Mpemba was a secondary school student in Tanzania in 1963 who had the fortune of re-discovering some interesting physics during one of his cookery lessons.
Having boiled some milk for making ice cream, his class were told to let the mixture cool before putting it in the refrigerator. Mpemba, however was anxious of ensuring himself a space so put his mixture in straight away.
The other students waited and put their mixtures in later, after they’d cooled down. Having noted the time his ice cream entered the freezer compared with the rest of his class, Mpemba realised his mixture had frozen significantly faster than everyone else’s.
He came away with the simple observation that “hot liquids freeze faster than cold liquids”.
His science teacher told him this was impossible and he must have got mixed up. So why exactly is this impossible?
In a subsequent year at high school Mpemba was taught about Newton’s law of cooling in science: the rate at which a body cools is proportional to the temperature difference between that body and its surroundings:
…which leads to the solution…
Any set of cooling curves plotted from such a function will never cross, no matter what the initial starting temperature. So a curve which starts at a higher temperature will never undercut a curve starting at a lower temperature and will therefore always take longer to cool. Varying the parameter k on the other hand could well cause graphs to cross. But this parameter is determined from some initial conditions, if both systems are not identical in such things as geometry or arrangement, with the exception of starting temperature, then it is hardly appropriate to compare cooling times for different initial temperatures.
However, Mpemba was undeterred by a theory which didn’t seem to support his observations: he’d asked a friend who sold ice cream in a nearby town who told him he routinely used hot mixtures because they froze more quickly.
Still persisting with this, in 1969 a visiting academic from University College in the capital called Dr Osborne came to visit Mpemba’s school and he jumped at the opportunity to quiz him about this apparent violation of Newton’s Law. Thankfully he didn’t dismiss it outright, and upon returning to Dar es Salaam, he instructed a lab-assistant to carry out an experiment to see if hot water would freeze more quickly than cold water.
The lab-assistant reported the hot water had frozen first, but not to worry, "I'll keep on repeating the experiment until we get the right result." After several attempts it seemed Mpemba was right – hot water would freeze faster than cold water.
Publish or perish
Osborn and Mpemba published these results in a journal called “Physics Education”, coincidentally the same year that George Kell at the National Research Council of Canada in Ottawa reported the same phenomenon that year in the “American Journal of Physics”.
I said Mpemba re-discovered this; having mentioned this “Mpemba Effect” in one of their articles, the “New Scientist” was subsequently flooded with anecdotes from all over the world of only the hot water pipes freezing during a short cold snap, ice-rink operators preferring to use hot water and so on.
So this clearly wasn’t unheard of.
Surely the validity of this effect can be deduced by carrying out experiments – however this has proved surprisingly difficult. The Mpemba effect is only observed under certain conditions – there are clearly many factors which could affect how quickly water cools such as the geometry of the container, the volume of water and the temperature of the refrigerator.
In 1977, Jearl Walker published results in the “Scientific American” whereby the time to freeze was measured against the initial temperature for a variety of containers. His results showed two things. Firstly where negative gradients occur, water at an initially higher temperature appeared to be freezing more quickly. Secondly, this is by no means a universal effect, since most of the curves showed very little (if any) in the way of negative gradients.
On the aspect of repeatability, Walker reported that whilst most of his results were repeatable, he sometimes observe large variations in his results and said “I have not been able to resolve the controversy”.
So assuming both Newton and Mpemba are correct – how do we understand what is going on here? Can we somehow reconcile these two arguments?
CHECK BACK NEXT WEEK TO FIND OUT…
by Will Frass
