After some simplifications, the internal energy density perunit frequency is given by
U(ω) =
8 π ̄h
c^3(
ω
2 π) 3
1
e ̄hω/(kBT)− 1(20.46)
Expressing the formula alternatively in terms of frequencyν=ω/(2π), and “Planck’s constant”
h= 2π ̄h, we have
U(ω) =W(ν) =
4 hν^3
c^31
ehν/(kBT)− 1(20.47)
which is the original Planck black body radiation formula.