Universality and Kirchhoff's Law of Thermal Emission

Kirchhoff's law is derived in `The Theory of Heat Radiation', by Max Planck, but without properly addressing reflection. This is rectified in part by modifying his equation in \S 25 to $dt\cdot \nu\cdot 8\pi\int_0^\infty\left({\bf\epsilon}_\nu+\rho_\nu{\bf K}_\nu\right)d\nu$, and \S 26 (i.e. Eq. 25) to $dt\cdot \nu\cdot 8\pi\int_0^\infty\left(\alpha_\nu+\rho_\nu\right){\bf K}_\nu d\nu$, respectively. When these are equated, solutions are either $\bf K_\nu=\epsilon_\nu/\alpha_\nu$ (Eq. 27), or $\epsilon_\nu={\bf K}_\nu-\rho_\nu {\bf K}_\nu$. The former, which leads to Kirchhoff's law, is undefined when $\alpha_\nu=0$. Planck tries to prove Kirchhoff's law by placing two separate media in contact. Each medium is characterized by its own emission, for which Planck uses the notation ($\epsilon_\nu$), absorptivity ($\alpha_\nu$), and reflectivity ($\rho_\nu$). The critical step in the derivation involves Planck's need to set $\left(1-\rho_\nu\right)$=$\left(1-\rho_\nu'\right)$, which he astonishingly achieves by initially deducing that $\rho_\nu$=$\rho_\nu'$=0 and then, in Eq. 40, setting $\rho_\nu$=$\rho_\nu'$ (see \S 37). This is a contradiction of known physics for frequency dependent reflectivities in differing materials. Kirchhoff's law and universality are invalid concepts.