If you haven’t read part 1 (why would you do that?), here is a review of the scenario we are considering in part 2:
Two identical containers of water (same volume, same container size and material) are placed into a freezer. One container contains water at just below its’ boiling point (< 100 °C) and the other at roughly room temperature (21 °C). Which will freeze first?
In part 1 I discussed the Leidenfrost effect, named after a guy named Leidenfrost. In part 2 I will discuss the Mpemba effect named after, you guessed it, a guy named Mpemba. Interestingly, Erasto Mpemba was a young student when he made the initial observation that hot water can freeze faster than cold water. While he was not the first to make this discovery, his observation led to the first scientific study of the topic so it bares his name.
At first glance, the second scenario is decidedly less exciting. No boiling, no sizzling, and unfortunately no shoddy videography, but unlike the Leidenfrost effect the mechanism behind the Mpemba effect is still hotly debated. During the boiling experiment the lower thermal conductivity of a trapped steam layer prevented efficient heat transfer to the remaining liquid droplet. Several competing explanations are offered for the Mpemba effect, but I will only consider the influence of variation in heat transfer upon freezing. In general “heat transfer” can be considered to explain both the Mpemba and the Leidenfrost effect, and there are three modes of heat transfer. Last time I described conduction which is the transfer of heat within a solid material or between two physically connected bodies. Conduction assumes that the atoms involved in the transfer of heat are fixed in space, like they would be in the solid pan from the Leidenfrost scenario or the walls of the container for the Mpemba effect. Thermal conductivity as described in part 1 is a measure of heat conduction. In a fluid convection is the major mode of heat transfer and implies that atoms or molecules are free to move around. Convection is the reason a bath of cold water with hot water poured into it will eventually reach a single homogenous temperature or opening the front door on a cold day will “let the cold in”. When dealing with both solids and “fluid” phases (a fluid means a non-solid phase) both conduction and convection can be considered. A more detailed explanation of conduction and convection can be found here.
The third mode of heat transfer is radiation, which is the transfer and absorption of electromagnetic radiation. This was indirectly discussed in a previous article but is not important for these scenarios. A nice animation of each of the three modes mentioned here can be found on the web.
To observe the Mpemba effect I took two identical salsa jars and ate their contents. This did not result in the Mpemba effect so I cleaned the jars and set about a second experiment. In one jar I put ¼ cup of tap water and allowed the water to reach room temperature by setting it on the counter for a few minutes. The temperature of my room was about 24 °C (75 °F). In the second jar I put ¼ cup of boiling water. By the time I poured the water it had cooled slightly from the boiling point (100 °C or 212 °F) to about 88 °C (190 °F). I checked these temperatures with a meat thermometer intended for porkchops and roasted chickens so the accuracy is not perfect but for this experiment it doesn’t matter – we only want to confirm that one container has water at a significantly higher temperature than the other. I placed both containers into my freezer which according to the same thermometer is somewhere around -15 °C (5 °F). After two hours I took the containers out and had a look-see. The room temperature water was mostly frozen except for a cavity between the ice at the top of the jar and the bottom of the jar itself. The boiled water was frozen solid. If I moved both jars around motion of the remaining liquid water in the tap water jar was obvious. From left to right below is both jars from the top after freezing, the room temperature jar from the bottom, and the boiling water jar from the bottom. The opening image for this article shows both jars unfrozen.
The heat transfer explanation that fits my results goes something like this: due to a difference in density between hot and cold water, hot water in the boiled container rises to the top and delays freezing. When the hotter water cools slightly it sinks to the bottom of the jar and stirs the rest of the container, keeping the temperature in the container homogenous. These movement within the water due to relative density differences are called convective currents. The convective currents are strong enough to keep the average temperature in boiled hot water jar above freezing until the entire container freezes simultaneously. Convective currents due to temperature differences are responsible for many naturally occurring events like the movement of an atmosphere around a planet. Meanwhile, the initially cooler tap water freezes at the top of the container preventing convective heat transfer between the water and the cold air in the freezer. Convective currents are also present in the tap water jar, but the remaining heat distributed by them is not enough to prevent a top layer of ice from forming.
I feel obligated to admit that I had some difficulty getting this experiment to work. At first I tried using a whole cup of water in the same jars, checking the temperature in each container every five minutes. In this test I found that the boiled water dropped in temperature very rapidly at first whereas the tap water changed temperature very slowly. Both jars reached around 34 °F, just above the freezing point, at about the same time. The tap water jar froze on the top first making subsequent measurements of the underlying liquid difficult. Eventually both containers were mostly frozen but I couldn’t tell when the interior of either jar had frozen. Repeatedly opening the freezer door to inspect the jars also manipulates the experimental conditions, so when trying this at home I recommend you only check the freezer once an hour or so to see if anything is frozen. Transparent containers like my glass salsa jars make a quick inspection easier, but using containers of different materials could lead to some interesting results. It is this apparent sensitivity to experimental conditions that makes the mechanism responsible for the Mpemba effect subject to question. You can read more about some of these on the Wikipedia article for the Mpemba effect, but I encourage you to try some of your own tests and see what you find!
When you first pick a door, there is approximately 33.3% chance (1/3) that your door contains the coveted concert tickets and about 66.7% that the doors you didn’t choose contain the tickets.
