Can someone explain why Newton's Law of Cooling isn't a sufficient explanation? The temperature delta is clearly larger with hot water, do one would expect it to cool faster, no?
dT/dt = kT
Where T is temperature delta, t is time, and k is some proportionality constant. So the rate of cooling is changing as the delta temperature reduces, specifically, it is getting exponentially reducing as it gets closer to thermodynamic equilibrium (where no heat is exchanged):
T(t) = Ce^kt C = T(0)
Which means there is a larger cool down with the hot water at first, but under this simple model, once the T(t) hits the same temperature of the cool water it's being compared to, it's cooling rate should be equivalent (and a lot slower).