Step 1:
Start with Planck's law for black body radiation, which gives the energy density \( u(\lambda, T) \) as a function of wavelength \( \lambda \) and temperature \( T \):
\[
u(\lambda, T) = \frac{8\pi hc}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda kT}} - 1}
\]
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