Question

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

Answer 1

Yes. If `A` is the ambient temperature of the room and `T_{0}` 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+(T_{0}-A)e^{-kt}`, where `-k<0`. If `T_{0} > A`, this model predicts cooling (a decreasing function) and if `T_{0} < A`, this model predicts heating (an increasing function).

In terms of calculus-related ideas, this equation can be rewritten as `T-A=(T_{0}-A)e^{-kt}` and can be interpreted as saying that the function `T-A` undergoes exponential decay (a constant relative rate of decay) to zero as time `t` increases (from above if `T_{0} > A` and from below if `T_{0} < A`).