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Homework Statement
I've been asked to calculate the energy of a photon gas in terms of the temperature. Assume non-interacting.
I'll spare the details, unless someone would like to see them, because the calculations can be found in most textbooks. Here's the problem:
When I do it using the partition function with Hamiltonian H = pc, I get
[tex]E = 3NkT[/tex]
where N is the number of photons, k is Boltzmann's constant, and T is temperature.
When I do it by finding the density of states, i get
[tex]E \propto VT^4[/tex]
Both answers are consistent with stuff I already know:
The first expression agrees with the equipartition theorem, but the second expression is the stefan-boltzmann law. So what the heck is going on here?
Homework Equations
The Attempt at a Solution
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