ =5.64•-8 J/m 2 K 4 s is the Stephan-Boltzmann constant, A is the surface area, and ε eff is the weighted average of the wavelength dependent emissivity, ε ( λ ,T) . TASK 1:

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Blackbody - Department of Physics, Indiana University (HOM...

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