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Blackbody Radiation: Wien and Stefan-Boltzmann Laws

The first edition of this book was previously published by Pearson Education, Inc. It was The second edition, version 10 is copyright ©2020 by Howard DeVoe. This work is licensed under a Creative Commons Attribution 40 International License: https://creativecommons org/licenses/by/4 0/ The book was typeset using the LATEX typesetting system and the memoir class. Most of the figures were produced with PSTricks, a related software program. The fonts are Adobe Times, MathTime, and Computer Modern Typewriter. A Solutions Manual is available at the Web site linked below. I thank the Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland for hosting the Web site for this book:

Figures (10)

Black-body radiation as a function of wavelength for various temperatures. Each temperature curve peaks at a different wavelength and Wien's law describes the shift of that peak.
There are a variety of ways of associating a characteristic wavelength or frequency with the Planck black-body emission spectrum. Each of these metrics scales similarly with temperature, a principle referred to as Wien's displacement law. For different versions of the law, the proportionality constant differs—so, for a given temperature, there is no unique characteristic wavelength or frequency.
Planck blackbody spectrum parameterized by wavelength, fractional bandwidth (log wavelength or log frequency), and frequency, for a temperature of 6000 K
As the temperature of a black body decreases, the emitted thermal radiation decreases in intensity and its maximum moves to longer wavelengths. Shown for comparison is the classical Rayleigh–Jeans law and its ultraviolet catastrophe.
Color of a black body from 800 K to 12200 K. This range of colors approximates the range of colors of stars of different temperatures, as seen or photographed in the night sky.
The color of a star is determined by its temperature, according to Wien's law. In the constellation of Orion, one can compare Betelgeuse (T ≈ 3800 K, upper left), Rigel (T = 12100 K, bottom right), Bellatrix (T = 22000 K, upper right), and Mintaka (T = 31800 K, rightmost of the 3 "belt stars" in the middle).
The color (chromaticity) of black-body radiation scales inversely with the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.
The temperature of a Pāhoehoe lava flow can be estimated by observing its color. The result agrees well with other measurements of temperatures of lava flows at about 1,000 to 1,200 °C (1,830 to 2,190 °F).
Nine-year WMAP image (2012) of the cosmic microwave background radiation across the universe.[22][23]
Photo of person in the visible spectrum

Key Points

  • A temperature at which the initial slope is zero is called the Boyle temperature, which for CO2 is 710 K.
  • The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan–Boltzmann law.
  • The albedo and emissivity of the Moon are about 0.1054 and 0.95 respectively, yielding an estimated temperature of about 1.36 °C.
  • For a black body (a perfect absorber) there is no reflected radiation, and so the spectral radiance is entirely due to emission.

Terms

Tap a term for a plain-language explanation.

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