This tutorial explores some of the radiation laws: Planck's law, Sefan-Boltzmann-law, Wien's law.

Some constants ...

Planck's law for power radiated normally from a unit area (energy flux density) of a blackbody radiator at temperature T into a unit solid angle within a wavelength band of unit width centered at wavelength @@0@@ is given by

@@1@@

where k = 1.381 @@2@@ 10@@3@@ is the vacuum speed of light.

T in K, wl in @@4@@m

Same, but within a frequency band of unit width centered at frequency f. Units: W/(m@@0@@·sr·Hz)

T in K, f in Hz

The total power emitted per unit area (i.e., radiant flux density) at the surface of a blackbody at a temperature T (i.e., by integrating Planck's function over the whole spectrum and over the solid angles corresponding to a hemisphere above the surface. Units: Wm@@0@@ (T in K)

This radiant flux density is reduced when moving from the Sun's surface to the Earth. The ratio (@@0@@ then leads to the solar constant:

plotting ...

and with logarithmic axes:

...and everything normalized to 1: