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DISCUSSIONI. Firth, a physicist who carried out re-
search on the Mpemba effect, stated:
“There is a wealth of experimental vari-
ation in the problem, so that any labo-
ratory undertaking such investigations
is guaranteed different results from all
others”.5 That hits the nail on the head.
We learned that little changes in para-
meters lead to substantially different
results. Additionally one must be careful
in interpreting scientifi c observations. A
single curve might or might not show
the Mpemba effect but is neither a proof
for its existence nor for its non-existence.
On the one hand physical knowledge is
badly needed to design a reasonable experiment,
but on the other hand one has to accompany the
measurements as unbiased as a naive child. There-
by a scientist avoids that experimental results might
be infl uenced, by strongly expecting a certain out-
come.
Even today there is no conclusive description and
broad misbelieve about the Mpemba effect, alt-
hough it is known for more than 2000 years. As-
tonishingly a short and understandable question
leads to a complex physical phenomenon and shows
that even in the 21st century, where many physical
mysteries are believed to be solved, there are some
effects which can neither be described theoretically
nor be proofed wrong by experiments.
ACKNOWLEDGMENTSWe carried out our measurements at the chair of
semiconductor physics at Dresden University of
Technology and would like to thank Dr. Kluge for
his support.
1 Grimm, H., Dr-Ing. (2004). Wissenschaft-Technik-Ethik: Der “Mpemba Effekt” Heißes Wasser gefriert schneller als kaltes Wasser”, Retrieved June 9, 2006, from http://www.wissenschaft-technik-ethik.de/wasser_mpemba-effekt.html.2 Auerbach, D. (1994). Supercooling and the Mpem-ba effect: When hot water freezes quicker than cold. Am. Journal of Physics 63, 882-885.3 Kell, G.S. (1969). The Freezing of Hot and Cold Water. Am. Journal of Physics 37, 564-565.4 Jeng, M. (2004). Hot Water can freeze faster than cold?!? Physics Department, Box 1654 Southern Illi-nois University Edwardsville5 Firth. I. (1971). Cooler. Physics Education, 6, 32-41.6 Kuhn, T.S. (1970) The Structure of Scientifi c Revo-
an initial temperature around 85 degree Celsius.
Therefore we used a methanol tempering bath at
about minus nine degree Celsius.
Sometimes we observed an unexpected behavior of
the water whilst cooling down. Although we tried
to carry out the measurements under equal conditi-
ons, there are a number of infl uences having a much
bigger impact on the cooling than we estimated
beforehand. The air condition e.g. produces very
low humidity. As a result the samples didn’t freeze
but supercooled to the temperature of the tempe-
ring bath or the cooling curves did show different
irregularities. Furthermore the time the water was
exposed to air before the experiment started had
infl uence on the freezing time. Water exposed for
a longer time froze sooner. We used water from
different taps and also deionized water. The latter
became a gel-like substance instead of ice.
When a sample supercooled strongly we could in-
duce the freezing by a slight mechanical bump or
a little motion of the thermocouple. The freezing
front spread out in the beaker within less than a
second and all the water was instantly frozen.
All cooling curves we observed showed the alrea-
dy discussed DCR phase at about two degree Cel-
sius where the temperature was almost constant
for some seconds. Due to the statistical nature of
freezing there is a need for a large number of me-
assurements carried out in order to get reliable
results. The conclusions drawn so far are of cause
preliminary and have to be confi rmed by numerous
further runs. Remarkable is that the cooling curves
could be described by the theoretical derived equa-
tion (derivation given in the textbox on page 2).3
65 70 75 80 85 90
400
450
500
550
600
Figure 3: Dependance of time of freezing on initial temperature
The Mpemba EffectDoes hot water freeze faster than cold?
The so called Mpemba Effect describes the physical phenomenon that of two water
samples, identical in all physical properties apart from one having a higher initial tem-
perature, exposed to the same subzero surroundings, the hotter one might freeze fi rst.
We will track the story of this more than 2000 year old miracle, discuss possible expla-
nations and report about our own experimental observations.
STORYThe Mpemba Effect, although primarily not known
by this name was already mentioned by Aristotle
350 b.c. He described that hot water poured on an
icy surface would freeze quicker than cold and sta-
ted that this can be explained by with the thesis of
antiperistasis, the sudden increase of the intensity
of something surrounded by its contrary.6 Roger
Bacon picked up this idea in the 13th century by
doubting the statement that hot water generally
freezes faster than cold and emphasizing that all
theses have to be verifi ed by experiments. In the
17th century Francis Bacon wrote that “water a litt-
le warmed is more easily frozen than that which
is quite cold”.4 In his famous work “Discourse on
method” (1637) Descartes reports of experiments,
carried out by himself, showing the effect. All tho-
se experiments fell into oblivion with the advent
of the modern theory of heat for more than 300
years.
While making ice cream the Tanzanian student Eras-
to Mpemba observed the effect in 1963 and rein-
troduced the phenomena to modern thermodyna-
mics. At the end of a cooking lesson Mpemba put a
mixture containing hot milk in the freezer whereas
his colleagues waited until theirs had cooled down.
Surprisingly Mpemba found his mixture to be fro-
zen fi rst. Asking his teacher Mpemba was said that
he must have been misled. Nevertheless Mpemba
started more systematic experiments and talked to
Dr Osborne from a nearby University. A few weeks
after Osborne had asked an assistant to carry out
some measurements, he got the report, that they
had measured the effect together with the remark,
“We’ll keep on repeating the experiment until we
get the right results”.4 Mpemba’s and Osborne’s
studies were followed by numerous different ex-
periments which led to contradictory results. This
confusion was strengthened by the fact that there
was no conclusive theoretical explanation for the
effect.
When scientists from all over the world discussed
the phenomenon it turned out to be known as folk-
lore in some parts of the world. Nevertheless text-
book authors and teachers still withhold the cont-
radictory Mpemba effect.
QUESTIONPrior to examine an effect scientifi cally one has to
defi ne precise conditions and aims. In our case, we
have to specify the question and to clarify what
time to freeze means.
Evidently a drop of hot will freeze sooner than an
ocean of cold water, but we are comparing the
freezing times of two water samples initially equal
in all parameters except from one being at a high-
er temperature. This leads directly to the question,
when one defi nes a sample as frozen: Is freezing
the occurrence of fi rst ice crystals, the temperature
reaching zero degree Celsius or when the sample
appears to be completely frozen? Finally we outli-
ned the crucial question of our experiment as fol-
lows: Are there pairs of initial temperatures of two
samples of water which are exposed to the same
subzero temperatures under the same conditions
for which the initially hotter one will freeze fi rst, i.
e. a characteristic temperature jump occurs?2
EXPLANATIONAfter exponential temperature decay, called New-
tonian cooling phase the freezing phase begins.
Therefore on has to distinguish two kinds of free-
zing, spontaneous freezing (the one we observed)
and the subsequent motion of a freezing front
from the wall toward the center of the beaker.2 In
this content freezing means the formation of ice
crystals around nucleators.
A superfi cial approach to the Mpemba effect might
result in a simple argument against it: Once the
warm water is cooled down to the temperature of
Tobias Baldauf & Titus Neupert, Dresden University of Technology, June 2006
the initially cold water it will undergo
the same regime as the initially cold
water and from than on need the same
time to freeze. So all in all it takes lon-
ger to cool the hot water down.
However, the Mpemba effect was ob-
served, so one could draw a simple
conclusion: While the hot water cools
down to the temperature of the initial-
ly cold water it has to change in a way
that it then overtakes the cold water
in freezing. The question is, what that
change in particular is. Although part-
ly contradictory and not conclusive,
common explanations on the Mpem-
ba effect are based on the following
arguments:
Evaporation. Evaporation is the esca-
pe of high energetic molecules from
the water surface into vapor phase.
This escape causes a reduction of the
mass and withdraws energy (enthal-
py of evaporation) from the system.
It was observed that if a majority of
heat was drawn from the system by
evaporation the Mpemba effect seems
to occur more often. A higher surface
temperature of the water increases
the heat loss by evaporation, whereas
additionally less water remains for the
further cooling. If the time gained
by the evaporation process compen-
sates the longer cooling time for the
hot sample the initially hotter samp-
le might freeze fi rst. When the heat
loss is caused only by evaporation, the
maximum mass of water evaporated
amounts to 17 percent.1 Evaporation is
proportional to the difference of the
partial pressure of the water and the
vapor pressure and is therefore very
sensitive to air convection and changes
in humidity. Consequently the Mpem-
ba effect is not likely to be observed
in closed systems, where no matter is
exchanged with the surrounding and
a equilibrium between water and its
vapor developes.
Supercooling. In contrast to common
knowledge water does usually not
Celsius without becoming solid, a phenomenon not
likely to be observed under normal conditions. Con-
nected with the latter, the hot water might show
some kind of memory and tend to stronger super-
cooling.
Solved gases. Solved gases in water might have an
infl uence to the effective heat capacity, the free-
zing temperature and convection. Although water
once degassed by boiling absorbs gases from the
air2, a slightly lower ratio of gas content might have
an infl uence on the cooling process in general and
especially to the tendency to supercool. Gas bub-
bles included in the ice reduce the thermal conduc-
tivity and thus increase the freezing time.
Convection. There is a higher temperature gra-
dient for the initially hotter sample, because the
temperature difference between liquid and wall
or liquid and air is higher. Consequently it forms a
much stronger and faster circulation than the col-
der sample and therefore enhanced heat dissipati-
on leads to faster cooling rates. The fastest molecu-
les gather at the surface and are released as vapor
due to their energy content. Furthermore one has
to consider, that the density of water is a function
of its temperature. Therefore the cooling process
leads to an inhomogeneous temperature distribu-
tion. This becomes obvious during the DCR (densi-
ty caused reorder) period in cooling curves. During
this phase, the temperature stays almost constant
for about 40 seconds. This is due to density caused
reorder processes: The so far developed convec-
tions have to change their direction because of the
anomaly of the density of water. When the colder
parts at the bottom pass four degree Celsius their
density decreases, which causes them to rise to the
top. In addition one has to take into consideration
that freezing is a statistical process
and only a large number of measu-
rements will lead to reliable results.
OUR EXPERIMENTThe Mpemba seems to contradict
our daily experiences. Therefore
our major aim was to observe the
effect with our own eyes to convin-
ce ourselves of its existence. When
creating our experimental setup we
made efforts to generate constant
parameters for the different runs.
Although it is most likely to cool the
samples in a freezer we decided to use an ethanol
tempering bath for realization of constant surroun-
ding temperature. The tempering bath was con-
stantly agitated by a magnetic stirrer and cooled
itself by a copper heat pipe connected to a dewar
fl ask containing liquid nitrogen. The pre-cooled
glass beaker with the sample liquid was prepared
and put in the ethanol. No lid was used to cover
the glass beaker in order to enable free evaporati-
on out of the six square centimeter water surface.
To measure the temperatures of ethanol bath and
water we relied on a combination of a digital ther-
mometer and a copper/constantan thermocouple
connected to a highly sensitive Keithley 182 volt-
meter. Its resolution amounts to 0.1 Kelvin. The
solder connection had to be placed at exatly the
same position, next the surface and about 0.3 cen-
timeters from the wall, for each run.The data were
recorded and visualized automatically. The cooling
curve showed the already mentioned temperature
jump at the moment of spontaneous freezing and
indicated the end of the freezing process. The in-
tensive use of thermal insulation and reduction of
heat input by wires were our attempts to minimize
undesired thermal infl uences.
RESULTSWe all in all carried out about 50 runs, out of which
20 were reasonable and could be used for further
analysis. We created intervals of initial temperatures
and calculated mean values for the freezing time in
each of them. Above all we can state that we have
indeed measured the Mpemba effect. We found
that, under our experimental circumstances, water
with an initial temperature slightly below 80 degree
Celsius will need longer to freeze than water with
Figure 1: Typical cooling curve
Figure 2: Experimental setupFigure 2: Experimental setup
MODELING OF COOLING PROCESS
freeze at exactly zero degree Celsius. It will instead cool down
far below zero degree Celsius and spontaneously freeze accom-
panied by a characteristic temperature jump to zero.1,2 This ef-
fect, caused by a lack of nucleators is called supercooling. Un-
der laboratory conditions water might cool down to -70 degree
the initially cold water it will undergo
the same regime as the initially cold
water and from than on need the same
time to freeze. So all in all it takes lon-
ger to cool the hot water down.
However, the Mpemba effect was ob-
served, so one could draw a simple
conclusion: While the hot water cools
down to the temperature of the initial-
ly cold water it has to change in a way
that it then overtakes the cold water
in freezing. The question is, what that
change in particular is. Although part-
ly contradictory and not conclusive,
common explanations on the Mpem-
ba effect are based on the following
arguments:
Evaporation. Evaporation is the esca-
pe of high energetic molecules from
the water surface into vapor phase.
This escape causes a reduction of the
mass and withdraws energy (enthal-
py of evaporation) from the system.
It was observed that if a majority of
heat was drawn from the system by
evaporation the Mpemba effect seems
to occur more often. A higher surface
temperature of the water increases
the heat loss by evaporation, whereas
additionally less water remains for the
further cooling. If the time gained
by the evaporation process compen-
sates the longer cooling time for the
hot sample the initially hotter samp-
le might freeze fi rst. When the heat
loss is caused only by evaporation, the
maximum mass of water evaporated
amounts to 17 percent.1 Evaporation is
proportional to the difference of the
partial pressure of the water and the
vapor pressure and is therefore very
sensitive to air convection and changes
in humidity. Consequently the Mpem-
ba effect is not likely to be observed
in closed systems, where no matter is
exchanged with the surrounding and
a equilibrium between water and its
vapor developes.
Supercooling. In contrast to common
knowledge water does usually not
Celsius without becoming solid, a phenomenon not
likely to be observed under normal conditions. Con-
nected with the latter, the hot water might show
some kind of memory and tend to stronger super-
cooling.
Solved gases. Solved gases in water might have an
infl uence to the effective heat capacity, the free-
zing temperature and convection. Although water
once degassed by boiling absorbs gases from the
air2, a slightly lower ratio of gas content might have
an infl uence on the cooling process in general and
especially to the tendency to supercool. Gas bub-
bles included in the ice reduce the thermal conduc-
tivity and thus increase the freezing time.
Convection. There is a higher temperature gra-
dient for the initially hotter sample, because the
temperature difference between liquid and wall
or liquid and air is higher. Consequently it forms a
much stronger and faster circulation than the col-
der sample and therefore enhanced heat dissipati-
on leads to faster cooling rates. The fastest molecu-
les gather at the surface and are released as vapor
due to their energy content. Furthermore one has
to consider, that the density of water is a function
of its temperature. Therefore the cooling process
leads to an inhomogeneous temperature distribu-
tion. This becomes obvious during the DCR (densi-
ty caused reorder) period in cooling curves. During
this phase, the temperature stays almost constant
for about 40 seconds. This is due to density caused
reorder processes: The so far developed convec-
tions have to change their direction because of the
anomaly of the density of water. When the colder
parts at the bottom pass four degree Celsius their
density decreases, which causes them to rise to the
top. In addition one has to take into consideration
that freezing is a statistical process
and only a large number of measu-
rements will lead to reliable results.
OUR EXPERIMENTThe Mpemba seems to contradict
our daily experiences. Therefore
our major aim was to observe the
effect with our own eyes to convin-
ce ourselves of its existence. When
creating our experimental setup we
made efforts to generate constant
parameters for the different runs.
Although it is most likely to cool the
samples in a freezer we decided to use an ethanol
tempering bath for realization of constant surroun-
ding temperature. The tempering bath was con-
stantly agitated by a magnetic stirrer and cooled
itself by a copper heat pipe connected to a dewar
fl ask containing liquid nitrogen. The pre-cooled
glass beaker with the sample liquid was prepared
and put in the ethanol. No lid was used to cover
the glass beaker in order to enable free evaporati-
on out of the six square centimeter water surface.
To measure the temperatures of ethanol bath and
water we relied on a combination of a digital ther-
mometer and a copper/constantan thermocouple
connected to a highly sensitive Keithley 182 volt-
meter. Its resolution amounts to 0.1 Kelvin. The
solder connection had to be placed at exatly the
same position, next the surface and about 0.3 cen-
timeters from the wall, for each run.The data were
recorded and visualized automatically. The cooling
curve showed the already mentioned temperature
jump at the moment of spontaneous freezing and
indicated the end of the freezing process. The in-
tensive use of thermal insulation and reduction of
heat input by wires were our attempts to minimize
undesired thermal infl uences.
RESULTSWe all in all carried out about 50 runs, out of which
20 were reasonable and could be used for further
analysis. We created intervals of initial temperatures
and calculated mean values for the freezing time in
each of them. Above all we can state that we have
indeed measured the Mpemba effect. We found
that, under our experimental circumstances, water
with an initial temperature slightly below 80 degree
Celsius will need longer to freeze than water with
Figure 1: Typical cooling curve
Figure 2: Experimental setupFigure 2: Experimental setup
MODELING OF COOLING PROCESS
freeze at exactly zero degree Celsius. It will instead cool down
far below zero degree Celsius and spontaneously freeze accom-
panied by a characteristic temperature jump to zero.1,2 This ef-
fect, caused by a lack of nucleators is called supercooling. Un-
der laboratory conditions water might cool down to -70 degree
DISCUSSIONI. Firth, a physicist who carried out re-
search on the Mpemba effect, stated:
“There is a wealth of experimental vari-
ation in the problem, so that any labo-
ratory undertaking such investigations
is guaranteed different results from all
others”.5 That hits the nail on the head.
We learned that little changes in para-
meters lead to substantially different
results. Additionally one must be careful
in interpreting scientifi c observations. A
single curve might or might not show
the Mpemba effect but is neither a proof
for its existence nor for its non-existence.
On the one hand physical knowledge is
badly needed to design a reasonable experiment,
but on the other hand one has to accompany the
measurements as unbiased as a naive child. There-
by a scientist avoids that experimental results might
be infl uenced, by strongly expecting a certain out-
come.
Even today there is no conclusive description and
broad misbelieve about the Mpemba effect, alt-
hough it is known for more than 2000 years. As-
tonishingly a short and understandable question
leads to a complex physical phenomenon and shows
that even in the 21st century, where many physical
mysteries are believed to be solved, there are some
effects which can neither be described theoretically
nor be proofed wrong by experiments.
ACKNOWLEDGMENTSWe carried out our measurements at the chair of
semiconductor physics at Dresden University of
Technology and would like to thank Dr. Kluge for
his support.
1 Grimm, H., Dr-Ing. (2004). Wissenschaft-Technik-Ethik: Der “Mpemba Effekt” Heißes Wasser gefriert schneller als kaltes Wasser”, Retrieved June 9, 2006, from http://www.wissenschaft-technik-ethik.de/wasser_mpemba-effekt.html.2 Auerbach, D. (1994). Supercooling and the Mpem-ba effect: When hot water freezes quicker than cold. Am. Journal of Physics 63, 882-885.3 Kell, G.S. (1969). The Freezing of Hot and Cold Water. Am. Journal of Physics 37, 564-565.4 Jeng, M. (2004). Hot Water can freeze faster than cold?!? Physics Department, Box 1654 Southern Illi-nois University Edwardsville5 Firth. I. (1971). Cooler. Physics Education, 6, 32-41.6 Kuhn, T.S. (1970) The Structure of Scientifi c Revo-
an initial temperature around 85 degree Celsius.
Therefore we used a methanol tempering bath at
about minus nine degree Celsius.
Sometimes we observed an unexpected behavior of
the water whilst cooling down. Although we tried
to carry out the measurements under equal conditi-
ons, there are a number of infl uences having a much
bigger impact on the cooling than we estimated
beforehand. The air condition e.g. produces very
low humidity. As a result the samples didn’t freeze
but supercooled to the temperature of the tempe-
ring bath or the cooling curves did show different
irregularities. Furthermore the time the water was
exposed to air before the experiment started had
infl uence on the freezing time. Water exposed for
a longer time froze sooner. We used water from
different taps and also deionized water. The latter
became a gel-like substance instead of ice.
When a sample supercooled strongly we could in-
duce the freezing by a slight mechanical bump or
a little motion of the thermocouple. The freezing
front spread out in the beaker within less than a
second and all the water was instantly frozen.
All cooling curves we observed showed the alrea-
dy discussed DCR phase at about two degree Cel-
sius where the temperature was almost constant
for some seconds. Due to the statistical nature of
freezing there is a need for a large number of me-
assurements carried out in order to get reliable
results. The conclusions drawn so far are of cause
preliminary and have to be confi rmed by numerous
further runs. Remarkable is that the cooling curves
could be described by the theoretical derived equa-
tion (derivation given in the textbox on page 2).3
65 70 75 80 85 90
400
450
500
550
600
Figure 3: Dependance of time of freezing on initial temperature
The Mpemba EffectDoes hot water freeze faster than cold?
The so called Mpemba Effect describes the physical phenomenon that of two water
samples, identical in all physical properties apart from one having a higher initial tem-
perature, exposed to the same subzero surroundings, the hotter one might freeze fi rst.
We will track the story of this more than 2000 year old miracle, discuss possible expla-
nations and report about our own experimental observations.
STORYThe Mpemba Effect, although primarily not known
by this name was already mentioned by Aristotle
350 b.c. He described that hot water poured on an
icy surface would freeze quicker than cold and sta-
ted that this can be explained by with the thesis of
antiperistasis, the sudden increase of the intensity
of something surrounded by its contrary.6 Roger
Bacon picked up this idea in the 13th century by
doubting the statement that hot water generally
freezes faster than cold and emphasizing that all
theses have to be verifi ed by experiments. In the
17th century Francis Bacon wrote that “water a litt-
le warmed is more easily frozen than that which
is quite cold”.4 In his famous work “Discourse on
method” (1637) Descartes reports of experiments,
carried out by himself, showing the effect. All tho-
se experiments fell into oblivion with the advent
of the modern theory of heat for more than 300
years.
While making ice cream the Tanzanian student Eras-
to Mpemba observed the effect in 1963 and rein-
troduced the phenomena to modern thermodyna-
mics. At the end of a cooking lesson Mpemba put a
mixture containing hot milk in the freezer whereas
his colleagues waited until theirs had cooled down.
Surprisingly Mpemba found his mixture to be fro-
zen fi rst. Asking his teacher Mpemba was said that
he must have been misled. Nevertheless Mpemba
started more systematic experiments and talked to
Dr Osborne from a nearby University. A few weeks
after Osborne had asked an assistant to carry out
some measurements, he got the report, that they
had measured the effect together with the remark,
“We’ll keep on repeating the experiment until we
get the right results”.4 Mpemba’s and Osborne’s
studies were followed by numerous different ex-
periments which led to contradictory results. This
confusion was strengthened by the fact that there
was no conclusive theoretical explanation for the
effect.
When scientists from all over the world discussed
the phenomenon it turned out to be known as folk-
lore in some parts of the world. Nevertheless text-
book authors and teachers still withhold the cont-
radictory Mpemba effect.
QUESTIONPrior to examine an effect scientifi cally one has to
defi ne precise conditions and aims. In our case, we
have to specify the question and to clarify what
time to freeze means.
Evidently a drop of hot will freeze sooner than an
ocean of cold water, but we are comparing the
freezing times of two water samples initially equal
in all parameters except from one being at a high-
er temperature. This leads directly to the question,
when one defi nes a sample as frozen: Is freezing
the occurrence of fi rst ice crystals, the temperature
reaching zero degree Celsius or when the sample
appears to be completely frozen? Finally we outli-
ned the crucial question of our experiment as fol-
lows: Are there pairs of initial temperatures of two
samples of water which are exposed to the same
subzero temperatures under the same conditions
for which the initially hotter one will freeze fi rst, i.
e. a characteristic temperature jump occurs?2
EXPLANATIONAfter exponential temperature decay, called New-
tonian cooling phase the freezing phase begins.
Therefore on has to distinguish two kinds of free-
zing, spontaneous freezing (the one we observed)
and the subsequent motion of a freezing front
from the wall toward the center of the beaker.2 In
this content freezing means the formation of ice
crystals around nucleators.
A superfi cial approach to the Mpemba effect might
result in a simple argument against it: Once the
warm water is cooled down to the temperature of
Tobias Baldauf & Titus Neupert, Dresden University of Technology, June 2006
Recommended