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