130_notes.dvi

Now suppose thewalls of the cavity are blackso that they emit and absorb photons at any
energy. Then the result for the number of photons above is true for all the radiation modes of the
cavity. Theenergy in the frequency interval(ω,ω+dω)per unit volume can be calculated
by multiplying the number of photons by the energy per photon timesthe number of modes in that
frequency interval and dividing by the volume of the cavity.

U(ω)dω=

̄hω

e ̄hω/kT− 1

2

(

L

2 π

) 3

4 πk^2 dk

1

L^3

U(ω) = 8π

̄hω

e ̄hω/kT− 1

(

1

2 π

) 3

k^2

dk

dω

U(ω) =

8 π ̄h

c^3

(ω

2 π

) (^31)
e ̄hω/kT− 1
U(ν) =U(ω)
dω
dν

=

8 π

c^3

hν^3

e ̄hω/kT− 1

This was the formula Plank used to start the revolution.