The second law in relation to thermal radiative transfer - Jesudason, C.G. (2011)
Planck introduced the quantum hypothesis from his Blackbody radiation studies, where he and subsequent workers opined that classical mechanics and electrodynamical theories could not account for the phenomenon. Hence a statistical mechanics with an appropriate Second law entropy was invented and coupled to the First law to account for quantum effects. Here, as an academic exercise we derive the quantum of energy by considering two structures, that of the dipole oscillators on a 2-D surface and the scattering of radiation into the 3-D cavity. Previous derivations are briefly cited and reviewed where none followed this. approach. One prediction from this first order Brownian motion development is that a 2-D sheet of oscillators should emit radiation largely with energy density factor T I of the Kelvin temperature T, rather than that deduced as T4 from detailed balance. Preliminary measurements conducted here seemed to verify the the TI density. The first order theory also admits a possibility of nonlinear quanta and the consequences are explored briefly.It was noticed in passing during the experimentation that certain bodies suspended in a vacuum exhibited small persistent temperature differentials. A Second law statement is presented for such cases and consequences explored for processes that are not coupled by Newtonian momentum energy transfer mechanisms, such as for the radiation field as deduced by Planck. The different forms of heat transfer due to different laws (e.g. gravity waves and electromagnetic waves) are strictly separable and cannot be confused or forced to an equivalence. We generalize on the Zeroth law, the Kirchoff law and postulate an appropriate entropy form due to these generalizations.