Estimate the wavelength corresponding to maximum emission from each of the following surfaces: the sun, a tungsten filament at 2500 K, a heated metal at 1500 K, human skin at 305 K, and a cryogenically cooled metal surface at 60 K. Estimate the fraction of the solar emission that is in the following spectral regions: the ultraviolet, the visible, and the infrared.

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wagonbelleville wagonbelleville · Answer 1 · 2019-11-06T14:16:34+01:00

Answer

Applying Wein's displacement

[tex]\lamda_{max}\ T = 2898 \mu_mK[/tex]

1) for sun T = 5800 K

[tex]\lambda_{max} = \dfrac{2898}{5800}[/tex]

[tex]\lambda_{max} = 0.5 \mu_m[/tex]

2) for tungsten T = 2500 K

[tex]\lambda_{max} = \dfrac{2898}{2500}[/tex]

[tex]\lambda_{max} = 1.16 \mu_m[/tex]

3) for heated metal T = 1500 K

[tex]\lambda_{max} = \dfrac{2898}{1500}[/tex]

[tex]\lambda_{max} = 1.93 \mu_m[/tex]

4) for human skin T = 305 K

[tex]\lambda_{max} = \dfrac{2898}{305}[/tex]

[tex]\lambda_{max} = 9.50 \mu_m[/tex]

5) for cryogenically cooled metal T = 60 K

[tex]\lambda_{max} = \dfrac{2898}{60}[/tex]

[tex]\lambda_{max} = 48.3 \mu_m[/tex]

range of different spectrum

UV ----0.01-0.4

visible----0.4-0.7

infrared------0.7-100

for sun T = 5800

λ 0.01 0.4 0.7 100

λT 58 2320 4060 5.8 x 10⁵

F 0 0.125 0.491 1

fractions

for UV = 0.125

for visible = 0.441-0.125 = 0.366

for infrared = 1 -0.491 = 0.509