Step 1: Start with the assumption that the energy density of blackbody radiation is given by Planck's law, which is expressed as:
\[ u(\nu, T) = \frac{8\pi h\nu^3}{c^3} \frac{1}{e^{\frac{h\nu}{kT}} - 1} \]
where:
- \( u(\nu, T) \) is the energy density of
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