Modified Law of Cooling: Continuum and Discreet Effect

We derive a modified law of cooling (and heating) which extends the standard Newton’s law of cooling/heating. A critical feature of our formulation is the inclusion of both continuum and discreet physical aspects of the system. One consequence of our mathematical equation ( a first-order, nonlinear differential equation) is that the temperature reaches its equilibrium value at a finite time. We also show that this equation has an exact solution which can be explicitly calculated in terms of elementary functions.