How does Planck's radiation law relate to temperature? What conclusions can be drawn from it?
Planck's radiation law expresses the radiant energy density
#rho_(nu)(nu,T) = (2hnu^3)/(c^2) 1/(e^(hnu"/"k_BT) - 1)#
or in terms of the wavelength
#rho_(lambda)(lambda,T) = (2hc^2)/(lambda^5) 1/(e^(hc"/"lambdak_BT) - 1)#
For the frequency version, it is a cubic function of
For the wavelength version, since
It can be seen that at higher and higher temperature
A useful relation called Wien's law is derived from this, which is:
#lambda_(max) = (2900 mu"m"cdot"K")/T#,
#2900# #mu"m"cdot"K"#is Wien's displacement constant.
From this, if we knew the color of something we observe and approximate that as a blackbody, we could approximate the temperature.
For example, if we knew that the wavelength of the color radiated by the Beeteljeuse star was about