The Mpemba Effect, named after Erasto Mpemba, is the observation that, in some circumstances, warmer water can freeze faster than colder water. Although there is evidence of the effect, there is disagreement on exactly what the effect is and under what circumstances it occurs. There have been reports of similar phenomena since ancient times, although with insufficient detail for the claims to be replicated. A number of possible explanations for the effect have been proposed. Further investigations will need to decide on a precise definition of "freezing" and control a vast number of starting parameters in order to confirm or explain the effect.
The phenomenon, when taken to mean "hot water freezes faster than cold", is difficult to reproduce or confirm, because this statement is ill defined. Jeng proposes as 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.".
However, even with this 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 reached 0 °C.
With the above definition there are simple ways in which the effect might be observed, for example if the hotter temperature melts the frost on a cooling surface and thus increases the thermal conductivity between the cooling surface and the water container. On the other hand there may be many circumstances in which the effect is not observed.
Various effects of heat on the freezing of water were described by ancient scientists such as 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. So the inhabitants of Pontus when they encamp on the ice to fish (they cut a hole in the ice and then fish) pour warm water round their reeds that it may freeze the quicker, for they use the ice like lead to fix the reeds." Aristotle's explanation involved antiperistasis, "the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality."
Early modern scientists such as Francis Bacon noted that "slightly tepid water freezes more easily than that which is utterly cold." In the original Latin, "aqua parum tepida facilius conglacietur quam omnino frigida."
René Descartes wrote in his Discourse on the Method, "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." This relates to Descartes' vortex theory.
The effect is named after Tanzanian Erasto Mpemba. He described in 1963 in Form 3 of Magamba Secondary School, Tanganyika, when freezing ice cream mix that was hot in cookery classes and noticing that it froze before the cold mix. After passing his O-level examinations, he became a student at Mkwawa Secondary (formerly High) School in Iringa. The headmaster invited Dr. Denis G. Osborne from the University College in Dar Es Salaam to give a lecture on physics. After the lecture, Erasto Mpemba asked him the question "If you take two similar containers with equal volumes of water, one at 35 °C (95 °F) and the other at 100 °C (212 °F), and put them into a freezer, the one that started at 100 °C (212 °F) freezes first. Why?", only to be ridiculed by his classmates and teacher. After initial consternation, 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.
Mpemba and Osborne describe placing 70 ml samples of water in 100 ml beakers in the ice box 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 25 °C and that it was much less at around 90 °C. They ruled out loss of liquid volume by evaporation as a significant factor and the effect of dissolved air. In their setup most heat loss was found to be from the liquid surface.
David Auerbach describes how the effect can be observed in samples in glass beakers placed into a liquid cooling bath. In all cases the water supercools, reaching a temperature of typically -6 °C to -18 °C 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.
The behaviour seems contrary to natural expectation but many explanations have been proposed to explain the claimed effect.
- Evaporation: The evaporation of the warmer water reduces the mass of the water to be frozen. 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.
- Convection: Accelerating heat transfers. Reduction of water density below 4 °C (39 °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.
- Frost: Has 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.
- Supercooling: It is hypothesised that cold water, when placed in a freezing environment, supercools more than hot water in the same environment, thus solidifying slower than hot water. However, super-cooling tends to be less significant where there are particles that act as nuclei for ice crystals, thus precipitating rapid freezing.
- Solutes: The effects of calcium carbonate, magnesium carbonate among others.
- 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.
- 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.
A reviewer for Physics World writes, "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." He pointed out 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.
New Scientist recommends starting the experiment with containers at 35 °C (95 °F) and 5 °C (41 °F) to maximize the effect. In a related study, it was found that freezer temperature also affects the probability of observing the Mpemba phenomena as well as container temperature. For a liquid bath freezer, a temperature range of −3 °C (27 °F) to −8 °C (18 °F) was recommended.
In 2012, the Royal Society of Chemistry held a competition calling for papers offering explanations to the Mpemba effect. More than 22,000 people entered and Erasto Mpemba himself announced Nikola Bregović as the winner, suggesting that convection and supercooling were the reasons for the effect.
1) Heat emission: Hydrogen bond (O:H-O) memory defines that P:H-O bond emits energy at a rate depending on its initial storage. Heating stores energy to water by O:H nonbond elongation and H-O bond contraction through the inter-electron-pair Coulomb repulsion. Cooling does the opposite to emit energy with a thermal momentum that is history dependent, being like releasing a deformed coupled bungee pair whose rate depends on the initial extent of deformation
2) Heat conduction: Heating  and skin molecular undercoordination lowers the local mass density to 0.75 gcm^-3, which raises the skin supersolidity and thermal diffusivity by 4/3  which promotes outward heat flow in the liquid path. The thermal diffusivity is proportional to thermal conductivity and inversely proportional to the mass density and the specific heat at constant pressure.
3) Heat dissipation: Highly non-adiabatic ambient ensures the immediate energy dissipation at the source-drain interface. The Mpemba crossing temperature is not only sensitive to the volume of liquid source but also to the drain temperature and to the radiation rate.
4) Other factors: Being insensitive to thermal convection or mass loss in evaporation, the Mpemba effect takes place with a characteristic relaxation time that drops exponentially with the increase of the initial temperature or the initial energy storage of the liquid.
- Y. Huang, X. Zhang, Z. Ma, Y. Zhou, W. Zheng, J. Zhou, and C.Q. Sun, Hydrogen-bond relaxation dynamics: resolving mysteries of water ice. Coord. Chem. Rev., 2014. DOI: 10.1016/j.ccr.2014.10.003.
- C.Q. Sun, Relaxation of the Chemical Bond. Springer Series in Chemical Physics 108. Heidelberg. 807 pp. 2014 ISBN 978-981-4585-20-0
Other phenomena in which large effects may be achieved faster than small effects are
- Leidenfrost effect lower temperature boilers can sometimes vaporize water faster than higher temperature boilers
- Region-beta paradox people can sometimes recover more quickly from more intense emotions or pain than from less distressing experiences
- Latent heat turning 0 °C water to 0 °C ice takes the same amount of energy from the water as cooling it from 80 °C
- Ball, Philip (April 2006). Does hot water freeze first?. Physics World, pp. 19-26.
- Jeng, Monwhea (2006). "Hot water can freeze faster than cold?!?". American Journal of Physics 74 (6): 514. arXiv:physics/0512262v1. doi:10.1119/1.2186331.
- Aristotle, Meteorology I.12 348b31–349a4
- Francis Bacon, Novum Organum, Lib. II, L
- Descartes, Les Meteores
- Mpemba, Erasto B.; Osborne, Denis G. (1969). "Cool?". Physics Education (Institute of Physics) 4: 172–175. Bibcode:1969PhyEd...4..172M. doi:10.1088/0031-9120/4/3/312. republished as Mpemba, E B; Osborne, D G (1979). "The Mpemba effect". Physics Education (Institute of Physics) 14: 410–412. Bibcode:1979PhyEd..14..410M. doi:10.1088/0031-9120/14/7/312.
- Auerbach, David (1995). "Supercooling and the Mpemba effect: when hot water freezes quicker than cold". American Journal of Physics 63 (10): 882–885. Bibcode:1995AmJPh..63..882A. doi:10.1119/1.18059.
- Edwards, Lin (26 March 2010). "Mpemba effect: Why hot water can freeze faster than cold". SUNY: Science X Network, Phys.org.
- Kell, G. S. (1969). "The freezing of hot and cold water". Am. J. Phys. 37 (5): 564–565. Bibcode:1969AmJPh..37..564K. doi:10.1119/1.1975687.
- CITV Prove It! Series 1 Programme 13
- S. Esposito, R. De Risi and L. Somma (2008). "Mpemba effect and phase transitions in the adiabatic cooling of water before freezing". Physica A 387 (4): 757–763. arXiv:0704.1381. Bibcode:2008PhyA..387..757E. doi:10.1016/j.physa.2007.10.029.
- Gholaminejad, Amir; Reza Hosseini (March 2013). "A Study of Water Supercooling". Journal of Electronics Cooling and Thermal Control 3: 1–6. Bibcode:2013JECTC...3....1G. doi:10.4236/jectc.2013.31001.
- Katz, Jonathan (April 2006). "When hot water freezes before cold". arXiv:physics/0604224 [physics.chem-ph].
- How to Fossilize Your Hamster: And Other Amazing Experiments For The Armchair Scientist, ISBN 1-84668-044-1
- Mpemba Competition. Royal Society of Chemistry. 2012.
- Winner of the Mpemba Competition. Royal Society of Chemistry. 2013.
- X. Zhang, Y. Huang, Z. Ma, Y. Zhou, J. Zhou, W. Zheng, Q. Jiang, and C.Q. Sun, Hydrogen-bond memory and water-skin supersolidity resolving the Mpemba paradox. PCCP, 2014. 16(42): 22995-23002
- Y. Huang, X. Zhang, Z. Ma, Y. Zhou, W. Zheng, J. Zhou, and C.Q. Sun, Hydrogen-bond relaxation dynamics: resolving mysteries of water ice. Coord. Chem. Rev., 2014. DOI: 10.1016/j.ccr.2014.10.003
- C.Q. Sun, X. Zhang, X. Fu, W. Zheng, J.-l. Kuo, Y. Zhou, Z. Shen, and J. Zhou, Density and phonon-stiffness anomalies of water and ice in the full temperature range. J Phys Chem Lett, 2013. 4: 3238-3244.
- C. Q. Sun, X. Zhang, X. Fu, W. Zheng, J. Kuo, Y. Zhou, Z. Shen, J. Zhou, Density and phonon-stiffness anomalies of water and ice in the full temperature range, J Phys Chem Lett. 4: 3238-3244
- C. Q. Sun, X. Zhang, J. Zhou, Y. Huang, Y. Zhou, W. Zheng, Density, elasticity, and stability anomalies of water molecules with fewer than four neighbors,J Phys Chemi Lett 4, 2565-2570
- X. Zhang, Y. Huang, Z. Ma, Y. Zhou, W. Zheng, J. Zhou, and C.Q. Sun, A common supersolid skin covering both water and ice. PCCP, 2014. 16(42): 22987-22994
- Dorsey, N. Ernest (1948). "The freezing of supercooled water". Trans. Am. Phil. Soc. (American Philosophical Society) 38 (3): 247–326. doi:10.2307/1005602. JSTOR 1005602. An extensive study of freezing experiments.
- Auerbach, David (1995). "Supercooling and the Mpemba effect: when hot water freezes quicker than cold". American Journal of Physics 63 (10): 882–885. Bibcode:1995AmJPh..63..882A. doi:10.1119/1.18059. Auerbach attributes the Mpemba effect to differences in the behaviour of supercooled formerly hot water and formerly cold water.
- Knight, Charles A. (May 1996). "The MPEMBA effect: The freezing times of hot and cold water". American Journal of Physics 64 (5): 524. Bibcode:1996AmJPh..64..524K. doi:10.1119/1.18275.
- Monwhea, Jeng (2006). "The Mpemba effect: When can hot water freeze faster than cold?". American Journal of Physics 74 (6): 514. arXiv:physics/0512262. doi:10.1119/1.2186331.
- Chown, Marcus (June 2006). "Why water freezes faster after heating". New scientist.
- Mpemba Competition - Royal Society of Chemistry
- Xi Zhang Yongli Huang, Zengsheng Ma, Chang Q Sun. "O:H-O Bond Anomalous Relaxation Resolving Mpemba Paradox".
- Mpemba, E B; Osborne, D G. "The Mpemba effect". Institute of Physics.
- Adams, Cecil; Mary M.Q.C. (1996). "Which freezes faster, hot water or cold water?". The Straight Dope. Chicago Reader, Inc. Retrieved January 2008.
- Brownridge, James (2010). "A search for the Mpemba effect: When hot water freezes faster than cold water". arXiv:1003.3185 [physics.pop-ph].
- "Heat questions". HyperPhysics. Georgia State University.
- "The Mpemba Effect". - History and analysis of the Mpemba Effect.
- Jeng, Monwhea (November 1998). "Can hot water freeze faster than cold water?". in the University of California Usenet Physics FAQ
- "The Phase Anomalies of Water: Hot Water may Freeze Faster than Cold Water". An analysis of the Mpemba effect. London South Bank University.
- "Mpemba effect: Why hot water can freeze faster than cold". A possible explanation of the Mpemba Effect
- "The story of the Mpemba effect told by the protagonists". An historical interview with Erasto Mpemba, Dr Denis Osborne and Ray deSouza