(adsbygoogle = window.adsbygoogle || []).push({}); QM-- Stefan's constant vs radiation constant

1. The problem statement, all variables and given/known data

(a) Using Planck's formula for the energy density ρ(λ,T), prove that the total energy density is given by ρ(T)=aT^{4}where a = 8π^{5}k^{4}/(15h^{3}c^{3}). (b) Does this agree with the Stefan-Boltzmann law for the total emissive power?

3. The attempt at a solution

I had no problem with the proof in part (a), starting with the equation

ρ(T)dλ = 8πhc/λ^{5}* dλ/(e^{hc/λkT}-1) and integrating over λ 0→∞.

However, I am confused by the question in part (b). The answers are obviously related. I know that a, the radiation constant, is equal to 4σ/c, and I know you can derive the precise Stefan-Boltzmann equation from Planck's formula. I also suspect the professor is looking for an answer other than "no" or "sort-of." Does anyone know where the difference between that derivation and the one I completed and the one that yields P = σT^{4}is? What is the utility difference between the radiation constant and Stefan's constant?

Thanks guys!

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# QM- Stefan's constant vs radiation constant

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