Lecture7

# Lecture7 - Chapter 6 Thermal Emission 1 Four concepts...

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1 1 Chapter 6 Thermal Emission 2 Four concepts regarding thermal emission: Planck Function Describes the maximum amount of radiation that an object can emit. Unique function of the radiation wavelength and object temperature. Any object that emits according to the Planck Function is a Blackbody . Wien’s Displacement Law The Planck Function wavelength of maximum emission is inversely proportional to the object’s temperature Stefan-Boltzmann Law The maximum amount of radiation, integrated over all wavelengths, that an object can emit is proportional to T 4 , where T is the object temperature (K). Kirchhoff’s law A good absorber is also a good emitter, for a given wavelength band, and assuming thermodynamic equilibrium. “Good” is relative to Planck function. Limiting cases : No absorption means no emission Perfect absorption means maximum emission: Planck function.

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2 3 Another B&Cism : “Whatever fame Snel might deserve for discovering (empirically) the law of refraction. ...he likely has the dubious honor of having his name misspelled more than that of any other scientist in history.” “Kirchhoff probably runs a close second.” “A resurrected Snel, upon seeing his name in hundreds of textbooks and thousands of papers, might exclaim, ‘What the l!’, whereas Kirchhoff’s reaction might be, ‘Where the h?’ ” There are, indeed, two “h”s in Kirchhoff ! 4 Blackbody : A body in thermodynamic equilibrium whose surface absorbs all radiation incident on it and emits radiation according to the Planck Function. Recall : Absorptivity (a, unitless) = Fraction of incident radiation that is absorbed. a λ = F λ ,a / F λ ,o a = 1 for a blackbody Empirical Blackbody Cavity Insulated cavity, isolated from its environment. Radiation in the cavity is in thermodynamic equilibrium with the cavity walls. Small pin-hole for radiation. http://www.astro.ucla.edu /~wright/CMB.html Absorption Small hole allows radiation in, but reflections prevent radiation from escaping – fraction of light reflected = (1-a) N for N reflections: Perfect Absorber Emission (Blackbody Radiation) Radiation leaving the cavity is negligible compared to total energy (does not upset equilibrium), but carries the spectral signature of the radiation trapped in the cavity. Distribution of trapped photon energies is determined by the distribution of energy states in the matter making up the cavity walls: Depends on Temperature!
3 5 Relative population of two energy states in a system in thermodynamic equilibrium is described by a Boltzmann Distribution : N i /N j = exp[-(E i -E j )/kT] N i = Population in upper state N j = Population in lower state E i = Energy of upper state E j = Energy of lower state k = Boltzmann Constant = 1.38×10 -23 J K -1 Thus: Populations of upper level states decrease exponentially as upper level energy increases (relative to a particular lower state).

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Lecture7 - Chapter 6 Thermal Emission 1 Four concepts...

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