### On the Theoretical Foundations of Newton's Law of Cooling

#### Abstract

Unlike the Stefan-Boltzmann Law (SBL), Newton (1700)'s Law of Cooling (NLC) lacks theoretical foundations. 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 ndings, we show that NLC invariably points to the existence of

thermal states associated with every possible quantum mechanical state a d the density of states *D _{TS}* of these thermal states varies inversely with the energy (E) of the associated quantum mechanical state, i.e. (

*D*∝ 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 physics would 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.

_{TS}