Editing Mpemba effect

{{Short description|Natural phenomenon that hot water freezes faster than cold}}
[[File:Mpemba Effect temperatures plot.png|thumb|upright=1.35|Temperature vs time plots, showing the Mpemba Effect.]]
The '''Mpemba effect''' is the [[observation]] that a [[liquid]] (typically [[water]]) that is initially hot can [[freezing|freeze]] faster than the same liquid which begins cold, under otherwise similar conditions. There is disagreement about its theoretical basis and the parameters required to produce the effect.<ref name="Burridge">{{cite journal|doi=10.1038/srep37665 |pmid=27883034 |pmc=5121640 |title=Questioning the Mpemba effect: Hot water does not cool more quickly than cold |journal=Scientific Reports |volume=6 |pages=37665 |year=2016 |last1=Burridge |first1=Henry C. |last2=Linden |first2=Paul F. |bibcode=2016NatSR...637665B}}</ref><ref name="Tao">{{cite journal|doi=10.1021/acs.jctc.6b00735 |pmid=27996255 |title=Different Ways of Hydrogen Bonding in Water - Why Does Warm Water Freeze Faster than Cold Water? |journal=Journal of Chemical Theory and Computation |volume=13 |issue=1 |pages=55–76 |year=2017 |last1=Tao |first1=Yunwen |last2=Zou |first2=Wenli |last3=Jia |first3=Junteng |last4=Li |first4=Wei |last5=Cremer |first5=Dieter}}</ref>

The Mpemba effect is named after Tanzanian [[Erasto B. Mpemba|Erasto Bartholomeo Mpemba]], who described it in 1963 as a [[secondary school]] student. The initial discovery and observations of the effect originate in ancient times; [[Aristotle]] said that it was common knowledge.<ref>[[Aristotle]] in E. W. Webster, ''[[Meteorology (Aristotle)|Meteorologica I]]'', Oxford: Oxford University Press, 1923, pp. 348b–349a.</ref>

== Definition ==
The phenomenon, when taken to mean "hot water freezes faster than cold", is difficult to reproduce or confirm because it is ill-defined.<ref name="ball" /> Monwhea Jeng proposed a more precise wording: "There exists a set of initial parameters, and a pair of temperatures, such that given two bodies of water identical in these parameters, and differing only in initial uniform temperatures, the hot one will freeze sooner."<ref name="Jeng">{{Cite journal |title=Hot water can freeze faster than cold?!? |journal=American Journal of Physics |year=2006 |first=Monwhea |last=Jeng |volume=74 |issue=6 |pages=514–522 |arxiv=physics/0512262 |doi=10.1119/1.2186331 |bibcode=2006AmJPh..74..514J}}</ref>

Even with Jeng's definition, it is not clear whether "freezing" refers to the point at which water forms a visible surface layer of ice, the point at which the entire volume of water becomes a solid block of ice, or when the water reaches {{convert|0|C|F K}}.<ref name="ball" /> Jeng's definition suggests simple ways in which the effect might be observed, such as if a warmer temperature melts the frost on a cooling surface, thereby increasing thermal conductivity between the cooling surface and the water container.<ref name="ball" /> Alternatively, the Mpemba effect may not be evident in situations and under circumstances that at first seem to qualify.<ref name="ball" />

== Observations ==

=== Historical context ===
Various effects of heat on the freezing of water were described by ancient scientists, including [[Aristotle]]: "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 water quickly, begin by putting it in the sun."<ref>{{cite web|url=http://classics.mit.edu/Aristotle/meteorology.1.i.html |author=Aristotle |author-link=Aristotle |title=Meteorology |at=Book I, part 12, pp.&nbsp;348b31–349a4 |access-date=2020-10-16 |via=MIT}}</ref> Aristotle's explanation involved ''[[antiperistasis]]'': "...the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality."{{citation needed|date=March 2022}}

[[Francis Bacon]] noted that "slightly tepid water freezes more easily than that which is utterly cold."<ref>[[Francis Bacon|Bacon, Francis]]; ''Novum Organum'', [http://www.thelatinlibrary.com/bacon/bacon.liber2.shtml Lib. II], L. In the original [[Latin]]: "Aqua parum tepida facilius conglacietur quam omnino frigida."</ref> [[René Descartes]] wrote in his ''[[Discourse on the Method]]'', relating the phenomenon to his [[Descartes' vortex theory|vortex theory]]: "One can see by experience that water that has been kept on a fire for a long time freezes faster than other, the reason being that those of its particles that are least able to stop bending evaporate while the water is being heated."<ref>{{Cite web |last=Descartes |first=René |author-link=René Descartes |title=Les Météores |url=http://posner.library.cmu.edu/Posner/books/pages.cgi?call=423_D44D_1637&layout=vol0/part0/copy0&file=0247 |access-date=2024-03-19}}</ref>

Scottish scientist [[Joseph Black]] in 1775 investigated a special case of the phenomenon by comparing previously boiled with unboiled water.<ref>{{cite journal |last1=Black |first1=Joseph |title=The Supposed Effect of Boiling upon Water, in Disposing It to Freeze More Readily, Ascertained by Experiments. By Joseph Black, M. D. Professor of Chemistry at Edinburgh, in a Letter to Sir John Pringle, Bart. P. R. S. |journal=Philosophical Transactions of the Royal Society of London |date=1 January 1775 |volume=65 |pages=124–128 |doi=10.1098/rstl.1775.0014 |bibcode=1775RSPT...65..124B |s2cid=186214388}}</ref> He found that the previously boiled water froze more quickly, even when evaporation was [[Scientific control|controlled]] for. He discussed the influence of stirring on the results of the experiment, noting that stirring the unboiled water led to it freezing at the same time as the previously boiled water, and also noted that stirring the very-cold unboiled water led to immediate freezing. Joseph Black then discussed [[Daniel Gabriel Fahrenheit|Daniel Gabriel Fahrenheit's]] description of [[supercooling]] of water, arguing that the previously boiled water could not be as readily supercooled.{{citation needed|date=March 2022}}

=== Mpemba's observation ===
The effect is named after Tanzanian student [[Erasto B. Mpemba|Erasto Mpemba]]. He described it in 1963 in Form 3 of Magamba Secondary School, [[Tanganyika (1961–1964)|Tanganyika]]; when freezing a hot ice cream mixture in a cookery class, he noticed that it froze before a cold mixture. He later became a student at Mkwawa Secondary (formerly High) School in [[Iringa]]. The headmaster invited Dr. [[Denis Osborne]] from the University College in [[Dar es Salaam]] to give a lecture on physics. After the lecture, Mpemba asked him, "If you take two similar containers with equal volumes of water, one at {{convert|35|C}} and the other at {{convert|100|C}}, and put them into a freezer, the one that started at {{convert|100|C}} freezes first. Why?" Mpemba was at first ridiculed by both his classmates and his teacher. After initial consternation, however, Osborne experimented on the issue back at his workplace and confirmed Mpemba's finding. They published the results together in 1969, while Mpemba was studying at the [[College of African Wildlife Management]].<ref name="Mpemba">{{Cite journal|last1=Mpemba |first1=Erasto B. |last2=Osborne |first2=Denis G. |title=Cool? |journal=Physics Education |year=1969 |volume=4 |issue=3 |pages=172–175 |doi=10.1088/0031-9120/4/3/312 |bibcode=1969PhyEd...4..172M|s2cid=250771765 |doi-access=free }} republished as {{Cite journal|title=The Mpemba effect |journal=Physics Education |year=1979 |volume=14 |issue=7 |pages=410–412 |doi=10.1088/0031-9120/14/7/312 |last1=Mpemba |first1=Erasto B. |last2=Osborne |first2=Denis G. |bibcode=1979PhyEd..14..410M|s2cid=250736457 }}</ref>

Mpemba and Osborne described placing {{convert|70|ml|abbr=on}} samples of water in {{convert|100|ml|abbr=on}} beakers in the icebox of a domestic refrigerator on a sheet of polystyrene foam. They showed the time for freezing to start was longest with an initial temperature of {{convert|25|C}} and that it was much less at around {{convert|90|C}}. They ruled out loss of liquid volume by evaporation and the effect of dissolved air as significant factors. In their setup, most heat loss was found to be from the liquid surface.<ref name="Mpemba" />

=== Modern experimental work ===
David Auerbach has described an effect that he observed in samples in glass beakers placed into a liquid cooling bath. In all cases the water supercooled, reaching a temperature of typically {{convert|-6|to|-18|C|F K}} before spontaneously freezing. Considerable random variation was observed in the time required for spontaneous freezing to start and in some cases this resulted in the water which started off hotter (partially) freezing first.<ref>{{Cite journal
| first=David
| last=Auerbach
| url=http://robot-tag.com/evan/ajp-mpemba.pdf
| title=Supercooling and the Mpemba effect: when hot water freezes quicker than cold
| journal=[[American Journal of Physics]]
| volume=63
| year=1995
| pages=882–885
| doi=10.1119/1.18059
| issue=10
| bibcode = 1995AmJPh..63..882A }}</ref>

In 2016, Burridge and Linden defined the criterion as the time to reach {{convert|0|°C|°F K}}, carried out experiments, and reviewed published work to date. They noted that the large difference originally claimed had not been replicated, and that studies showing a small effect could be influenced by variations in the positioning of thermometers: "We conclude, somewhat sadly, that there is no evidence to support meaningful observations of the Mpemba effect."<ref name="Burridge" />

In controlled experiments, the effect can entirely be explained by undercooling and the time of freezing was determined by what container was used.<ref name="Brownridge 2011" >{{Cite journal
| title=When does hot water freeze faster then &#91;sic&#93; cold water? A search for the Mpemba effect
| journal=American Journal of Physics
| volume=79
| issue=78
|first1=James |last1=Brownridge
| year=2011
| pages=78–84
| doi=10.1119/1.3490015
| bibcode=2011AmJPh..79...78B
}}

Experimental results confirming the Mpemba effect have been criticized for being flawed, not accounting for dissolved solids and gasses, and other confounding factors.</ref> Experimental results confirming the Mpemba effect have been criticized for being flawed, not accounting for dissolved solids and gasses, and other confounding factors.<ref name="arxiv.org">{{Cite book|arxiv=2010.07287|last1=Elton|first1=Daniel C.|last2=Spencer|first2=Peter D.|title=Water in Biomechanical and Related Systems|chapter=Pathological Water Science – Four Examples and What They Have in Common|series=Biologically-Inspired Systems|year=2021|volume=17|pages=155–169|doi=10.1007/978-3-030-67227-0_8|isbn=978-3-030-67226-3|s2cid=222381017}}</ref>

Philip Ball, a reviewer for ''[[Physics World]]'' wrote: "Even if the Mpemba effect is real — if hot water can sometimes freeze more quickly than cold — it is not clear whether the explanation would be trivial or illuminating."<ref name="ball" /> Ball wrote that investigations of the phenomenon need to control a large number of initial parameters (including type and initial temperature of the water, dissolved gas and other impurities, and size, shape and material of the container, and temperature of the refrigerator) and need to settle on a particular method of establishing the time of freezing, all of which might affect the presence or absence of the Mpemba effect. The required vast multidimensional array of experiments might explain why the effect is not yet understood.<ref name="ball">{{Cite web |last=Ball |first=Philip |date=2006-03-29 |title=Does hot water freeze first? |url=https://physicsworld.com/a/does-hot-water-freeze-first/ |access-date=2024-03-19 |website=Physics World |pages=19–26 |language=en-GB}}</ref>

''[[New Scientist]]'' recommends starting the experiment with containers at {{convert|35|and|5|C|F K}}, respectively, to maximize the effect.<ref>''How to Fossilize Your Hamster: And Other Amazing Experiments for the Armchair Scientist'', {{ISBN|1-84668-044-1}}</ref>

== Suggested explanations ==
While the actual occurrence of the Mpemba effect is disputed,<ref name="arxiv.org" /> several theoretical explanations could explain its occurrence.

In 2017, two research groups independently and simultaneously found a theoretical Mpemba effect and also predicted a new "inverse" Mpemba effect in which heating a cooled, far-from-equilibrium system takes less time than another system that is initially closer to equilibrium. Zhiyue Lu and Oren Raz yielded a general criterion based on [[Andrey Markov|Markovian]] statistical mechanics, predicting the appearance of the inverse Mpemba effect in the [[Ising model]] and diffusion dynamics.<ref>{{Cite journal |last1=Lu |first1=Zhiyue |last2=Raz |first2=Oren |date=2017-05-16 |title=Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse |journal=Proceedings of the National Academy of Sciences |language=en |volume=114 |issue=20 |pages=5083–5088 |arxiv=1609.05271 |bibcode=2017PNAS..114.5083L |doi=10.1073/pnas.1701264114 |issn=0027-8424 |pmc=5441807 |pmid=28461467 |doi-access=free}}</ref> Antonio Lasanta and co-authors also predicted the direct and inverse Mpemba effects for a [[Granular material#Granular gases|granular gas]] in a far-from-equilibrium initial state.<ref name=":0">{{Cite journal |last1=Lasanta |first1=Antonio |last2=Vega Reyes |first2=Francisco |last3=Prados |first3=Antonio |last4=Santos |first4=Andrés |date=2017 |title=When the Hotter Cools More Quickly: Mpemba Effect in Granular Fluids |journal=Physical Review Letters |volume=119 |issue=14 |pages=148001 |arxiv=1611.04948 |bibcode=2017PhRvL.119n8001L |doi=10.1103/physrevlett.119.148001 |pmid=29053323 |s2cid=197471205 |hdl=10016/25838}}</ref> Lasanta's paper also suggested that a very generic mechanism leading to both Mpemba effects is due to a particle velocity [[Distribution function (physics)|distribution function]] that significantly deviates from the [[Maxwell–Boltzmann distribution]].<ref name=":0" /> 

James Brownridge, a physicist at [[Binghamton University]], has said that [[supercooling]] is involved.<ref>{{cite news |last1=Chown |first1=Marcus |date=24 March 2010 |title=Revealed: why hot water freezes faster than cold |work=New Scientist |url=https://www.newscientist.com/article/mg20527535.200-revealed-why-hot-water-freezes-faster-than-cold/}}</ref><ref name="Brownridge 2011" /> Several [[molecular dynamics]] simulations have also supported that changes in [[hydrogen bonding]] during supercooling take a major role in the process.<ref name="Jin" /><ref name="Sun">{{Cite journal |last1=Xi |first1=Zhang |last2=Huang |first2=Yongli |last3=Ma |first3=Zengsheng |last4=Zhou |first4=Yichun |last5=Zhou |first5=Ji |last6=Zheng |first6=Weitao |last7=Jiange |first7=Qing |last8=Sun |first8=Chang Q. |year=2014 |title=Hydrogen-bond memory and water-skin supersolidity resolving the Mpemba paradox |journal=Physical Chemistry Chemical Physics |volume=16 |issue=42 |pages=22995–23002 |arxiv=1310.6514 |bibcode=2014PCCP...1622995Z |doi=10.1039/C4CP03669G |pmid=25253165 |s2cid=119280061}}</ref> In 2017, Yunwen Tao and co-authors suggested that the vast diversity and peculiar occurrence of different hydrogen bonds could contribute to the effect. They argued that the number of strong hydrogen bonds increases as temperature is elevated, and that the existence of the small strongly bonded clusters facilitates in turn the [[nucleation]] of [[Ice Ih|hexagonal ice]] when warm water is rapidly cooled down. The authors used [[vibrational spectroscopy]] and modelling with [[density functional theory]]-optimized water clusters.<ref name="Tao" />

The following explanations have also been proposed:
* [[Microbubble]]-induced heat transfer: The process of boiling induced microbubbles in water that remain stably suspended as the water cools, then act by convection to transfer heat more quickly as the water cools.<ref>{{cite journal |last1=Zimmerman |first1=William B. |title=Towards a microbubble condenser: Dispersed microbubble mediation of additional heat transfer in aqueous solutions due to phase change dynamics in airlift vessels |journal=Chemical Engineering Science |date=20 July 2021 |volume=238 |pages=116618 |doi=10.1016/j.ces.2021.116618 |language=en|doi-access=free |bibcode=2021ChEnS.23816618Z }}</ref><ref>{{cite news |last1=Whipple |first1=Tom |title=Cracked, the cold case of why boiling water freezes faster |url=https://www.thetimes.com/uk/science/article/cracked-the-cold-case-of-why-boiling-water-freezes-faster-h0v3j2d2f |work=[[The Times]] |date=13 April 2021 |language=en}}</ref>
* [[Evaporation]]: The evaporation of the warmer water reduces the mass of the water to be frozen.<ref name="Kell">{{Cite journal|last=Kell |first=George S. |title=The freezing of hot and cold water |journal=American Journal of Physics |year=1969 |volume=37 |pages=564–565 |doi=10.1119/1.1975687 |issue=5 |bibcode=1969AmJPh..37..564K|doi-access=free }}</ref> Evaporation is [[endothermic]], meaning that the water mass is cooled by vapor carrying away the heat, but this alone probably does not account for the entirety of the effect.<ref name="Jeng" />
* [[Convection]], accelerating [[heat transfer]]s: Reduction of water density below {{convert|4|°C|°F}} tends to suppress the convection currents that cool the lower part of the liquid mass; the lower density of hot water would reduce this effect, perhaps sustaining the more rapid initial cooling. Higher convection in the warmer water may also spread ice crystals around faster.<ref>[[CITV]] ''[[Prove It!]]'' [http://www.proveit.tv/series-1/fs.html?p=13&s=3 Series 1 Programme 13] {{Webarchive|url=https://web.archive.org/web/20120227055109/http://www.proveit.tv/series-1/fs.html?p=13&s=3 |date=27 February 2012 }}</ref>
* [[Frost]]: Frost has [[Thermal insulation|insulating]] effects. The lower temperature water will tend to freeze from the top, reducing further heat loss by radiation and air convection, while the warmer water will tend to freeze from the bottom and sides because of water convection. This is disputed as there are experiments that account for this factor.<ref name="Jeng" />
* [[Solutes]]: [[Calcium carbonate]], [[magnesium carbonate]], and other mineral salts dissolved in water can precipitate out when water is boiled, leading to an increase in the freezing point compared to non-boiled water that contains all the dissolved minerals.<ref>{{Cite journal|arxiv=physics/0604224 |title=When hot water freezes before cold |journal=American Journal of Physics |volume=77 |issue=27 |pages=27–29 |last=Katz |first=Jonathan |year=2009 |doi=10.1119/1.2996187 |bibcode=2009AmJPh..77...27K |s2cid=119356481}}</ref>
* [[Thermal conductivity]]:
*# The container of hotter liquid may melt through a layer of frost that is acting as an insulator under the container (frost is an insulator, as mentioned above), allowing the container to come into direct contact with a much colder lower layer that the frost formed on (ice, refrigeration coils, etc.) The container now rests on a much colder surface (or one better at removing heat, such as refrigeration coils) than the originally colder water, and so cools far faster from this point on.
*# {{clarify|this passage is written as if in a textbook, to a point where the meaning is not clear ("sticky frozen"? "it is a mistake to think"?); better rephrase it using more encyclopedic style|date=March 2024}} Conduction through the bottom is dominant, when the bottom of a hot beaker has been wetted by melted ice, and then sticky frozen to it. In context of Mpemba effect it is a mistake to think that bottom ice insulates, compared to poor air cooling properties.<ref>{{Cite web|last=Tier|first=Ren|date=2022-01-18|title=Mpemba Effect Demystified|url=https://osf.io/3ejnh|doi=10.31224/osf.io/3ejnh}}</ref>
* [[Dissolution (chemistry)|Dissolved gases]]: Cold water can contain more dissolved gases than hot water, which may somehow change the properties of the water with respect to convection currents, a proposition that has some experimental support but no theoretical explanation.<ref name="Jeng" />
* [[Hydrogen bonding]]: In warm water, hydrogen bonding is weaker.<ref name="Tao" />
* [[Crystallization]]: Another explanation suggests that the relatively higher population of water hexamer states in warm water might be responsible for the faster crystallization.<ref name="Jin">{{Cite journal|last1=Jin |first1=Jaehyeok |last2=Goddard III |first2=William A. |title=Mechanisms Underlying the Mpemba Effect in Water from Molecular Dynamics Simulations |journal=[[Journal of Physical Chemistry C]] |year=2015 |volume=119 |issue=5 |pages= 2622–2629 |doi=10.1021/jp511752n |doi-access=free}}</ref>
* [[Distribution function (physics)|Distribution function]]: {{clarify|is it a "potential" effect (i.e. not demonstrated or observed)? Then these deviations do not "result" but are hypothesized. Needs rephrasing to be based on the actual meaning presented in the source|date=March 2024}} Strong deviations from the [[Maxwell–Boltzmann distribution]] result in potential Mpemba effect showing up in gases.<ref name=":0" />

== Similar effects ==
Other phenomena in which large effects may be achieved faster than small effects are:
* [[Latent heat]]: Turning {{convert|0|C}} ice to 0&nbsp;°C water takes the same amount of energy as heating water from 0&nbsp;°C to {{convert|80|C}}.
* [[Leidenfrost effect]]: Lower temperature boilers can sometimes vaporize water faster than higher temperature boilers.

== Strong Mpemba effect ==
The possibility of a "strong Mpemba effect" where exponentially faster cooling can occur in a system at particular initial temperatures was predicted in 2019 by Klich, Raz, Hirschberg and Vucelja.<ref>{{Cite journal |last1=Klich |first1=Israel |last2=Raz |first2=Oren |last3=Hirschberg |first3=Ori |last4=Vucelja |first4=Marija |date=2019-06-26 |title=Mpemba index and anomalous relaxation |journal=Physical Review X |language=en |volume=9 |issue=2 |pages=021060|arxiv=1711.05829 |doi=10.1103/PhysRevX.9.021060 |doi-access=free|bibcode=2019PhRvX...9b1060K }}</ref> In 2020 the strong Mpemba effect was demonstrated experimentally by Avinash Kumar and John Boechhoefer in a colloidal system.<ref>{{Cite journal |last1=Kumar |first1=Avinash |last2=Bechhoefer |first2=John |date=2020-08-01 |title=Exponentially faster cooling in a colloidal system |journal=Nature |language=en |volume=584 |number=7819 |pages=64–68|arxiv=2008.02373 |doi=10.1038/s41586-020-2560-x |pmid=32760048 |bibcode=2020Natur.584...64K }}</ref>

== Quantum Mpemba effect ==
In 2024, Goold and coworkers described their quantum-mechanical analysis of an abstract problem wherein "an initially hot system is quenched into a cold bath and reaches equilibrium faster than an initially cooler system."<ref>{{cite journal |last1=Moroder |first1=Mattia |last2=Culhane |first2=Oisín |last3=Zawadzki |first3=Krissia |last4=Goold |first4=John |title=Thermodynamics of the Quantum Mpemba Effect |journal=Physical Review Letters |date=4 October 2024 |volume=133 |issue=14 |page=140404 |doi=10.1103/PhysRevLett.133.140404 |pmid=39423396 |arxiv=2403.16959 |bibcode=2024PhRvL.133n0404M }}</ref>In addition to their theoretical work, which used non-equilibrium quantum dynamics, their paper includes computational studies of [[Ising model|spin systems]] which exhibit the effect.<ref>{{cite journal |last1=Moroder |first1=Mattia |last2=Culhane |first2=Oisín |last3=Zawadzki |first3=Krissia |last4=Goold |first4=John |title=Thermodynamics of the Quantum Mpemba Effect |journal=Physical Review Letters |date=4 October 2024 |volume=133 |issue=14 |page=140404 |doi=10.1103/PhysRevLett.133.140404 |pmid=39423396 |arxiv=2403.16959 |bibcode=2024PhRvL.133n0404M }}</ref> They concluded that certain initial conditions of a quantum-dynamical system can lead to a simultaneous increase in the thermalization rate and the [[Gibbs free energy|free energy]].<ref>{{Cite web |last=Dublin |first=Trinity College |title=Ice cream-inspired physics – Trinity team uncovers a quantum Mpemba effect, with a host of "cool" implications |url=https://www.tcd.ie/news_events/articles/2024/ice-cream-inspired-physics--trinity-team-uncovers-a-quantum-mpemba-effect-with-a-host-of-cool-implications/ |access-date=2025-01-16 |website=www.tcd.ie |language=en}}</ref> 

== See also ==
* [[Density of water]]
* [[Heat capacity]]
* [[Water cluster]]
* [[Newton's law of cooling]]

== References ==
'''Notes'''
{{Reflist}}

==Bibliography==
* {{Cite journal |first=David |last=Auerbach |url=http://robot-tag.com/evan/ajp-mpemba.pdf |title=Supercooling and the Mpemba effect: when hot water freezes quicker than cold |journal=[[American Journal of Physics]] |volume=63 |year=1995 |pages=882–885 |doi=10.1119/1.18059 |issue=10 |bibcode=1995AmJPh..63..882A}}
** Auerbach attributes the Mpemba effect to differences in the behaviour of supercooled formerly hot water and formerly cold water.
* {{Cite journal |last=Chown |first=Marcus |journal=New Scientist |url=http://www.eurekalert.org/pub_releases/2006-05/ns-wwf053106.php |title=Why water freezes faster after heating |date=June 2006}}
* {{cite journal|last1=Conover|first1=Emily|title=Debate heats up over claims that hot water sometimes freezes faster than cold|journal=Science News|date=2017|volume=191|issue=2|page=14|url=https://www.sciencenews.org/article/debate-heats-over-claims-hot-water-sometimes-freezes-faster-cold|access-date=2 April 2018}}
* {{Cite journal|last=Dorsey |first=N. Ernest |year=1948 |title=The freezing of supercooled water |journal=Trans. Am. Philos. Soc. |volume=38 |pages=247–326 |doi=10.2307/1005602 |jstor=1005602 |issue=3 |hdl= 2027/mdp.39076006405018 |url=https://babel.hathitrust.org/cgi/imgsrv/download/pdf?id=mdp.39076006405018;orient=0;size=100;seq=3;attachment=0 |hdl-access=free}}
** An extensive study of freezing experiments.
* {{Cite journal |doi=10.1119/1.2186331 |first=Monwhea |last=Jeng |year=2006 |title=The Mpemba effect: When can hot water freeze faster than cold? |journal=American Journal of Physics |volume=74 |issue=6 |pages=514–522 |arxiv=physics/0512262|bibcode=2006AmJPh..74..514J}}
* {{cite journal |last1=Knight |first1=Charles A. |title=The MPEMBA effect: The freezing times of hot and cold water |journal=American Journal of Physics |date=May 1996 |volume=64 |issue=5 |pages=524 |doi=10.1119/1.18275 |bibcode=1996AmJPh..64..524K }}

== External links ==
{{Commons category|Mpemba effect}}
* {{Cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/freezhot.html |publisher=[[Georgia State University]] |work=HyperPhysics |title=Heat questions}}
* {{Cite web|url=http://www.physorg.com/news188801988.html |title=Mpemba effect: Why hot water can freeze faster than cold}} A possible explanation of the Mpemba Effect
* {{cite book |doi=10.3390/ecea-5-06658 |doi-access=free |chapter=New Explanation for the Mpemba Effect |title=The 5th International Electronic Conference on Entropy and Its Applications |date=2019 |last1=Tyrovolas |first1=Ilias J. |page=2 }}
* {{Cite web|url=https://water.lsbu.ac.uk/water/mpemba_effect.html |title=The Mpemba effect: Hot Water may Freeze Faster than Cold Water}} An analysis of the Mpemba effect [[London South Bank University]]
* {{Cite web|url=http://www.thecolourblue.co.uk/mpemba.shtml |title=The Mpemba Effect |url-status=dead |archive-url=https://web.archive.org/web/20111009001208/http://www.thecolourblue.co.uk/mpemba.shtml |archive-date=9 October 2011 |df=dmy-all}} – History and analysis of the Mpemba effect
* {{Cite web|url=https://www.youtube.com/watch?v=dOAUdJR0SIo  |archive-url=https://ghostarchive.org/varchive/youtube/20211212/dOAUdJR0SIo| archive-date=2021-12-12 |url-status=live|title=The story of the Mpemba effect told by the protagonists|website=[[YouTube]]|date=10 January 2013 }}{{cbignore}} An historical interview with Erasto B. Mpemba, Dr Denis G. Osborne and Ray deSouza
* {{Cite web|url= https://www.picotech.com/library/experiment/freezing-hot-cold-water |title= Which freezes quicker, hot or cold water? |author=<!--Not stated--> |access-date=2021-08-25}} High school experiment description, with link to experimental results
* {{Cite web |first1=Cecil |last1=Adams |first2=Mary |last2=M. Q. C. |title=Which freezes faster, hot water or cold water? |work=The Straight Dope |publisher=Chicago Reader, Inc |year=1996 |url=http://www.straightdope.com/classics/a2_098b.html}}
* {{cite arXiv |last=Brownridge |first=James |title=A search for the Mpemba effect: When hot water freezes faster than cold water |year=2010 |eprint= 1003.3185 |class=physics.pop-ph}}
* {{Cite web|url=http://math.ucr.edu/home/baez/physics/General/hot_water.html |title=Can hot water freeze faster than cold water? |date=November 1998 |first=Monwhea |last=Jeng}} in the [[University of California]] Usenet Physics FAQ
* [http://www.rsc.org/mpemba-competition/ Mpemba Competition - Royal Society of Chemistry]
* {{cite journal |last1=Mpemba |first1=E B |last2=Osborne |first2=D G |title=Cool? |journal=Physics Education |date=November 1979 |volume=14 |issue=7 |pages=410–413 |doi=10.1088/0031-9120/14/7/312 |bibcode=1979PhyEd..14..410M }}
* {{cite book |doi=10.1007/978-981-10-0180-2 |title=The Attribute of Water |series=Springer Series in Chemical Physics |date=2016 |volume=113 |isbn=978-981-10-0178-9 }}
* {{cite journal |last1=Mossop |first1=S C |title=The Freezing of Supercooled Water |journal=Proceedings of the Physical Society. Section B |date=April 1955 |volume=68 |issue=4 |pages=193–208 |doi=10.1088/0370-1301/68/4/301 |bibcode=1955PPSB...68..193M }}

{{States of matter}}
{{Use dmy dates|date=August 2019}}

{{DEFAULTSORT:Mpemba Effect}}
[[Category:Physical paradoxes]]
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[[Category:Phase transitions]]
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[[Category:Hysteresis]]
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