(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(a) Find the average energy per photon for photons in thermal equilibrium with a cavity at temperature T.

(b) Calculate the average photon energy in electron volts at T = 6000K.

2. Relevant equations

[tex] u(E)dE = \frac{8 \pi}{(hc)^3} \frac{E^3 dE}{e^{E/k_B T} - 1}[/tex]

3. The attempt at a solution

Integrate both sides of the equation.

[tex] \frac{E}{V} = \int_0^\infty u(E)dE = \int_0^\infty \frac{8 \pi}{(hc)^3} \frac{E^3 dE}{e^{E/k_B T} - 1}[/tex]

Use the fact that

[tex]\frac{z^3 dz}{e^z - 1} = \frac{\pi^4}{15}[/tex]

and that the equation can be rewritten as

[tex] \frac{8 \pi (k_{B}T)^3}{(hc)^3} \int_0^\infty \frac{ (\frac{E}{k_B T})^3 dE}{e^{E/k_B}-1} [/tex]

which finally gives

[tex] \frac{E}{V} = \frac{8 \pi (k_{B}T)^3}{(hc)^3} \frac{\pi^4}{15}[/tex]

Did I do this right?

Part b will be easy, just plug in the value for T if (a) is right.

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# Bose-Einstein Statistics

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