Planck

Planck's blackbody radiation law (Seinfeld & Pandis 2006 Ch. 4, Eq. 4.2) — the monochromatic emissive power F_B_λ of a blackbody at temperature T as a function of wavelength λ via Planck's constant h, the speed of light c, and the Boltzmann constant k_B: F_B_λ = 2π·c²·h·λ⁻⁵ / (exp(c·h/(k_B·λ·T)) - 1). The component is observed-only: one algebraic equation on one state variable (F_B_λ the monochromatic emissive power per unit wavelength in W/m³) driven by two input parameters (T temperature in K, λ wavelength in m) and four constants (h Planck's constant, c speed of light, k_B Boltzmann constant, π_val mathematical π as a Float64 value). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:73 (`BlackbodyRadiation` @component). The Planck function is the spectral energy density of thermal radiation from an opaque, non-reflective body in thermodynamic equilibrium — the foundational equation of quantum radiative transfer. Integrating F_B_λ over all wavelengths gives the Stefan-Boltzmann total flux σT⁴ (see stefan_boltzmann.esm); the wavelength where F_B_λ peaks is λ_max = b/T from Wien's displacement law (see wien.esm). At the default T=5800 K (Sun's effective surface temperature) and λ=500 nm (visible green, the canonical solar-peak wavelength), F_B_λ ≈ 8.46e13 W/m³ — the peak intensity that anchors the Sun's irradiance at Earth's distance and the solar-driven photochemistry of the atmosphere. At T=300 K (Earth surface) and λ=10 μm (thermal-IR), F_B_λ ≈ 3.12e7 W/m³ — the canonical longwave outgoing radiation peak that drives the planetary energy balance.

Photon energy equation (Seinfeld & Pandis 2006 Ch. 4, Eq. 4.1) — the energy Δε and frequency ν of a photon as a function of wavelength λ via Planck's constant h and the speed of light c: ν = c/λ and Δε = hν, equivalently the chained form Δε = hc/λ. The component is observed-only: two algebraic equations on two state variables (Δε the photon energy in J and ν the frequency in Hz) driven by one input parameter (λ the wavelength) and two constants (h Planck's constant and c the speed of light). No time derivatives, no PDE, no coupling. Migrated from GasChem.jl@8c12c048 src/radiation_fundamentals.jl:25 (`PhotonEnergy` @component). The photon energy equation is the foundational quantum-radiative bridge that maps continuous-wave radiation to the discrete photon picture: paired with the Planck spectral distribution (BlackbodyRadiation), Stefan-Boltzmann total flux (StefanBoltzmann), and Wien peak displacement (WienDisplacement), it lets a radiative-transfer model convert spectral irradiance to photon fluxes and back — the quantity needed for actinic-flux / photolysis-rate calculations that drive atmospheric photochemistry (e.g., O2 + hν → 2 O at ~242 nm and O3 + hν → O + O2 at ~310 nm, the two Chapman-cycle photolysis channels). The defaults (λ = 500 nm) give ν ≈ 600 THz and Δε ≈ 3.97e-19 J ≈ 2.48 eV — visible green light, the canonical solar-peak wavelength matching Wien's law applied to T_sun ≈ 5800 K.