1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What do the terms mean in the energy density for photon gas ##u(\omega) d\omega ## ?

  1. May 12, 2012 #1
    1. The problem statement, all variables and given/known data

    ##u(\omega) d\omega \propto \frac{(\hbar \omega) (\omega^2)}{e^{\hbar \omega \over k_B T}-1} d \omega ##


    2. Relevant equations



    3. The attempt at a solution

    ##\hbar \omega ## is the energy of a photon

    ##\frac{1}{e^{\hbar \omega \over k_B T}-1} ##and this is the density of states for bosons. So you have the energy of the photon and the density of states. Why is there an extra ##\omega^2## term? I can't work out what it represents. I thought that it could be a consequence of the ##d\omega## but I am unsure.
     
  2. jcsd
  3. May 13, 2012 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Re: What do the terms mean in the energy density for photon gas ##u(\omega) d\omega #

    If I recall correctly (which I may very well not be doing), ##\omega^2## comes from the phase space factor. Essentially, you need to account for all the different direction the photon can be moving.
     
  4. May 17, 2012 #3
    Re: What do the terms mean in the energy density for photon gas ##u(\omega) d\omega #

    the phase space factor is proportional to
    d^3(k)=k^2dkd(cosθ)dβ,where k^2 can be written as ω^2/c^2.
     
  5. May 17, 2012 #4
    Re: What do the terms mean in the energy density for photon gas ##u(\omega) d\omega #

    The term [itex]\left[\exp(\hbar \omega/k_{B} T) - 1\right]^{-1}[/itex] is the average number of photons with energy [itex]\hbar \omega[/itex] according to the Bose-Einstein distribution. The density of states is proportional to [itex]\omega^2[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What do the terms mean in the energy density for photon gas ##u(\omega) d\omega ## ?
Loading...