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 #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#).