Hot Water vs. Cold Water

I recently came across a really cool phenomenon, and I feel compelled to share it with you. We’re going to consider a thought experiment, something Albert Einstein and other scientists love(d) to have. In this experiment, we envision two pails of water—one of them has hot water in it, the other has cold water, each of equal water level. We then go outside on a cold winter morning and leave them in the snow. Now, we consider the following question: which will freeze first, the hot water or the cold water?

I know what you’re thinking. “Why are you asking me this? Clearly the cold water freezes first!” It would make sense, right? By the time the hot water gets cold enough to start freezing, the cold water should already be frozen. Common sense makes this seem trivial…but then science gets in the way. It turns out, the hot water may be able to freeze first! There are actually many scientific phenomena that are thought to be able to help the hot water freeze first. Here are a few of them.

The first one is evaporation. This is something we encounter all the time, though you may not think about it…it’s why you sweat! When you sweat, the water in it will evaporate off of your skin, and when this happens, it absorbs heat (it’s called an endothermic reaction), cooling you off. The water has to take in heat in order to make this phase change from liquid to gas, and so it can help cool your body down when it gets heated. The same thing happens to the hot water. The hot water will be evaporating off the surface, taking away extra heat from the liquid water still in the pail. This will also happen to the cold water, but on a much smaller scale. Additionally, because the water is more readily evaporating in the hot pail, there will end up being less water in this pail that needs to freeze.

The second effect comes from frost. The cold pail will be sitting in fluffy, airy snow. The hot pail will melt the snow around it, but as the water (and pail) cools and freezes, the melted snow will once again freeze, this time freezing around the surface of the pail. This snow is much more form-fitting, and will allow conduction much better than the fluffy snow around the cold pail (conduction is when two objects of different temperature touch each other—the heat from the hotter object will flow to the colder object until they are at the same temperature. It’s why if you stick a metal spoon into a fire, the other end you’re touching gets hot).

The third effect has to do with gas bubbles inside the water. The hot water is less likely to contain tiny gas bubbles dissolved in it, because they would have (at least mostly) escaped while being heated. The cold water therefore should have more gas bubbles dissolved in it. When gases are dissolved in water, it lowers the freezing point, and so the cold water is more likely to have a lower freezing point than the hot water!

Lastly, I’d like to mention the effect of convection currents in the hot water. As hot water cools, something called convection occurs—the temperature, due to movement of the water within the pail, will become non-uniform (different at various parts of the liquid). When temperature increases, the density decreases, and so hot water will rise to the surface, giving the water in the pail a “hot top”. Heat can then more easily be released at the surface, furthering the cooling effect on the water. The water in the hot pail will be more easily able to develop convection currents as it cools. Convection has a lot of cool applications for cooling—in addition to being a driver for global climate (convection currents in the ocean), convection is also used to help keep your computer cooled.

So, as you can see, the hot water can sometimes come out victorious! Often referred to as the Mpemba effect, this shocking phenomenon is one really cool application of thermodynamics, and can be easily tested. Obviously this doesn’t always work, and is highly dependent on your initial conditions (air temperature, environment, difference in temperature between the hot and cold water initially, etc.), but it is often shown to work. It has been highly tested, and it’s not fully understood what the main driver of this effect is.

A more complicated effect that I didn’t mention before, that is thought to possibly play a role, is supercooling. When water cools, it wants to go to the least energetic state possible (ice crystals), but in order to do so, it has to latch onto what are known as nucleation points. Nucleation points are places in which these ice crystals can begin to form (ice has to start freezing somewhere, right? The point is, the starting points for phase changes aren’t just random. An example of nucleation with gas bubbles occurs when you stick your finger into a glass of soda, and bubbles form around your finger). If there are no places for the ice crystals to form, then the liquid can stay a liquid at lower temperatures than the normal freezing point, and becomes “supercooled.” It is thought that perhaps the cold water can become (more) supercooled than the hot water, and so the hot water will have a higher freezing point.

This is the type of experiment that can be set up very simply during the winter. It’s now getting into late October, so in a few months, I encourage you to go out in the snow (or just a really cold day) and turn this thought experiment into a real one. If you do, feel free to come back and post your results!

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