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Newton's Law of cooling states that the rate of loss of heat in proportional to the temperature difference. or $-dQ/dt = k(T' - T)$

Q → heat transferred, t → time, k → constant, T' - T → temperature difference.

Anyone not knowing about Mpemba effect here's a link


marked as duplicate by John Rennie thermodynamics Feb 13 '17 at 6:59

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  • $\begingroup$ your question is very vague. Please improve it by explaining what is Mpemba effect and how do you want the two things to be connected. $\endgroup$ – Ari Feb 13 '17 at 5:47
  • $\begingroup$ Newton's Law of cooling doesn't "explain" anything. It's just a mathematical equation. For the Mpemba effect, it completely ignores phase changes (i.e. evaporation) and radiative heat loss. Even in situation where it is relevant, the physics is what determines the value of the "constant" $k$ - and in most real world situations $k$ is not constant! $\endgroup$ – alephzero Feb 13 '17 at 11:20

This seems more of p-chem problem than physics.

The Mpemba effect is that hot water will freeze faster than cold water which is counter intuitive.

Actually Newton's Law of cooling would predict that cold water would freeze faster than hot. If the hot water is a temperature $\text{T}_\text{H}$ and the cold water is at $\text{T}_\text{C}$ then the hot water would have to cool through temperature $\text{T}_\text{C}$ to reach the freezing point. So hot water should take longer.


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