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.

Answer

Applying Wein's displacement

1) for sun T = 5800 K

2) for tungsten T = 2500 K

3) for heated metal T = 1500 K

4) for human skin T = 305 K

5)  for cryogenically cooled metal T = 60 K

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