On the Fundamental Theoretical Foundations of Newton’s Law of Cooling

Abstract

Unlike the famous Stefan-Boltzmann Law (SBL), one can safely say that Newton (1700)’s Law of Cooling (NCL) is without any fundamental theoretical foundations and that – no importance has been placed to seek the most fundamental basis of this law. We herein seek these foundation. We demonstrate that NLC points to the existence of thermal states associated with every quantum mechanical energy state and these thermal density of state vary inversely as the energy of the given quantum state. From our findings, we show that NLC invariably points to the existence of thermal states associated with every possible quantum mechanical state and the density of states DTS of these thermal states varies inversely with the energy (E) of the associated quantum mechanical state, i.e. (DTS µ 1/E). Further, in agreement with Heisenberg (1927)’s quantum mechanical uncertainty principle, we find out that NCL invariably points to the existence of a minimum quantum mechanical momentum & energy state and as-well a minimum temperature. If such a state did not existence, the resulting physicswould require thermodynamic bodies to emit an infinite amount of thermal radiation. Thus, the existence of this minimum quantum mechanical momentum & energy state guards against this catastrophe.