Can Newton's Law of Cooling be used to describe heating?

1 Answer
Apr 15, 2015

Yes. If A is the ambient temperature of the room and T0 is the initial temperature of the object in the room, Newton's Law of Cooling/Heating predicts the temperature T of the object will be given as a function of time by T=A+(T0A)ekt, where k<0. If T0>A, this model predicts cooling (a decreasing function) and if T0<A, this model predicts heating (an increasing function).

In terms of calculus-related ideas, this equation can be rewritten as TA=(T0A)ekt and can be interpreted as saying that the function TA undergoes exponential decay (a constant relative rate of decay) to zero as time t increases (from above if T0>A and from below if T0<A).