"Inspiring African young scientist to pursue scientific studies."
The Mpemba effect is named after a Tanzanian student called Erasto Mpemba, who observed that “hot ice cream mix froze before the cold mix.”
Scientists have known
for generations that hot water can sometimes freeze faster than cold, an effect
known as the Mpemba effect, but until
now have not understood why. Several theories have been proposed, but one
scientist believes he has the answer
| The story of its rediscovery by a Tanzanian high school pupil named Mpemba is written up in the New Scientist. The story provides a dramatic parable cautioning scientists and teachers against dismissing the observations of non-scientists and against making quick judgements about what is impossible(The Times 2013). |
Theories
for the Mpemba effect have included (Auerbach
1995):
- Faster evaporation of hot water, which reduces the volume left to freeze
- Formation of a frost layer on cold water, insulating it
- Different concentrations of solutes such as carbon dioxide, which is driven off when the water is heated
The
problem is that the effect does not always appear, and cold water often freezes
faster than hot water.
In
1963, Mpemba was making ice cream at school, which he did by mixing boiling
milk with sugar. He was supposed to wait for the milk to cool before
placing it the refrigerator, but in a rush to get scarce refrigerator space,
put his milk in without cooling it. To his surprise, he found that his hot
milk froze into ice cream before that of other pupils (“The
Mpemba Effect: When Can Hot Water Freeze Faster than Cold?” 2006). He asked his physics teacher
for an explanation, but was told that he must have been confused, since his
observation was impossible.
Mpemba
believed his teacher at the time. But later that year he met a friend of
his who made and sold ice cream in Tanga town. His friend told Mpemba
that when making ice cream, he put the hot liquids in the refrigerator to make
them freeze faster. Mpemba found that other ice cream sellers in Tanga
had the same practice.
Later,
when in high school, Mpemba learned “Newton's
law of cooling”, that describes how hot bodies are supposed to cool. Mpemba
asked his teacher why hot milk froze
before cold milk when he put them in the freezer. The teacher
answered that Mpemba must have been confused (Thomas
2007).
When
Mpemba kept arguing, the teacher said "All I can say is that is Mpemba's physics and not the universal physics" and from then
on, the teacher and the class would criticize Mpemba's mistakes in mathematics
and physics by saying "That is Mpemba's
mathematics" or "That is Mpemba's
physics." But when Mpemba later tried the experiment with hot and cold
water in the biology laboratory of his school, he again found that the hot
water froze sooner.
Earlier,
Dr Osborne, a professor of physics, had visited Mpemba's high school.
Mpemba had asked him to explain “why hot
water would freeze before cold water”. Dr Osborne said that he could
not think of any explanation, but would try the experiment later. When
back in his laboratory, he asked a young technician to test Mpemba's
claim. The technician later reported that the hot water froze first, and
said "But we'll keep on repeating the experiment until we get the right
result." However, repeated tests gave the same result, and in 1969 Mpemba
and Osborne wrote up their results.
 |
| Dr.Kelly |
In
the same year, in one of the coincidences so common in science, Dr Kell
independently wrote a paper on hot water freezing sooner than cold water.
Kell showed that if one assumed that the water cooled primarily by evaporation,
and maintained a uniform temperature, the hot water would lose enough mass to
freeze first. Kell thus argued that the phenomenon (then a common urban
legend in Canada) was real and could be explained by evaporation.
However, he was unaware of Osborne's experiments, which had measured the mass
lost to evaporation and found it insufficient to explain the effect.
Subsequent experiments were done with water in a closed container, eliminating
the effects of evaporation, and still found that the hot water froze first.
 |
| University of Dar Es salaam (UDSM), Tanzania |
Together
with a physics professor at University College at Dar es Salaam, he published a
paper in 1969 that showed equal volumes of boiling water and cold in similar
containers would freeze at different times, with the hot water freezing first.
Dr
Denis Osborne, a lecturer at University College in Dar es Salaam who published
the paper with Mr Mpemba on the effect they had observed, said: "Several
different mechanisms may cause or contribute to an Mpemba effect”(The Telegraph. 2013; The Daily Mail 2013).
 |
| Logo of the University of Dar Es salaam |
The Mpemba effect is the name given to
the assertion that:-
“It is quicker to cool water to a given
temperature when the initial temperature is higher”. The experiments
were carried out to explore evidence on Mpemba effects by cooling water in carefully
controlled conditions.
The
statement “hot water does not cool more
quickly than cold” is vague and imprecise; “hot water can be made to cool more quickly than cold by supplying more
energy to the cooling of hot water”, but it is under such a non-specific
premise that the Mpemba effect has become an artefact in popular science.
Broadly
speaking, when two samples of water are
cooled to the same temperature, in the same manner with the two samples being
identical except for their initial temperature, and the initially hotter sample
cools in less time, one can consider the Mpemba effect to have been
observed. The temperature at which cooling times are compared has often been
chosen to be 0 °C (or below) making careful measurements more difficult because
of the phase change that occurs as water freezes.
 |
| Nikola Bregovic |
The
Royal Society of Chemistry offered a £1,000 prize to anyone who could explain
how the Mpemba effect worked. Nikola
Bregovic, a chemistry research assistant at the University of Zagreb, was announced as the winner for the prize (Bregović,
n.d.).
He
conducted experiments using beakers of water in his laboratory and his
resulting paper suggested that the effect of convection was probably
responsible.
He
said that “convection currents set up in
the warm water cause it to cool more rapidly”.
 |
| Dr Changqing |
However, Dr Changqing and Dr Zhang have attempted to explain the effect furtherin and Dr Zhang have attempted to explain the effect further by
examining the process at a molecular level.
They
said; the “interaction between the hydrogen
bonds and the stronger bonds that hold the hydrogen and oxygen atoms in each
molecule together, known as covalent
bonds,” is what causes the effect.
Normally
“when a liquid is heated, the covalent
bonds between atoms stretch and store energy”.
The
scientists argue that in water, “the
hydrogen bonds produce an unusual effect that causes the covalent bonds to
shorten and store energy when heated.”
This
they say leads to the bonds to release their energy in an exponential way
compared to the initial amount stored when they are cooled in a freezer. So
“hot water will lose more energy faster
than cool water”.
Dr
Changqing said: “Heating stores energy by
shortening and stiffening the H-O covalent bond”.
“Cooling
in a refrigerator, the H-O bond releases its energy at a rate that depends
exponentially on the initially stored energy, and therefore, Mpemba effect
happens.”
The
Royal Society of Chemistry received more than 22,000 responses to its call for
a solution to the Mpemba effect and it is still receiving theories despite the
competition closing a year ago, Dr Sun Changqing and Dr Xi Zhang from Nanyang
Technological University, argue this also determines the way water molecules
store and release energy.
They
argue that the rate at which energy is released varies with the initial state
of the water and so calculate that “hot
water is able to release energy faster when it is placed into a freezer.”
Dr
Changqing said: “The processes and the rate of energy release from water vary
intrinsically with the initial energy state of the sources”.
Mr
Bregovic, who was judged to have developed the best solution by a panel of
experts a conference at Imperial College London, said: “This small simple
molecule amazes and intrigues us with its magic.”
Aeneas
Wiener, from Imperial College who helped to judge the competition, added: The
new paper demonstrates that even though a phenomenon seems simple, delving
deeper reveals even more complexity and that is certainly worth looking at. "What
the authors describe as a property of H-O bonding may be one of these."
More
modern awareness of this apparent anomaly range from the accidental experiments
of the Tanzanian school boy, Mpemba (after whom the phenomenon is popularly
known), to the competition calling for explanations of the phenomenon by the
RSC.
The
Mpemba effect is an oft cited scientific anomaly and has been widely used in
high-school and undergraduate physics projects. In
the presence of an initially hot sample the freezer may remain on, and doing
work, to drive the cooling for longer. This, however, by no means explains the
Mpemba effect; the hot water must take some time to cool to the initial
temperature of the cooler sample of water, after which all else being equal
one would expect the further cooling of the warm sample to take the same time
as the cooling of the colder sample.
Warm
water, in total, would take longer to cool. Thus for the Mpemba effect to be
observed there must be some difference in the chemistry of the samples or the
physics of their cooling either initially or when at equivalent temperatures understanding
and examining the various mechanisms that might give rise to such differences
remains the focus of scientific debate.
The
winning entry to the RSC competition, for example, cites four factors as
possibly contributing to the Mpemba effect, namely:
- Evaporation
- Dissolved gases
- Mixing by convective currents
- Supercooling.
No
doubt all four processes affect the cooling rate of water, albeit to differing
extents, and crucially their effects may be strongly coupled.
Evaporation
One
explanation of the effect is that as the hot water cools, it loses mass to
evaporation. With less mass, the liquid has to lose less heat to cool,
and so it cools faster. With this explanation, the hot water freezes
first, but only because there's less of it to freeze. Calculations done
by Kell in 1969 showed that if the water cooled solely by evaporation, and
maintained a uniform temperature, the warmer water would freeze before the
cooler water (Thomas
2007).
This
explanation is solid, intuitive, and undoubtedly contributes to the Mpemba
effect in most physical situations. However, many people have incorrectly
assumed that it is therefore "the" explanation for the Mpemba
effect. That is, they assume that the only reason hot water can freeze
faster than cold is because of evaporation, and that all experimental results
can be explained by the calculations in Kell's article.
However,
the experiments currently do not bear out this belief. While experiments
show evaporation to be important, they do not show that it is the only
mechanism behind the Mpemba effect. A number of experimenters have argued
that evaporation alone is insufficient to explain their results; in particular,
the original experiment by Mpemba and Osborne measured the mass lost to
evaporation, and found it substantially less that the amount predicted by
Kell's calculations. And most convincingly, an experiment by
Wojciechowski observed the Mpemba effect in a closed container, where no mass
was lost to evaporation.
Dissolved Gasses
Another
explanation argues that the dissolved gas usually present in water is expelled
from the initially hot water, and that this changes the properties of the water
in some way that explains the effect. It has been argued that the lack of
dissolved gas may change the ability of the water to conduct heat, or change
the amount of heat needed to freeze a unit mass of water, or change the
freezing point of the water by some significant amount (Thomas
2007). It is certainly true that
hot water holds less dissolved gas than cold water, and that boiled water
expels most dissolved gas. The question is whether this can significantly
affect the properties of water in a way that explains the Mpemba effect.
As far as I know, there is no theoretical work supporting this explanation for
the Mpemba effect.
Indirect
support can be found in two experiments that saw the Mpemba effect in normal
water which held dissolved gasses, but failed to see it when using degassed
water. However, an attempt to measure the dependence of the enthalpy of
freezing on the initial temperature and gas content of the water was
inconclusive.
One
problem with this explanation is that many experiments pre-boiled both the
initially hot and initially cold water, precisely to eliminate the effect of
dissolved gasses, and yet they still saw the effect. Two somewhat
unsystematic experiments found that varying the gas content of the water made
no substantial difference to the Mpemba effect.
Mixing by convective currents
It
has also been proposed that the Mpemba effect can be explained by the fact that
the temperature of the water becomes non-uniform. As the water cools,
temperature gradients and convection currents will develop. For most
temperatures, the density of water decreases as the temperature increases (Vynnycky
and Kimura 2015). So over time, as water cools
we will develop a "hot top" the surface of the water will be warmer
than the average temperature of the water, or the water at the bottom of the
container. If the water loses heat primarily through the surface, then
this means that the water should lose heat faster than one would expect based
just on looking at the average temperature of the water. And for a given
average temperature, the heat loss should be greater the more inhomogenous the
temperature distribution is (that is, the greater the range of the temperatures
seen as we go from the top to the bottom).
How
does this explain the Mpemba effect? Well, the initially hot water will
cool rapidly, and quickly develop convection currents and so the temperature of
the water will vary greatly from the top of the water to the bottom. On
the other hand, the initially cool water will have a slower rate of cooling,
and will thus be slower to develop significant convection currents. Thus,
if we compare the initially hot water and initially cold water at the same
average temperature, it seems reasonable to believe that the initially hot
water will have greater convection currents, and thus have a faster rate of
cooling. To consider a concrete example, suppose that the initially hot
water starts at 70°C, and the initially cold water starts at 30°C. When
the initially cold water is at an average 30°C, it is also a uniform
30°C. However, when the initially hot water reaches an average 30°C, the
surface of the water is probably much warmer than 30°C, and it will thus lose
heat faster than the initially cold water for the same average
temperature.
Surroundings
The
initially hot water may change the environment around it in some way that makes
it cool faster later on. One experiment reported significant changes in
the data simply upon changing the size of the freezer that the container sat
in. So conceivably it is important not just to know about the water and
the container, but about the environment around it (The Times 2013).
For
example, one explanation for the Mpemba effect is that if the container is
resting on a thin layer of frost, than the container holding the cold water
will simply sit on the surface of the frost, while the container with the hot
water will melt the frost, and then be sitting on the bottom of the
freezer. The hot water will then have better thermal contact with the
cooling systems. If the melted frost refreezes into an ice bridge between
the freezer and the container, the thermal contact may be even better (Bregović,
n.d.; J. and A. 2015; Auerbach 1995).
Supercooling
Finally,
supercooling may be important to the effect. Supercooling occurs when
water freezes not at 0°C, but at some lower temperature (Auerbach
1995). This happens because the
statement that "water freezes at 0°C" is a statement about the lowest
energy state of the water: at less than 0°C, the water molecules
"want" to be arranged as an ice crystal. This means that they
will stop zooming around randomly as a liquid, and instead form a solid ice
lattice.
However,
they don't know how to form themselves into an ice lattice, but need some small
irregularity or nucleation site to tell them how to arrange themselves.
Sometimes, when water is cooled below 0°C, the molecules will not see a
nucleation site for some time, and then water will cool below 0°C without
freezing. This happens quite often.
One
experiment found that initially hot water would supercool only a little (say to
about −2°C), while initially cold water would supercool more (to around
−8°C). If true, this could explain the Mpemba effect because the
initially cold water would need to "do more work"; that is, get
colder in order to freeze.
For
example, in two volumes of water, only differing in initial temperature and
then cooled in identical conditions, one would expect that different convective
currents might develop. Therefore, for significantly different initial
temperatures the characteristic times that a given water particle remains in
contact with an imperfection in the container or impurity within the water
(e.g. dissolved gases) would vary between the two samples and so the level of
supercooling required to form ice crystals would vary also.
Thus
it can be reasoned that the observed variations in the extent to which
supercooling occurs must arise, at least in part, due to differences in
convective currents and the relative levels of dissolved gases (further
affected if evaporation occurs). Hence all the factors which have been proposed
to individually cause the Mpemba effect may alter the extent of supercooling
required to cause water to freeze.
Can hot water freeze faster than cold water?
Hot
water can in fact freeze faster than cold water for a wide range of
experimental conditions. This phenomenon is extremely counterintuitive,
and surprising even to most scientists, but it is in fact real. It has
been seen and studied in numerous
experiments.
While
this phenomenon has been known for centuries, and was described by Aristotle,
Bacon, and Descartes, it was not introduced to the modern scientific community
until 1969, by a Tanzanian high school pupil named Mpemba (The Telegraph. 2013; The New York Times 2008).
Three widely cited historical references to Mpemba-like effects in water
The
cooling and freezing of water has intrigued some great scientific minds.
Aristotle, Sir Francis Bacon and René Descartes have all been credited with
consideration of the Mpemba effect
and, although this list is by no means comprehensive, it is worth documenting
the precise observations of these three renowned scientists.
The fact that the water has previously been warmed
contributes to its freezing quickly: for so it cools sooner. Hence many people,
when they want to cool hot water quickly, begin by putting it in the sun. So
the inhabitants of Pontus when they encamp on the ice to fish (they cut a hole in the ice and
then fish) pour warm water round their reeds that it may freeze the
quicker, for they use the ice like lead to fix the reeds.
The
reference to ice as ‘like lead’ in connection to fishing potentially raises
confusion since the use of lead to weight fishing lines is widespread in
traditional fishing; ice being less dense than water clearly makes it
unsuitable for weighting fishing lines. It is our interpretation of the
description ‘like lead to fix the reeds’ that it refers to the stiffening of
the reeds by the formation of ice so that the reeds can be plunged beneath the
water, hence avoiding the need to weight the reeds so that they might sink. It
would, therefore, seem that Aristotle and the peoples of ancient Greece
believed that warming water did make it freeze faster.
No
further discussion nor details are provided. Indeed, it is not clear whether
any of Bacon’s
More recent scientific investigations of the Mpemba effect
The,
now popular, adoption of the name ‘Mpemba effect’ is owed to the lack of
freezer space at a Tanzanian school. While making ice-cream one pupil placed
his mixture of milk and sugar in the freezer without first boiling it; another
pupil, Mpemba, worried that he would not find space in the freezer and put his
boiling mixture straight into the freezer without first allowing it to cool.
Both pupils returned an hour and a half later to find Mpemba’s mixture had
frozen while the other had not.
Mpemba
did not brush this curious observation aside, instead he asked friends (some of
whom made a living selling ice-cream and apparently exploited the time saving
effects of this anomalous behaviour) and teachers to explain his observations
but to no avail.
Mpemba
eventually asked a visiting lecturer from the University of Dar es Salaam to
explain his observations. The open-minded Dr Osborne was intrigued by Mpemba’s
observation and later began investigating the effect with his students,
ultimately publishing a scientific paper with Mpemba on the observed effect (The New York Times 2008).
References
Auerbach, D. 1995. “Supercooling and the Mpemba Effect: When
Hot Water Freezes Quicker than Cold.” American Journal of Physics 63:
882–885.
Bregović, N. n.d. “Mpemba Effect from a Viewpoint of an
Experimental Physical Chemist.”
http://www.rsc.org/learn-chemistry/resource/res00001018/the-mpemba-effect?cmpid=CMP00007615,
(Date of access:05/01/2016) (2012).
J., Jin, and Goddard W. A. 2015. “Mechanisms Underlying the
Mpemba Effect in Water from Molecular Dynamics Simulations.” J. Phys. Chem.
C 5 (119): 2622–29.
The Daily Mail.
2013. “Mystery of Why Hot Water Freezes Faster than Cold Is Solved - and It’s
All down to the Strange Behaviour of Atom Bonds.”
http://www.dailymail.co.uk/sciencetech/article-2483383/Mystery-hot-water-freezes-faster-cold-solved—strange-behaviour-atom-bonds.html,.
“The Mpemba Effect: When Can Hot Water Freeze Faster than
Cold?” 2006. American Journal of Physics 75 (514).
The New York Times.
2008. “The Claim: Cold Water Boils More Quickly than Hot Water.” http://www.nytimes.com/2008/03/18/health/18real.html,.
The Telegraph. 2013.
“Have Scientists Worked out Why Hot Water Freezes Faster than Cold Water?”
http://www.telegraph.co.uk/news/science/science-news/10420496/Have-scientists-worked-out-why-hot-water-freezes-faster-than-cold-water.html.
The Times. 2013. “22,000
Scientists Still Can’t Explain the Boy Who Kept His Cool.”
http://www.thetimes.co.uk/tto/science/physics/article3654099.ece.
Thomas, J. H. 2007. “The Mpemba Effect: Studying the Effects
of Initial Temperature, Evaporation, and Dissolved Gasses on the Freezing of
Water.”
Vynnycky, M, and S Kimura. 2015. “Can Natural Convection
Alone Explain the Mpemba Effect?” Int. J. Heat Mass Transfer 80: 243–225.
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How to cite this article: Haule I.M. Mpemba effect: The rediscovery by a Tanzanian high school pupil named Mpemba: "Inspiring
young scientist to pursue scientific studies." Sokoine University of Agriculture, Morogoro Tanzania. (2017)
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