Note on Classical Equipartition Derivation:
This calculation is performed purely according to the Rayleigh–Jeans Law (1900–1905). It relies strictly on classical electrodynamics (cavity mode density $\propto \lambda^{-4}$) and the classical equipartition theorem of energy ($\bar{\epsilon} = k_B T$). Comparing it against the real experimental blackbody observation demonstrates the classical failure known as the Ultraviolet Catastrophe.
Rayleigh–Jeans Spectral Distribution Equation:
$$E_\lambda(\lambda, T) = \frac{2\pi c \, k_B T}{\lambda^4}$$
(Corresponding Energy Density inside cavity: $\rho_\lambda = \frac{8\pi k_B T}{\lambda^4}$)
Effective Solar Temp (T)5778 K
Boltzmann Constant (k_B)1.38065 × 10⁻²³ J/K
Speed of Light (c)2.99792 × 10⁸ m/s
Classical Prediction at λ → 0E_λ → ∞ (UV Catastrophe)
Quick test:
Quantity / Parameter
Calculated Value
Spectral Regime
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Denominator Factor (λ4)
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Average Thermal Energy per Mode ($\bar{\epsilon} = k_B T$)