You might find this interesting...
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Hot water can in fact freeze faster than cold water for a wide range
of experimental conditions. This phenomenon is extremely counter-
intuitive, 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 [1-3], it was not introduced to the
modern scientific community until 1969, by a Tanzanian high school
student named Mpemba. Both the early scientific history of this
effect, and the story of Mpemba's rediscovery of it, are interesting
in their own right -- Mpemba's story in particular provides a dramatic
parable against making snap judgements about what is impossible. This
is described separately below.
The phenomenon that hot water may freeze faster than cold is often
called the Mpemba effect. Because, no doubt, most readers are
extremely skeptical at this point, we should begin by stating
precisely what we mean by the Mpemba effect. We start with two
containers of water, which are identical in shape, and which hold
identical amounts of water. The only difference between the two is
that the water in one is at a higher (uniform) temperature than the
water in the other. Now we cool both containers, using the exact same
cooling process for each container. Under some conditions the
initially warmer water will freeze first. If this occurs, we have
seen the Mpemba effect. Of course, the initially warmer water will
not freeze before the initially cooler water for all initial
conditions. If the hot water starts at 99.9° C, and the cold water at
0.01° C, then clearly under those circumstances, the initially cooler
water will freeze first. However, under some conditions the initially
warmer water will freeze first -- if that happens, you have seen the
Mpemba effect. But you will not see the Mpemba effect for just any
initial temperatures, container shapes, or cooling conditions.
This seems impossible, right? Many sharp readers may have already come
up with a common proof that the Mpemba effect is impossible. The
proof usually goes something like this. Say that the initially cooler
water starts at 30° C and takes 10 minutes to freeze, while the
initially warmer water starts out at 70° C. Now the initially warmer
water has to spend some time cooling to get to get down to 30° C, and
after that, it's going to take 10 more minutes to freeze. So since
the initially warmer water has to do everything that the initially
cooler water has to do, plus a little more, it will take at least a
little longer, right? What can be wrong with this proof?
What's wrong with this proof is that it implicitly assumes that the
water is characterized solely by a single number -- the average
temperature. But if other factors besides the average temperature are
important, then when the initially warmer water has cooled to an
average temperature of 30° C, it may look very different than the
initially cooler water (at a uniform 30° C) did at the start. Why?
Because the water may have changed when it cooled down from a uniform
70° C to an average 30° C. It could have less mass, less dissolved
gas, or convection currents producing a non-uniform temperature
distribution. Or it could have changed the environment around the
container in the refrigerator. All four of these changes are
conceivably important, and each will be considered separately below.
So the impossibility proof given above doesn't work. And in fact the
Mpemba effect has been observed in a number of controlled experiments
[5,7-14]
It is still not known exactly why this happens. A number of possible
explanations for the effect have been proposed, but so far the
experiments do not show clearly which, if any, of the proposed
mechanisms is the most important one. While you will often hear
confident claims that X is the cause of the Mpemba effect, such claims
are usually based on guesswork, or on looking at the evidence in only
a few papers and ignoring the rest. Of course, there is nothing wrong
with informed theoretical guesswork or being selective in which
experimental results you trust -- the problem is that different people
make different claims as to what X is.
Why hasn't modern science answered this seemingly simple question
about cooling water? The main problem is that the time it takes water
to freeze is highly sensitive to a number of details in the
experimental set- up, such as the shape and size of the container, the
shape and size of the refrigeration unit, the gas and impurity content
of the water, how the time of freezing is defined, and so on. Because
of this sensitivity, while experiments have generally agreed that the
Mpemba effect occurs, they disagree over the conditions under which it
occurs, and thus about why it occurs. As Firth [7] wrote "There is a
wealth of experimental variation in the problem so that any laboratory
undertaking such investigations is guaranteed different results from
all others."
So with the limited number of experiments done, often under very
different conditions, none of the proposed mechanisms can be
confidently proclaimed as "the" mechanism. Above we described four
ways in which the initially warmer water could have changed upon
cooling to the initial temperature of the initially cooler water.
What follows below is a short description of the four related
mechanisms that have been suggested to explain the Mpemba effect.
More ambitious readers can follow the links to more complete
explanations of the mechanisms, as well as counter- arguments and
experiments that the mechanisms cannot explain. It seems likely that
there is no one mechanism that explains the Mpemba effect for all
circumstances, but that different mechanisms are important under
different conditions.
1. Evaporation -- As the initially warmer water cools to the
initial temperature of the initially cooler water, it may lose
significant amounts of water to evaporation. The reduced mass will
make it easier for the water to cool and freeze. Then the initially
warmer water can freeze before the initially cooler water, but will
make less ice. Theoretical calculations have shown that evaporation
can explain the Mpemba effect if you assume that the water loses heat
solely through evaporation [11]. This explanation is solid,
intuitive, and evaporation is undoubtedly important in most
situations. However, it is not the only mechanism. Evaporation
cannot explain experiments that were done in closed containers, where
no mass was lost to evaporation [12]. And many scientists have
claimed that evaporation alone is insufficient to explain their
results [5,9,12].
2. Dissolved Gasses -- Hot water can hold less dissolved gas than
cold water, and large amounts of gas escape upon boiling. So the
initially warmer water may have less dissolved gas than the initially
cooler water. It has been speculated that this changes the properties
of the water in some way, perhaps making it easier to develop
convection currents (and thus making it easier to cool), or decreasing
the amount of heat required to freeze a unit mass of water, or
changing the boiling point. There are some experiments that favor
this explanation [10,14], but no supporting theoretical calculations.
3. Convection -- As the water cools it will eventually develop
convection currents and a non-uniform temperature distribution. At
most temperatures, density decreases with increasing temperature, and
so the surface of the water will be warmer than the bottom -- this has
been called a "hot top." Now if the water loses heat primarily through
the surface, then water with a "hot top" will lose heat faster than we
would expect based on its average temperature. When the initially
warmer water has cooled to an average temperature the same as the
initial temperature of the initially cooler water, it will have a "hot
top", and thus its rate of cooling will be faster than the rate of
cooling of the initially cooler water at the same average temperature.
Got all that? You might want to read this paragraph again, paying
careful distinction to the difference between initial temperature,
average temperature, and temperature. While experiments have seen the
"hot top", and related convection currents, it is unknown whether
convection can by itself explain the Mpemba effect.
4. Surroundings -- A final difference between the cooling of the
two containers relates not to the water itself, but to the surrounding
environment. The initially warmer water may change the environment
around it in some complex fashion, and thus affect the cooling
process. For example, if the container is sitting on a layer of frost
which conducts heat poorly, the hot water may melt that layer of
frost, and thus establish a better cooling system in the long run.
Obviously explanations like this are not very general, since most
experiments are not done with containers sitting on layers of frost.
Finally, supercooling may be important to the effect. Supercooling
occurs when the water freezes not at 0° C, but at some lower
temperature. One experiment [12] found that the initially hot water
would supercool less than the initially cold water. This would mean
that the initially warmer water might freeze first because it would
freeze at a higher temperature than the initially cooler water. If
true, this would not fully explain the Mpemba effect, because we would
still need to explain why initially warmer water supercools less than
initially cooler water.
In short, hot water does freeze sooner than cold water under a wide
range of circumstances. It is not impossible, and has been seen to
occur in a number of experiments. However, despite claims often made
by one source or another, there is no well-agreed explanation for how
this phenomenon occurs. Different mechanisms have been proposed, but
the experimental evidence is inconclusive. For those wishing to read
more on the subject, Jearl Walker's article in Scientific American
[13] is very readable and has suggestions on how to do home
experiments on the Mpemba effect, while the articles by Auerbach [12]
and Wojciechowski [14] are two of the more modern papers on the
effect.
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http://math.ucr.edu/home/baez/physics/General/hot_water.html |
