Question

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 1

Answer

Applying Wein's displacement

$\lamda_{max}\ T = 2898 \mu_mK$

1) for sun T = 5800 K

      $\lambda_{max} = \dfrac{2898}{5800}$

      $\lambda_{max} = 0.5 \mu_m$

2) for tungsten T = 2500 K

      $\lambda_{max} = \dfrac{2898}{2500}$

      $\lambda_{max} = 1.16 \mu_m$

3) for heated metal T = 1500 K

      $\lambda_{max} = \dfrac{2898}{1500}$

      $\lambda_{max} = 1.93 \mu_m$

4) for human skin T = 305 K

      $\lambda_{max} = \dfrac{2898}{305}$

      $\lambda_{max} = 9.50 \mu_m$

5)  for cryogenically cooled metal T = 60 K

      $\lambda_{max} = \dfrac{2898}{60}$

      $\lambda_{max} = 48.3 \mu_m$

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