# How does Planck's radiation law relate to temperature? What conclusions can be drawn from it?

##### 1 Answer

Planck's radiation law expresses the **radiant energy density** *frequency*

#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# ,where

#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