# My (hot) watery experiment at home…

This experiment is something I always wanna do, at home. I’m aware that it’s very unlikely and ordeal, but it was still worth a try. Because, the principle itself is almost certainly counter-intuitive.

## Can hot water freeze faster than cold water?

Yep, it’s a defiance to everyone’s intuition. But, that’s the whole point of this dull phenomena. You say, “Ugh.. How in the hell can something happen like that?” But, what if it does? Definitely something staggering. Right? To caress your curiosity, it has happened. Not once or twice. But, an overwhelming gazillion times. Although this wizardly effect has some interesting that dates back to centuries, however it was first demonstrated by Mpemba in the 1960s, and by that, this bloody thing got a name. It’s the Mpemba effect. I sense that you’re still on the brink of believing and not believing.

Look around you. Google it. and you’ll get articles from the Wikipedia and my beloved Physics FAQ. The thing is that scientists haven’t come up with a good explanation on that effect till now. They’re baffled (just as usual). They’ve got a big crunch of hypothesis. Well, you can have a look at the Physics FAQ article for a briefer and most satisfying (but, time-consuming) explanation. One thing should be noted that this effect can happen under a wide range of favorable conditions. It also depends on a lot of factors – evaporation, convection currents, cooling environment, nature of both water samples, etc. I’ll brief that out soon…

And, I’ve to admit that my intend was not to observe the effect, but try to reduce the influence caused by the above factors and observe whether the effect has occurred or not. So the question is, “what the heck did I do, during the first week of my vacation?” Actually, this experiment came into mind during my third semester exams (I guess it occurred on the eve of solid mechanics exam). I postponed it for the next three weeks. Vacation started and I had a lot of plans which had to be dumped for a while due to the merciless “non-availability-of-internet” for a week.

This phenomena and a few outdoor activities can’t be stopped. So, I did just as planned. But, not quite. I spent about 30 hours on the experiment. Because, my whirlpool refrigerator, at its maximum freezing (level 6) took about 4 damn hours to freeze water. Moreover, the freezer has very small volume where I have to crunch in the whole experimental setup. Okay, I admit. I screwed the setup about 7 times due to my unnecessary jerking offs. I mean, I shook the setup and water poured inside and outside, by which I gave a heck of work to my mom (yeah, I get scoldings in return).

## Don’t just do the experiment. Be clever…

I know I have to do the experiment. But, I’m not in a hurry (and, I shouldn’t be). I should have patience (which I really don’t). I should be clever, not smart. We have some prerequisites to think of. Because, I’m trying not to prevent the effect. Our home experiment needs homey stuff. You can decide choosing your own, based on your cooling environment. But, these were mine…

Two equal silver cups (both are 170 ml, in my case), a thermometer, two tupperware containers (small ones are enough) and thermocols (called out as Styrofoam or polystyrene, elsewhere) about 1 cm thick. Now, lemme brief out why, as well as how I used them.

Silver, being a good conductor of heat, is gonna be the only way the water is gonna get cooled. Why? Firstly, our fridge (so do, all the fridges) has frost. Right? If we simply place both the cups above the frost, the silver cup containing the hot water, will conduct the heat away from it very rapidly. Because, there’s a large temperature difference established between the hot water and frost ($\Delta T$ is probably around a 100 °F) compared to the cold water setup (where $\Delta T$ is barely 30 °F). Now, recall that the rate of heat flow depends on the temperature difference, just like the current depending on potential difference (voltage).

By this way, heat flows rapidly from hot water, to melt the frost, thereby lowering the temperature of hot water soon. Let’s pummel that horror. A thermocol is a very bad conductor of heat (so do all thick polythene, mica and plastic). The thermocol is placed below the cups. I placed thermocols below both of them just to ensure that I’m not biased towards a cup. Then, water evaporates. The evaporation (being a surface phenomena) depends on the temperature of the substance. Well, it’s just a matter of the water molecules acquiring sufficient kinetic energy, getting knocked out, and hence eloping out of the mixture with some neighbor, right?

The “getting kinetic energy” part depends on the temperature. So, hot water evaporates actively rapidly compared to cold water. Again, let’s bomb this searing factor. Both the tupperware containers can be used to close the tops of the cups. I’m not using lids because they’re always risky, and with my jerking-off, and within such a confined environment (small freezer), it’s most likely that I’ll ruin the setup. If I use containers, I can safely get the cups out, open them, pour the water drops (sticking to the container) back into the cup, measure and place them back. It should be noted that cooling takes place only via the silver cup, as both the top and bottom has been sealed by insulators…

And, you don’t have to be extremely accurate. After all, this is just a home experiment. Approximate is enough. But, it’s good to be careful. So, are we ready to take the readings? Nope.

## Now, when does “freezing” happen?

You say, “Hey, that’s an easy one. Freezing is when water turns to ice, exactly at 0 °C. Right?” Nope. This is where we need to be careful. Celsius scale is based on melting & freezing points of water. Yeah, but maybe “supercooling” didn’t appear during Celsius’ timeline. Try spending some time watching this video from Veritasium…

Ice-formation needs a process called nucleation. Think a while. Water is a liquid. The water molecules have cohesive forces acting on them, but the molecules can still run anywhere they want to. I mean, they’re still loose. They move like hell[1]. How can molecules with stupendously random motion arrange themselves by themselves, to a beautiful crystalline form? (which is a fantastic arrangement constituting a structure with definite lattice spacing, so & so). Order out of chaos? Oh, no..!!! This is an entropic universe. Disorderliness shouldn’t decrease with time (don’t worry, it won’t)…

Crudely speaking, as the molecular motion slows down a bit (with decreasing temperature), and a few molecules try to form a crystal structure, they’ll probably get knocked by other molecules swooshing through. They’re undergoing a random walk (run would fit better). So, they need something to stick to. Ions, dust, big molecules, anything can do the job. So, they start sticking and crystallizing.

Now you ask, “Very well then. What about pure water? Doesn’t it freeze at 0 °C, or based on what you said, doesn’t it freeze at all?” You exaggerated a little bit on what I just said. You’re right that pure water doesn’t freeze at 0 °C. But, as the temperature lowers down, the random motion weakens and weakens and finally, there comes a situation when there’s no crazy molecule around, to knock out the just-now frozen bunch. By that way, ice crystals form. Don’t create a misconception now. The nucleating process is what’s happening now. Just that it’s not been helped by the ions and dusty stuff doesn’t mean it’s not nucleation. The only difference is that water helps itself (due to extremely low temperatures)…

Now you can get what Derek’s been doing in that video on “supercooling water”. Even if you ignore my stupid talk above, here comes the issue. You close the fridge and move away, then you come at specific frequencies (like, note a value every “X” minute, etc.). Right? Let’s take this case. You note the readings often. After four hours, you come and see that both waters have just started to crystallize (you see ice bulks in the edges of the cup). How would you know which one did first? Because, that’s the whole point of this effect. No? So, this is rude. You can’t go with that definition..!!!

We haven’t still defined freezing. For the purpose of my experiment, here’s how I define freezing. Freezing is when my thermometer reads 35 °F. Actually, it should be 32 °F. But, never mind. It’s just a home experiment.

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[1]: In case you’d like to visualize them, my suggestion will always be OE Cake. It’s simply amazing. And, it works on probably any PCs that come out days. Users with the later OSes like Win7 or Win8 should change their compatibility, as it works perfectly for XP.

## Let the siege begin..!!!

We’re now ready to begin the experiment. I’ll remind you the setup again…

Don’t worry about the container size. We just need to ensure that the tops are covered good enough. Our containers are far enough for that purpose. My thermometer is based on a thermocouple (i.e) it’s conductive and so, it takes around 10-15 seconds to reach the equilibrium. Whenever I wanna measure the temperature, I take the containers out and just dip the thermometer inside. Because, I just need a rough measurement. I don’t have to be accurate (right?) I chose “10 minutes” as my frequency. I mean, I measured once every 10 minutes. But, this divine scheme of measuring temperature made me sick…

I tipped the cups 8 times. And sometimes, it’s very sad. Because, I’d have been measuring my 20th reading or so, before I tipped the cup. Last Saturday, I got lucky (probably due to the reason that I was alone in my home). I measured both the temperatures until both the waters reached around 38 °F. Because, the rate how the temperature of the waters decreased, was gradually slowing down as it neared 32 °F. In other words, it’s exponential. I got tired of the measurements and I just quitted my quest on attaining the freezing point. At the end, this was my plot…

Honestly, I wasn’t satisfied with the above result. Take a look at the plot again. I’ve been measuring the temperature once every 10 minutes. That means, I’ve been disturbing the system with my measuring frequency (once every 10 minutes). I know that for any plot, the frequency doesn’t matter. It matters, but if it’s greater than a threshold, then its okay. What do I mean by “threshold”? For instance, you take your frequency to be 3 hours. Meh, for such a long period, you’d miss most of the values that are necessary to make the curve appear exponential. This is something you must not do

I got ready for my next attempt, with some modifications. Water has dissolved gases you see. So, that could also lead to the effect. Because, hot water loses much of its gases compared to the cold water. Duh, experimentalists really suffer. To destroy this, I boiled a water sample and cooled it. Now, I boiled another sample and carried out the experiment with the first one. I chose 30 minutes as my frequency.

Then, I modified my style of measuring. Whenever I wanna measure the temperature, I take both the cups out, handle them with care (Am I not supposed to caress them?), measure, then place them back inside carefully above the respective thermocols, because I gotta follow some way to keep note of the cup that contains hot water. Surprisingly, I got the graph plot this time, quite perfectly.

It’s exponential. Right? So, I’m convinced now. Not only because the curve is exponential, but also the fact that Mpemba effect didn’t occur. Hurray!!!

## Here comes the comic conclusion…

How did the hot & cold waters froze at more or less the same time? At first, I thought this might be related to the Mpemba effect. Just that due to my crude approximations, hot water can’t overtake the cold water. Well, that’s what I thought. Later, I had a discussion with Brandon Enright & Chris White (friends of mine, at Physics Stack Exchange) in our chat room (h-bar). Brandon suggested me to make use of acetone to encourage evaporation and observe the effect. He also asked me to use glass beakers and infrared laser thermometer to improve the setup. My conductive thermometer takes 15 seconds to reach equilibrium, while the IR laser type takes barely a second. He uses that in one of his experiments.

So, it’s very likely that I’ll attempt doing that experiment again once I’ve bought those accessories. Later, Chris White spotted that the first graph looked weird (like I said, it shouldn’t be linear). While I was chatting, it caught my mind that the exponential result is due to convective cooling. In this kind, the rate of cooling depends on the difference in temperature at that instant of time. That is…

$\frac{dT}{dt}$ $\propto \Delta T_{i}$

This linear differential equation has the only solution that it should be exponential. So, that’s what we’ve been observing in the cooling curve. And, it wouldn’t amaze anyone that Newton found this in the 16th century nevertheless he had already shown his profound elegance in gravitation, optics, math, etc. But, this cooling doesn’t apply to a few systems. Anyways, that’s what’s been going on all the time…

$\frac{dT_H}{dt}$ $\propto \Delta T_{HF} \approx \mathrm{120\ ^oF}$

$\frac{dT_C}{dt}$ $\propto \Delta T_{CF}\approx \mathrm{50\ ^oF}$

Are you convinced now? The temperature difference between the hot water and the air inside freezer is a heck 120 °F, relative to the cold water which is barely 50 °F. That’s the reason why both the waters reached the freezing point at arbitrarily closer time period.

### Well, Mpemba effect didn’t appear whatsoever…

That’s just as expected. I’ve been saying all the way down, “I’m trying not to observe the effect”. Next time, I’ll try to get the effect (I’m sure I’ll attempt doing the same experiment again, at home)…