We present a comprehensive derivation of Planck's radiation law that explicitly derives Kirchhoff's law of thermal emission from thermodynamic equilibrium principles rather than postulating it [Boyer, 2018], [Gómez-Santos, 2019], [Marlan, 1993]. Our approach rigorously develops the statistical mechanics of electromagnetic field modes, derives the density of states from electromagnetic boundary conditions, and applies the canonical ensemble formalism with proper treatment of photon statistics [Pathria & Beale, 2011]. We demonstrate that Kirchhoff's law (ε(ν) = a(ν)) emerges as a necessary consequence of detailed balance in thermal equilibrium, while the Planck distribution follows from maximizing entropy in the canonical ensemble for a photon gas [Landau & Lifshitz, 1980]. The derivation explicitly addresses the role of energy quantization and connects to experimental observations of blackbody spectra [Fixsen, 2009]. This unified approach provides pedagogical clarity and demonstrates the deep connection between statistical mechanics, thermodynamics, and electromagnetic field theory [Reif, 1965]. This work constitutes a significant conceptual improvement over traditional approaches, including Planck's original derivation, by providing a first-principles derivation for Kirchhoff's law, a relationship previously accepted largely as an empirical postulate.