- #1
- 24,775
- 792
Benzun started a thread with this question:
I have replied to that question, and want to extend the question (without diverting Benzun's original thead).
the related question is, if you have a hollow box or cavity at some temperature T, then how many photons per cubic meter are in it?
there is a definite number of photons (per unit volume) associated with each temperature.
please confirm this if you can, IIRC the ENERGY DENSITY in an empty space at temp T is equal to
[tex]\frac{\pi^2}{15} \frac{k^4 T^4}{\hbar^3 c^3}[/tex]
notice that this is related to but different from the Stef-Boltz. radiation law brightness, which is energy per unit time per unit area:
[tex]\frac{\pi^2}{60} \frac{k^4 T^4}{\hbar^3 c^2}[/tex]
Now to find the NUMBER OF PHOTONS (per unit volume) all we do is
divide the energy density by the average energy per photon at temp T,
which IIRC is equal to 2.701 kT. As i recall this is a fact about thermal radiation.
If this is right then the number of photons per cubic meter that is in the room with you is given by
[tex]\frac{1}{2.701} \frac{\pi^2}{15} \frac{k^3 T^3}{\hbar^3 c^3}[/tex]
where T is the absolute temperature which, I am hoping, is a comfortable T = 293 kelvin or thereabouts.
benzun_1999 said:hi,
just out of curiosity. What is the maximum number of photons that can be accommodated in 1 cubic meter?
-benzun
I have replied to that question, and want to extend the question (without diverting Benzun's original thead).
the related question is, if you have a hollow box or cavity at some temperature T, then how many photons per cubic meter are in it?
there is a definite number of photons (per unit volume) associated with each temperature.
please confirm this if you can, IIRC the ENERGY DENSITY in an empty space at temp T is equal to
[tex]\frac{\pi^2}{15} \frac{k^4 T^4}{\hbar^3 c^3}[/tex]
notice that this is related to but different from the Stef-Boltz. radiation law brightness, which is energy per unit time per unit area:
[tex]\frac{\pi^2}{60} \frac{k^4 T^4}{\hbar^3 c^2}[/tex]
Now to find the NUMBER OF PHOTONS (per unit volume) all we do is
divide the energy density by the average energy per photon at temp T,
which IIRC is equal to 2.701 kT. As i recall this is a fact about thermal radiation.
If this is right then the number of photons per cubic meter that is in the room with you is given by
[tex]\frac{1}{2.701} \frac{\pi^2}{15} \frac{k^3 T^3}{\hbar^3 c^3}[/tex]
where T is the absolute temperature which, I am hoping, is a comfortable T = 293 kelvin or thereabouts.