A tungsten filament is heated to 2700 K. At what wavelength is the maximum amount of radiation emitted? What fraction of the total energy is in the visible range (0.4 to 0.75 ?m)? Assume that the filament radiates as a gray body.
GIVEN
• Heated tungsten filament
• Filament temperature (Tf) = 2700 K
FIND
(a) Wavelength at which the maximum radiation is emitted (?max)
(b) Percentage of radiation in the visible ranger (0.4 to 0.75 ?m)
ASSUMPTIONS
• The filament radiates as a gray body
SKETCH
(a) Since the tungsten is a gray body, the maximum emission occurs at the same wavelength as a black body.
(b) Gray body radiation is proportional to the black body radiation at all wavelengths. Therefore, the percentage of the gray body radiation in the visible spectrum is the same as the percentage of black body radiation in the visible spectrum.
For the limits of the visible range
The percent within the visible spectrum is
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