# Hot water freezing faster than cold water

This question has puzzled me for a long time. There is already a question like this on Physics.SE. John's answer to the question seems quite satisfying. But when I googled the cause I found this and this explanation. They maybe wrong but I think How Stuff Works is a reliable source.

And here's the original paper.

I am quite confused now reading the different explanations. Can anyone please shed some light on the issue?

• Related mathoverflow question: mathoverflow.net/q/153669/13917 Commented Jul 2, 2014 at 13:37
• I see that it's the same paper. But has this explanation been confirmed or is just a hypothesis? Commented Jul 2, 2014 at 13:41
• Maybe the reason for contradictory explanations is that we do not really know yet. Commented Jul 22, 2014 at 6:39
• @DanielMahler That is what the question is all about. Commented Jul 22, 2014 at 7:00
• @Yashbhatt The answers here & in the links tend sound like we do know the answer, even if they may disagree on what it is. The question is asking for a definite/canonical answer. I am suggesting that such an answer may not be possible at present. Commented Jul 22, 2014 at 7:16

To start with, "water freezes faster when it starts out hot" is not terribly precise. There are lots of different experiments you could try, over a huge range of initial conditions, that could all give different results. Wikipedia quotes an article Hot Water Can Freeze Faster Than Cold by Jeng which reviews approaches to the problem up to 2006 and proposes a more precise definition of the problem:

There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner.

However, even that definition still has problems, which Jeng recognizes: first, there's the question of what "freeze" means (some ice forms, or the water freezes solid all the way through); second, the hypothesis is completely unfalsifiable. Even if you restrict the hypothesis to the range of conditions reasonably attainable in everyday life, to explain why the effect is so frequently noted anecdotally, there's literally an infinite number of possible experimental conditions to test, and you can always claim that the correct conditions just haven't been tested yet.

So, the fact that the internet is awash in a variety of different explanations makes perfect sense: there really are a bunch of different reasons why initially hotter water may freeze faster than initially colder water, depending on the precise situation and the definition of "freeze" that you use.

The paper you link to, O:H-O Bond Anomalous Relaxation Resolving Mpemba Paradox by Zhang et al., with results echoed by the HowStuffWorks video, attempts to solve the problem for a very specific sub-hypothesis. They eliminate the problem of defining freezing by treating freezing as a proxy for cooling in general, and directly measuring cooling rates instead. That experimental design implicitly eliminates one internet-provided explanation right off the bat: it can't possibly be supercooling, because whether the water supercools or solidifies when it gets to freezing temperature is an entirely different question from how quickly it cools to a temperature where it could freeze.

They also further constrain the problem by looking for explanations that cannot apply to any other liquid. After all, the Mpemba effect is about why hot water freezes faster; nobody is reporting anomalous freezing of, say, hot alcohol. That might just be because people freeze water a lot, and we don't tend to work with a lot of other exotic chemicals in day-to-day life, but choosing to focus on that restriction makes the problem more well-defined, and again implicitly rules out a lot of potential explanations ahead of time- i.e., it can't have anything to do with evaporation (because lots of liquids undergo evaporative cooling, and that's cheating anyway 'cause it changes the mass of the liquid under consideration) or conduction coupling to the freezer shelf (because that has nothing to do with the physical properties of the liquid, and everything to do with an uncontrolled experimental environment, as explained by John Rennie.

So, there really isn't just one answer to "why does hot water freeze faster than cold water", because the question is ill-posed. If you give someone a specific experimental set-up, then you can get a specific answer, and there are a lot of different answers for different set-ups. But, if you want to know "why does initially-hotter water cool faster through a range of lower temperatures than water that started out at those lower temperatures, while no other known liquid appears to behave this way" (thus contributing to it freezing first if it doesn't supercool), Zhang has your answer, and it's because of the weird interplay between water's intra- and inter-molecular bond energies. As far as I can tell, that paper has not yet been replicated, so you may consider it unconfirmed, but it's a pretty well-reasoned explanation for a very specific question, which is probably an influencing factor in a lot of other cooling-down-hot-water situations. There is a follow-up article, Mpemba Paradox Revisited -- Numerical Reinforcement, which provides additional simulation evidence for the bond-energy explanation, but it can't really be considered independent confirmation because it's by the same four authors.

• Thanks for such a nice answer. That clears a lot of confusion. But I din't get what you are trying to say int the 4th Para. do you mean something like hot water cools faster but doesn't freeze faster? Commented Jul 18, 2014 at 16:53
• I'm saying "freezing" isn't very well defined, so Zhang measured something else. However you define freezing, we can at least agree it requires water to be cold, so how fast water cools is a good stand-in for the intuitive notion of how fast it freezes. Zhang determined that hot water can cool down faster, and therefore will probably freeze sooner, once you've controlled for all the different kinds of freezing (whether it supercools instead of solidifying, whether you count any crystal formation or solid-right-through, etc.), but "freezing" isn't part of the measured effect. Does that help? Commented Jul 18, 2014 at 17:02
• That's Zhang article is incredibly sketchy "science."
– user10851
Commented Jul 18, 2014 at 17:03
• @ChrisWhite Could you be more... specific? What do you find wrong with it? In any case, the accuracy / believability of the Zhang article is kind of irrelevant- whether or not their explanation is correct, the main point is that the Mpemba effect is ill-defined, and thus the correct explanation in a specific circumstance legitimately varies quite a bit, and the Zhang article linked by the OP represents an attempt to explain a much more constrained, much more well-defined version of the problem. Commented Jul 18, 2014 at 17:08
• @LoganR.Kearsley So, is there no way to check if Zhang is correct as the all the parameters cannot be adjusted for different instances of the experiment? Commented Jul 18, 2014 at 17:25

This happens due to cooling affect of evapourisation.

As you must be knowing, the temperature of the lquid is a factor of evapourisation. So as the temperature of hot water is more, the rate of evapourisation is also more. Now this is where thwe cooling effect of evapourisation takes place. As the water evapourates, it takes away some heat thus cooling the hot water . so as a equation we can write it as: Rate of cooling of hot water = cooling effect of evapourisation + cooling effect of freezer Rate of cooling of cold water = cooling effect of freezer

Thus we can state that cooling effect of hot water is more than cooling effect of cold water

There is also one more thing that affects the rate of cooling. As the differences between the temperature of surroundings and the temperature of liquid is more in hot water than in cool water, hot water again cools faster than cold water.

• Did you see the links I have mentioned? Commented Jul 18, 2014 at 16:53
• 1)Notice that there is a point where the temperatures are equalized.Afterwards the rates should be the same 2)This perspective seems to apply in all liquids,but this not happens. Commented Apr 22, 2020 at 19:15
• "This happens due to cooling affect of evapourisation." Has no one ever thought of putting lids on the containers? Commented Jul 20, 2022 at 13:22

It is because of convection effect. Convection is fluid (in our scenario) movement driven by temperature difference.

In this case grater temperature difference at the beginning - grater speed of fluid at the end. Fluid is cooling down near dish walls. This causes cooled water to sink faster in this part of dish.

Picture shows water movement in dish in cold environment. Arrows show fluid movement direction. Black arrow shows place where there is no heat exchange with environment. Blue arrows show where fluid is cooling down. Horizontal arrows are not important - fluid is not accelerated in this areas.

Lets name:

A - container with water hotter at the beginning of the experiment

B - container with water colder at the beginning of the experiment

At the moment when water freezes speed of water circulation in A is grater than in B. Grater speed of fluid in dish - grater heat exchange with cold environment. Water circulation momentum causes inertia in (resistance in changing) heat exchange ratio.

Experiment:

Repeat experiment with dense 3D grid inside dishes. Such a grid that it prevents significant convection movements. Convection movement will still appear in each grid cell separately but effect will be negligible.

Evaporation effect is negligible.

It is worth to notice that no matter what the truth is there is such a moment where:

average heat of A = average heat of B

This is exact moment where A overtake B. In this state A has some other property in better condition then B.

In my opinion those properties are (as I mentioned before): momentum of fluid and temperature distribution (A has temperature more levelled then B, B has bigger temperature gradients).

• Can you please elaborate on this point? And what do you say about the other effects mentioned in other answers here. Commented Jul 22, 2014 at 4:47
• @Pawel, I really like your proposal. It's definitely worth investigating. Commented Sep 27, 2014 at 20:12
• 1)"those properties" can be expressed by entropy.But why the effect is not always occurs? 2)This perspective seems to apply in all liquids,but this not happens. Commented Apr 22, 2020 at 19:01

Sometimes it occurs:New Explanation.Initially-hot water has lost much of its ordered clustering (higher entropy) and, if the cooling time is sufficiently short, this will not be fully re-attained before freezing. Experiments on the low-density water around macromolecules have shown that such clustering processes may take some time.Entropy reduction curves function of temperature S=f(T) appear retardation (lagging) relative to entropy growth curves.At any temperature point T the entropy S=mclnT during cooling is more than this during heating.The water after was heated and recooled at the initial temperature,has more entropy than before it was heated.This means that molecules have now the same average kinetic energy,but thermal motion before heating was more oriented by the structure mentioned above.Recooling random collisions are more possible leading to faster temperature’s reduction New explanation.

• Dear elias2010. For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself, not in attached links. Commented Apr 22, 2020 at 23:32

Consider this arxiv.
Most of people intuit that since at certain point the T(t) curves (temperature vs time) of systems with different initial temperatures cross - the cooled system somehow has memory or is aware of its cooling protocol. This last statement is what's causing trouble. During the cooling process the definition of temperature is ill defined since the system is not in equilibrium. The cooling protocols merely transfer one equilibrium state to another (asymptotically, of course), through non-equilibrium states. Since the initial conditions are considered to be substantially different - the path of the two systems through the non equilibrium states differ substantially as well. Different paths in general traversed at different rates. This is the solution to the paradox, and invitation to investigate optimal cooling protocols.

• Interesting link. My intuition has always been that the masses and timescales involved in the Mpemba effect are large and slow enough that the usual definition of temperature should still be quite good. A peer- reviewed paper which treats the non-equilibrium details quantitatively will make a good read.
– rob
Commented Jan 9, 2019 at 12:01
• 1)This perspective seems to apply in all liquids 2)What about the randomness and low repeatability of the effect in water? Commented Apr 22, 2020 at 18:55

If you are putting a metal ice tray onto a freezer shelf which is covered with a significant layer of frost, then a hot tray will melt the frost (which is a fair insulator) putting the tray into direct contact with the freezer element.

The surface tension, and therefore the droplet size in free-fall, of water is dependent on its temperature. Therefore, water thrown into the air will form smaller droplets with greater total surface area at higher water temperatures. A larger ratio of surface area to mass allows for more rapid heat transfer with the air through which it falls by conduction.

In very cold air, it is possible to throw a cup of boiling water into the air and have it turn into snow before it lands, due to the very high total surface area of the droplets thus formed. Under these conditions, it is feasible for a cup of cold water, which would form larger droplets, to take longer to reach freezing point.

Unfortunately it is not presently cold enough here to conduct such an experiment.