explain the “Mpemba effect” which claims warm water freezes faster than cold water.


explain the “Mpemba effect” which claims warm water freezes faster than cold water.

In: Physics

My 7th grade science teacher explained it like basically: the molecules are moving around much faster in hot water and circulate the cold just a little faster than just freezing from the outside in.
Edit: this was 25 years ago so I might be missing parts of it.

This is to do with the arrangement of H2O molecules in ice vs warm and cold water. For ice, the H2O molecules have a lot of distance between each other (this is why water expands when it freezes). Warm water has more energy so these H2O molecules and whizzing around and are likely to be further apart than closer together (as with cold water). Thus, warm water structure more closely resembles ice than cold water. This is why warm water freezes faster

The Mpemba effect breaks some laws of thermodynamics and is widely regarded as a result that exposes of a flawed interpretation of a badly designed experiment.

In particular the effect cannot be seen by observing hot and cold water return to room temperature by passive cooling. The effect has only been demonstrated in systems with active cooling, in which case the likely explanation is that the amount of energy the cooling engine does is being ignored and neglected.

I remember it as having to do with the triple point on the phase diagram. It converges faster because of the higher equilibrium differential.

Think of it as two cars racing. The cold car starts closer to the finish line, but has to go slow and steady. The hot car starts further away, but has a higher acceleration and top speed.

This is complete nonsense and it’s trivial to prove it.

Suppose you have one cup of water at 30^C (‘warm’) and another at 10^C (‘cold’). You place them both on a metal plate which is fixed at -10^C (by some method) to freeze the cups of water and observe the Mpemba effect. Think about what journey each cup of water has to take in order to eventually reach 0^C and freeze.

The cold cup has to go from 10^C to 9^C, then from 9^C to 8^C, and so on until 1^C to 0^C where the water freezes. The rate at which is does this is given by Newton’s Law of Cooling, which states that the bigger the difference in temperature between the cup and the plate, the faster the rate of cooling. So it will cool quickly at first where the temperature difference between the water and the cold plate is largest, then slow down as the temperatures get closer together.

Now think of the warm cup. It has to go from 30^C to 29^C, then 29^C to 28^C, and so on until 11^C to 10^C. Now, after some amount of time, it has reached the original temperature of the cold cup. From here it takes *exactly the same* journey as the cold cup does to the finish line. Going from 10^C to 9^C to 8^C … to 1^C to 0^C .

Provided the cups are identical, and contain identical amounts of water, and all other things are identical besides the starting water temperature, the warm cup will take an identical amount of time to go from 10^C to 0^C as the cold cup did, because if all else is equal, Newton’s law says that the only remaining factor is the temperature difference. But in addition, the warm cup had to get from 30^C to 10^C before it could do that.

Unless warm water is able to become cold in a negative amount of time, the Mpemba effect is easily disproven using only Newton’s Law of Cooling.