b) Derive Wien's law of energy distribution.

Another Explanation (5): Wien's Law derivation requires advanced physics (quantum mechanics and statistical thermodynamics) beyond a concise explanation. A simplified qualitative description focuses on the relationship between the peak wavelength (λ_max) of blackbody radiation and its temperature (T): As temperature increases, the peak wavelength shifts towards shorter wavelengths (higher frequencies). The precise mathematical derivation involves Planck's radiation law and finding the maximum of the spectral radiance function, resulting in: λ_maxT = b where 'b' is Wien's displacement constant (approximately 2.898 × 10^-3 m·K). This equation is Wien's displacement law, not a full energy distribution. A complete derivation of the Planck's law, which *does* describe the full energy distribution, is extensive and requires significant mathematical steps.