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Wien's displacement law states that the wavelength distribution of radiated heat energy from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced, or moved over, on the graph. The average heat energy in each mode with frequency only depends on the combination ν/T. Restated in terms of the wavelength λ c/ν, the distributions at corresponding wavelengths are related, where corresponding wavelengths are at locations proportional to 1/T.

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  • Wien's displacement law
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  • Wien's displacement law states that the wavelength distribution of radiated heat energy from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced, or moved over, on the graph. The average heat energy in each mode with frequency only depends on the combination ν/T. Restated in terms of the wavelength λ c/ν, the distributions at corresponding wavelengths are related, where corresponding wavelengths are at locations proportional to 1/T.
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abstract
  • Wien's displacement law states that the wavelength distribution of radiated heat energy from a black body at any temperature has essentially the same shape as the distribution at any other temperature, except that each wavelength is displaced, or moved over, on the graph. The average heat energy in each mode with frequency only depends on the combination ν/T. Restated in terms of the wavelength λ c/ν, the distributions at corresponding wavelengths are related, where corresponding wavelengths are at locations proportional to 1/T. From this general law, it follows that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature when expressed as a function of wavelength (frequency gives a different peak as noted later), and this less powerful consequence is often also called Wien's displacement law in many textbooks. where λmax is the peak wavelength, T is the absolute temperature of the blackbody, and b is a constant of proportionality called Wien's displacement constant, equal to .8.9776851000000029.7768510000000087.7685100000001067.68510000000060246.85100000000966258.5100000001257295.100000001490116±.×10− (2002 CODATA recommended value) The two digits between the parentheses denote the uncertainty (the standard deviation at 68.27% confidence level) in the two least significant digits of the mantissa. For wavelengths near the visible spectrum, it is often more convenient to use the nanometer in place of the meter as the unit of measure. In this case, b .5.099999997764826±. . In the field of plasma physics, where temperatures are often conveniently measured in units of electron volts, the proportionality constant becomes b .7.10660999999987551.06609999999875530.66099999998755276.6099999998750726.099999998754356 .
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