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The Mpemba effect is the name given to the observation that a liquid (typically water) that is initially hot can 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. [1] [2]
The Mpemba effect is named after Tanzanian 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. [3]
The phenomenon, when taken to mean "hot water freezes faster than cold", is difficult to reproduce or confirm because it is ill-defined. [4] 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." [5]
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 0 °C (32 °F; 273 K). [4] 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. [4] Alternatively, the Mpemba effect may not be evident in situations and under circumstances that at first seem to qualify. [4]
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." [6] 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 ]
Francis Bacon noted that "slightly tepid water freezes more easily than that which is utterly cold." [7] René Descartes wrote in his Discourse on the Method , relating the phenomenon to his 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." [8]
Scottish scientist Joseph Black investigated a special case of the phenomenon by comparing previously boiled with unboiled water; [9] he found that the previously boiled water froze more quickly. Evaporation was 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's description of supercooling of water, arguing that the previously boiled water could not be as readily supercooled.[ citation needed ]
The effect is named after Tanzanian scientist Erasto Mpemba. He described it in 1963 in Form 3 of Magamba Secondary School, 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 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?" 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. [10]
Mpemba and Osborne described placing 70 ml (2.5 imp fl oz; 2.4 US fl oz) samples of water in 100 ml (3.5 imp fl oz; 3.4 US fl oz) 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 25 °C (77 °F) and that it was much less at around 90 °C (194 °F). 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. [10]
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 −6 to −18 °C (21 to 0 °F; 267 to 255 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. [11]
In 2016, Burridge and Linden defined the criterion as the time to reach 0 °C (32 °F; 273 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." [1]
In controlled experiments, the effect can entirely be explained by undercooling and the time of freezing was determined by what container was used. [12] Experimental results confirming the Mpemba effect have been criticized for being flawed, not accounting for dissolved solids and gasses, and other confounding factors. [13]
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." [4] 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. [4]
New Scientist recommends starting the experiment with containers at 35 and 5 °C (95 and 41 °F; 308 and 278 K), respectively, to maximize the effect. [14]
While the actual occurrence of the Mpemba effect is disputed, [13] 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 Markovian statistical mechanics, predicting the appearance of the inverse Mpemba effect in the Ising model and diffusion dynamics. [15] Antonio Lasanta and co-authors also predicted the direct and inverse Mpemba effects for a granular gas in a far-from-equilibrium initial state. [16] Lasanta's paper also suggested that a very generic mechanism leading to both Mpemba effects is due to a particle velocity distribution function that significantly deviates from the Maxwell–Boltzmann distribution. [16]
James Brownridge, a physicist at Binghamton University, has said that supercooling is involved. [17] [12] Several molecular dynamics simulations have also supported that changes in hydrogen bonding during supercooling take a major role in the process. [18] [19] 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 hexagonal ice when warm water is rapidly cooled down. The authors used vibrational spectroscopy and modelling with density functional theory-optimized water clusters. [2]
The following explanations have also been proposed:
Other phenomena in which large effects may be achieved faster than small effects are:
In 2017, the possibility of a "strong Mpemba effect" where exponentially faster cooling can occur in a system at particular initial temperatures was predicted by Klich, Raz, Hirschberg and Vucelja. [26] In 2020 the strong Mpemba effect was demonstrated experimentally by Avinash Kumar and John Boechhoefer in a colloidal system. [27]
In physics, cryogenics is the production and behaviour of materials at very low temperatures.
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity. When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow.
Boiling or ebullition is the rapid phase transition from liquid to gas or vapour; the reverse of boiling is condensation. Boiling occurs when a liquid is heated to its boiling point, so that the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. Boiling and evaporation are the two main forms of liquid vapourization.
A vacuum flask is an insulating storage vessel that slows the speed at which its contents change in temperature. It greatly lengthens the time over which its contents remain hotter or cooler than the flask's surroundings by trying to be as adiabatic as possible. Invented by James Dewar in 1892, the vacuum flask consists of two flasks, placed one within the other and joined at the neck. The gap between the two flasks is partially evacuated of air, creating a near-vacuum which significantly reduces heat transfer by conduction or convection. When used to hold cold liquids, this also virtually eliminates condensation on the outside of the flask.
A cryopump or a "cryogenic pump" is a vacuum pump that traps gases and vapours by condensing them on a cold surface, but are only effective on some gases. The effectiveness depends on the freezing and boiling points of the gas relative to the cryopump's temperature. They are sometimes used to block particular contaminants, for example in front of a diffusion pump to trap backstreaming oil, or in front of a McLeod gauge to keep out water. In this function, they are called a cryotrap, waterpump or cold trap, even though the physical mechanism is the same as for a cryopump.
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.
Freezing is a phase transition in which a liquid turns into a solid when its temperature is lowered below its freezing point.
Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid below its freezing point without it becoming a solid. As per the established international definition, supercooling means ‘cooling a substance below the normal freezing point without solidification’ While it can be achieved by different physical means, the postponed solidification is most often due to the absence of seed crystals or nuclei around which a crystal structure can form. The supercooling of water can be achieved without any special techniques other than chemical demineralization, down to −48.3 °C (−54.9 °F). Supercooled water can occur naturally, for example in the atmosphere, animals or plants.
Liquid nitrogen (LN2) is nitrogen in a liquid state at low temperature. Liquid nitrogen has a boiling point of about −196 °C (−321 °F; 77 K). It is produced industrially by fractional distillation of liquid air. It is a colorless, mobile liquid whose viscosity is about one-tenth that of acetone (i.e. roughly one-thirtieth that of water at room temperature). Liquid nitrogen is widely used as a coolant.
Blanching is a cooking process in which a food, usually a vegetable or fruit, is scalded in boiling water, removed after a brief timed interval, and finally plunged into iced water or placed under cold running water to halt the cooking process. Blanching foods helps reduce quality loss over time. Blanching is often used as a treatment prior to freezing, dehydrating, or canning vegetables or fruits to deactivate enzymes, modify texture, remove the peel and wilt tissue. The inactivation of enzymes preserves colour, flavour, and nutritional value. The process has three stages: preheating, blanching, and cooling. The most common blanching methods for vegetables/fruits are hot water and steam, while cooling is either done using cold water or cool air. Other benefits of blanching include removing pesticide residues and decreasing microbial load. Drawbacks to the blanching process can include leaching of water-soluble and heat-sensitive nutrients and the production of effluent.
Cloud physics is the study of the physical processes that lead to the formation, growth and precipitation of atmospheric clouds. These aerosols are found in the troposphere, stratosphere, and mesosphere, which collectively make up the greatest part of the homosphere. Clouds consist of microscopic droplets of liquid water, tiny crystals of ice, or both, along with microscopic particles of dust, smoke, or other matter, known as condensation nuclei. Cloud droplets initially form by the condensation of water vapor onto condensation nuclei when the supersaturation of air exceeds a critical value according to Köhler theory. Cloud condensation nuclei are necessary for cloud droplets formation because of the Kelvin effect, which describes the change in saturation vapor pressure due to a curved surface. At small radii, the amount of supersaturation needed for condensation to occur is so large, that it does not happen naturally. Raoult's law describes how the vapor pressure is dependent on the amount of solute in a solution. At high concentrations, when the cloud droplets are small, the supersaturation required is smaller than without the presence of a nucleus.
In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled significantly below 0 °C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0 °C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay.
The Wegener–Bergeron–Findeisen process, is a process of ice crystal growth that occurs in mixed phase clouds in regions where the ambient vapor pressure falls between the saturation vapor pressure over water and the lower saturation vapor pressure over ice. This is a subsaturated environment for liquid water but a supersaturated environment for ice resulting in rapid evaporation of liquid water and rapid ice crystal growth through vapor deposition. If the number density of ice is small compared to liquid water, the ice crystals can grow large enough to fall out of the cloud, melting into rain drops if lower level temperatures are warm enough.
Erasto Bartholomeo Mpemba (1950–2023) was a Tanzanian game warden who, as a schoolboy, discovered the eponymously named Mpemba effect, a paradoxical phenomenon in which hot water freezes faster than cold water under certain conditions; this effect had been observed previously by Aristotle, Francis Bacon, and René Descartes.
Insect winter ecology describes the overwinter survival strategies of insects, which are in many respects more similar to those of plants than to many other animals, such as mammals and birds. Unlike those animals, which can generate their own heat internally (endothermic), insects must rely on external sources to provide their heat (ectothermic). Thus, insects persisting in winter weather must tolerate freezing or rely on other mechanisms to avoid freezing. Loss of enzymatic function and eventual freezing due to low temperatures daily threatens the livelihood of these organisms during winter. Not surprisingly, insects have evolved a number of strategies to deal with the rigors of winter temperatures in places where they would otherwise not survive.
Cryofixation is a technique for fixation or stabilisation of biological materials as the first step in specimen preparation for the electron microscopy and cryo-electron microscopy. Typical specimens for cryofixation include small samples of plant or animal tissue, cell suspensions of microorganisms or cultured cells, suspensions of viruses or virus capsids and samples of purified macromolecules, especially proteins.
Water is a polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound and is described as the "universal solvent" and the "solvent of life". It is the most abundant substance on the surface of Earth and the only common substance to exist as a solid, liquid, and gas on Earth's surface. It is also the third most abundant molecule in the universe.
Giovanni Marliani was an Italian physicist, doctor, philosopher and astrologer who was born and lived during the Late Medieval period in northern Italy. Marliani specialised in many mathematical fields and lectured on the phenomenon of natural body heat. He was known for experiments attempting to empirically prove that hot water freezes faster than cold water.
Denis Gordon Osborne was a British diplomat and academic.
Pictet's experiment is the demonstration of the reflection of heat and the apparent reflection of cold in a series of experiments performed in 1790 by Marc-Auguste Pictet—ten years before the discovery of infrared heating of the Earth by the Sun. The apparatus for most of the experiments used two concave mirrors facing one another at a distance. An object placed at the focus of one mirror would have heat and light reflected by the mirror and focused. An object at the focus of the counterpart mirror would do the same. Placing a hot object at one focus and a thermometer at the other would register an increase in temperature on the thermometer. This was sometimes demonstrated with the explosion of a flammable mix of gasses in a blackened balloon, as described and depicted by John Tyndall in 1863.
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