Last week we reached the conclusion that, in spite of Newton’s Law of Cooling, in certain circumstances, hot liquids cool faster than cold liquids. William Frass at some of the possible explanations scientists have come up with so far…Conduction Imagine two containers of equal geometry and material, one containing hot water and another containing an equal amount of cold water. Both of these are placed on a shelf in a freezer. Now any frost that collects on the container is likely to be melted by the warmth of a container made of a good conductor.This has the effect, later on, when the water inside has cooled somewhat, such that the frost outside refreezes, of creating very good thermal contact between, say, the cold freezer shelf and the vessel of water. Hence heat is drawn out of warmer water more quickly. The cooler container on the other hand won’t have the opportunity to melt any surrounding frost and will just sit on top of a layer of ice, which isn’t the best conductor of heat – so takes longer to cool down.This account seeks to ‘explain away’ the Mpemba effect in terms of bad experimental technique: if you don’t allow one container to gain better thermal contact, you won’t observe the effect. Well, the effect of conduction can be dramatically reduced by using a vessel made of a better insulator, in fact Mpemba himself used wooden buckets and still observed the effect. So assuming measures are taken to prevent conduction, convection seems the next likely candidate.
Convection As the warmer water cools rapidly at the surface it will develop convection currents within the container since warmer water is, at most temperatures, less dense than cooler water – creating an uneven distribution of temperature with hot water nearer the surface.So when the hot-water container reaches the temperature the cool water container started at, the hotter water is nearer to the surface, the so-called “hot-top”. This assists quicker evaporation and hence faster cooling since there is greater evaporation from hot water than from cold. This shows that the initially hot water cools faster, but of course it also has further to go. So whether it actually reaches 0°C first, is not immediately clear. In fact, to know which one finishes first would require theoretical modelling of the convection currents, which nobody has done. To add to the confusion, there are “cold tops”. Cooler water is not always more dense than hot water – below 4°C cold water is actually less dense than the surrounding warm water. This means that once the coolest part of the water gets below 4°C it rises to the top and soon freezes – creating a insulating plug slowing down further cooling. Convection currents in the warmer water might help to reduce this process.
EvaporationThe next phenomenon is evaporation. An evaporating substance will lose mass, which takes with it an associated latent heat of vaporisation. With less mass, the hot water has less heat to lose, and so it cools faster. Assuming this explanation, hot water freezes first, but only by virtue of the fact there's less of it to freeze. George Kell actually conducted some calculations that showed that if the water cooled solely by evaporation with a uniform temperature, the warmer water would freeze before the cooler water.This explanation is often citied by many as the explanation of the Mpemba effect – whilst it’s very important other experiments show that it cannot be the sole mechanism that drives the Mpemba effect. Dr Osborne measured the mass lost due to evaporation in his original experiment and found it incomparably less than that predicted by Kell’s article.
Super-coolingFinally, the last effect to offer an explanation is super-cooling. Once water reaches its freezing point, water molecules attempt to adopt the lowest energy state, which is an ice crystal. However they cannot do this without first encountering some irregularity in their surroundings, a nucleation site, which forces them to arrange themselves in a certain way, allowing an ice crystal to develop.
But if the molecules do not encounter such an irregularity they continue to cool below zero whilst still remaining in the liquid phase for a while longer. This is super-cooling. So a liquid that undergoes super-cooling will take longer to freeze since it stays liquid despite having reached 0°CThere have been some claims that initially hot water doesn’t super cool for very long – say only as far –2°C whereas initially cool water may remain super cooled as far –8°C. This is no more an explanation than a replacement problem – how can water remember what temperature is was at before it reached 0°C ? One possible explanation is that a heated water has more of its dissolved gases expelled in the boiling process. This supposedly helps the flow of convection currents and thus assists in cooling.But one would expect that with less dissolved gas to act as a nucleation point, the boiled water which starts off hotter would super cool for longer whilst the molecules searched for a comparatively rare nucleation point. Supporters of the super cooling theory point to symmetric molecules like nitrogen and methane, which are non-polar solvents, the solubility of which don’t necessarily vary linearly with temperature.More recently in 2005 Monwhea Jeng published some work with the most probable conclusion there simply isn’t a unique explanation, certainly not yet, as to why hot water sometimes cools more quickly than cold. So it’s tempting to believe, since freezing requires sufficiently cool molecules to encounter nucleation sites that it could largely be a matter of probability. This might explain why the Mpemba effect can sometimes be hard to reproduce and doesn’t always lead to consistent results.
The Mpemba Effect (continued)
