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Radiation Laws

Radiation Laws. Planck’s Law (expressed by the Planck Function):. Planck’s Law (cont’d). The Planck Function gives radiative flux as a function of wavelength and temperature for "blackbody" radiation.

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Radiation Laws

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  1. Radiation Laws

  2. Planck’s Law (expressed by the Planck Function):

  3. Planck’s Law (cont’d) • The Planck Function gives radiative flux as a function of wavelength and temperature for "blackbody" radiation. • Shows how much radiation at a particular wavelength per unit surface area  would be emitted by an object  based on its temperature, assuming it is emitting the maximum possible radiation, i.e., it is a "perfect" emitter. • Planck Function Applet • Planck Function is usually plotted by picking a temperature for an emitting object, then plugging in different wavelength values and shows radiation emission on the y-axis as a function of wavelength on the x-axis:

  4. Solar Spectrum vs. Planck Function

  5. Emissivity • Actual objects are not perfect emitters, so actual emission at a given wavelength typically is less than the blackbody value:

  6. Stefan_Boltzmann Law • Obtained by integrating the Planck Function with respect to wavelength across the entire spectrum. • E* has units of W m-2.  It is the area under the curve of the Planck Function. • It says that the total radiant energy emitted by an object across all wavelengths is proportional to the fourth power of temperature of the object. The warmer the object, the greater is its radiant energy output.

  7. Wien’s Law • Obtained by differentiating the Planck Function with respect to wavelength, and setting it equal to zero. • The wavelength of maximum emission is found where the slope of the Planck Function curve is equal to zero, i.e., the peak of the curve. • Wien's Law says that the wavelength of maximum emission by an object is inversely proportional to the temperature of the object. The warmer the object, the shorter will be its wavelength of maximum emission.

  8. Kirchoff’s Law • For an object in local thermodynamic equilibrium, radiation absorptivity equals radiation emissivity at a particular wavelength. • It says that efficient absorbers are efficient emitters at a particular wavelength and poor absorbers are poor emitters at a particular wavelength. • Radiation in the wavelength band around 6.7 micrometers (part of the IR spectrum) is strongly absorbed by water vapor.  This means that water vapor also strongly emits radiation in this part of the spectrum.  This fact is exploited by the 6.7 micrometer water vapor channels on weather satellites--they measure radiation that has been emitted by middle and upper tropospheric water vapor.

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