Mpemba effect

The Mpemba effect refers to the paradoxical phenomenon that hot water freezes faster than cold water under certain conditions. Was named the effect after his " re-discoverer " (1963), the Tanzanian students Erasto B. Mpemba.

• 6.1 A supercooled liquids or melts
• 6.2 temperature gradient
• 6.3 Dissolved contaminants

• 7.1 water vapor

• 8.1 Pressure dependence of the freezing point
• 8.2 Microscopic structure of liquid

Definition

If one cools warm same output quantities and cold water in the same vessels under the same pressure and the same environmental conditions under a temperature from which the freezing point of water at this pressure corresponds to (0 ° C or 273.15 K at a pressure of 101.325 kPa), so can be observed in a certain range of cooling rates that the warmer beginning of the experiment, water freezes at an earlier time ( crystallized ) as the original cooler water. This phenomenon is referred to as a paradoxical effect Mpemba.

However, the full statement that hot water freezes faster than cold water is incorrect because the Mpemba effect occurs only in special thermodynamic systems.

First considerations

It is a very long -known paradox that in the fourth century BC, the philosopher Aristotle ( Μετεωρολογικά, I, 12) was discussed; then again in the 13th century by the monk and philosopher Roger Bacon. In the 17th century, the philosopher and scientist Francis Bacon and René Descartes failed in the search for explanations.

1963 also met with the Tanzanian students Erasto B. Mpemba to this effect when he established ice cream. Together with Denis G. Osborne in 1969 he published the results of numerous experiments on this subject. However, it took several years until this effect has been scientifically studied.

Cause

The cause of this paradox is not yet fully explained scientifically. However, there are theories, which on the one hand see the main reason is that the amount of warmer water during cooling in an open system decreases disproportionately compared to the amount of cooler water through evaporation. This is because the vapor pressure of a liquid is increased (to which, in turn, the rate of evaporation is proportional ) exponentially with the temperature. That is, based on the same unit of time more hot water than cold water evaporated ( vapor pressure Augustsche formula ). This lie upon reaching the freezing point of getting different amounts of water before, in such a way that the amount of initially warmer water is always less than the amount of the initially cooler water, and a smaller amount of water freezes faster than a larger amount of water under otherwise identical conditions.

Secondly, there is the theory that the water turn dissolved salts ( carbonates ) at high temperatures and thus have no influence on the freezing point. In cold water, the concentration of salts in the growing after onset of crystallisation is still liquid water. This leads to a reduction in freezing point, since the entropy is increased in the water and thus the formation of the highly ordered crystalline structure of ice is difficult.

The Mpemba effect only occurs at certain thermodynamic conditions and by no means always. It occurs when the system parameters are chosen so that the non-uniform decrease in the cash amounts of water during cooling and the resulting faster crystallization process of the lower amount of water remaining determine the speed of the overall process ( plus cooling crystallization).

Although the uneven amount of substance loss of the systems during cooling and the removal of dissolved salts are usually the main cause of the effect, there is still no consensus in the scientific debate about whether other effects under specific experimental conditions can have an equally large impact. This point is controversial to this day and can, also because of the sparse present and partially afflicted with methodological flaws data material can not be answered clearly. Maybe under special experimental conditions, other effects may play a role. In the following, the evaporation is considered, as this is crucial rule for the occurrence of the Mpemba effect substantially.

Mpemba effect and thermodynamic systems

Open System

The Mpemba effect occurs usually only in open physical systems. Characteristic of open systems is a potential mass and heat exchange of the system with its environment, where the environment is not included in the mass and energy balance of the overall system in the case of an open system by definition ( in other words, the environment is not a relevant part of the open system ). Example: The evaporating from an open beaker of water escapes into the atmosphere. This decreases both the amount of water in the glass as well as the amount of heat contained in the water, whilst increasing the water and energy content of the atmosphere. This increase is not considered or quantified.

Variables are changed simultaneously Thermodynamically in experiments in open systems more intensive ( mass-independent ) and extensive ( mass-dependent ), whereby the measurement and interpretation of observed effects is made difficult by nature.

The main influencing parameters

The following parameters are in an open system is essential:

This should not be too small, so that the water is not completely evaporated before it reaches the freezing point.

This favors a large temperature difference between warmer and colder water the Mpemba effect by disproportionately more warmer water can evaporate. However, the temperature of the cooler water must also not be too close to the freezing point, since the hotter system will not have the opportunity to " overtake " the cooler upon cooling.

The size of the phase boundary between liquid and gaseous phase determines the per unit amount of water evaporated ( evaporation rate ), as this is proportional to the surface area, where the water does not boil. The surface area in turn is dependent on the vessel form. For the observation of the Mpemba effect is a large surface area which leads to a high amount of substance loss by evaporation, favorable.

Is the absolute temperature difference between the initial amount of water and the reservoir determines the course of the cooling curve. The greater the difference, the steeper the cooling curves, ie the faster cooling of the samples from only by heat conduction and heat radiation and the lower the amount of fuel loss through evaporation. Therefore, for the observation of the Mpemba effect, a temperature of the reservoir just low below the freezing point of water, as the reservoir temperature is on the one hand deep enough for the crystallization of liquid water, but on the other hand run the cooling curves of the liquid phases sufficiently flat and a maximum amount of water can evaporate during the cooling of the liquid phases.

This determines the degree to which cooling can be carried out of the water on the vessel wall. The larger the coefficient, the faster the water cools by heat conduction and heat radiation on the vessel from. For observing the Mpemba effect a low coefficient of thermal conductivity of the vessel is favorable because then more water may evaporate during the cooling of the liquid phases, on the other hand makes it difficult to lower coefficient of thermal conductivity, the heat dissipation of the heat of crystallization on the vessel wall during freezing, which reduces the effect in. In the practical test so no flasks should be used for example.

It still requires scientific experiments, whether and to what extent the Mpemba effect in the same or a comparable manner to be paradoxical result is obtained when the two filled containers at sea level or, for example at 7000 meters altitude and / or they are placed at the 45th degree of north latitude, or at one of the two poles. The boiling point and the freezing point in degrees Celsius or the relevant associated pressure of the air column at the site of measurement include highly likely to be the "decisive conditions " for the measurement result. Since water contains a lot of oxygen, could be close, besides also the reference to the with Height above sea level. N / N varying ( decreasing ) establish consistency of the oxygen content in the air. The test series could lead to a break-even point, at which point dissolves the paradox and freeze both water samples regularly at the same time.

Nuisance parameter

The following parameters are not critical for the occurrence of the Mpemba effect, although they are able to disturb him in reinforcing (positive ) or weakening (negative ) form. Therefore, they should be turned off when viewed from the outset by a suitable choice of conditions. Under certain experimental conditions, however, a non-negligible contribution of these effects is discussed for the Mpemba effect.

Supercooled liquids or melts

If you cool down very pure liquids below their freezing point, the crystallization may not occur when no nuclei are present in the liquid. To avoid, you can add the water samples some grains of quartz sand as a crystallization matrix. Contrary to popular belief, the concentration (ie, quantity) of nuclei for each crystallization process is meaningless decisive ending is simply whether there is a suitable nucleation least or not. The freezing point depression due to lack of crystallization is independent of the fact that the freezing point of a liquid as a function of pressure and volume of the system can move both to lower and to higher values ​​(see: Phase diagrams of one-component ) in the rest.

In principle, the effect of the supercooled liquid has no effect in the absence of seed crystals on the Mpemba effect, since it relates to the original sample cooler just like the original warmer. To the extent, however, assumed that the initially warmer water potential nuclei - for example, by outgassing of dissolved impurities such as carbon dioxide - loses compared to the initially cooler water, the effect of the supercooled liquids would attenuate the Mpemba effect, as the formerly hotter water just not now would freeze faster, but tended to hypothermia.

Temperature gradient

Temperature differences in the system are indicated by the temperature gradient. In a stagnant fluid occur during cooling as well as in the stationary environment, temperature differences on. The temperature at the vessel wall and at the phase boundary, for example, smaller than in the interior of the phase in which the ambient temperature in the vicinity of the blood vessels is higher than further away therefrom. At various temperatures starting vessels occurred upon cooling to different gradient waveforms, which are substantially equivalent to a change in the coefficient of thermal conductivity of the vessel. This effect (e.g., magnetic ) during the cooling and a fan in the reservoir, which ensures a constant and uniform temperature reservoir, avoided by the stirring of the fluids.

Dissolved contaminants

Total Dissolved Solids (also includes dissolved gases ) can reduce the freezing point of a liquid ( Raoult's law ), the freezing point depression is the foreign mole fraction proportional. In the case of dissolved gases (eg carbon dioxide in water ) is the concentration of dissolved gas in turn depends on the temperature ( Dampfdruck! ), that is, the different temperatures of water samples contain under equilibrium conditions, different amounts of dissolved gases and therefore also have a slightly different freezing. The effect is however very small ( in the range of 0.01 K to 0,001 K ), and thus plays convenient for the Mpemba effect does not matter. The influence of dissolved gases would increase the Mpemba effect, as the initially hotter water would contain less dissolved impurities and therefore its freezing point would be less reduced compared to the initially cooler water. Overall, it avoids this " dirt " effect by using for the trial of degassed water ( by pre- boiling and applying a vacuum ). The same also applies for volume and other effects that could be caused by ausfrierende gas bubbles.

Other parameters

Water vapor

The water vapor in the gaseous phase must be small compared to the saturation vapor pressure, otherwise can not evaporate or less water. This condition is guaranteed by the rule in the experiments were conducted in a dry environment. A high water vapor partial pressure in the gaseous phase of an open system would attenuate the Mpemba effect.

Influence Lose parameters

Pressure dependence of the freezing point

The exact freezing point of pure water is pressure-dependent, as with any fluid or melt. The exact value can be obtained from the so-called phase diagram of the water. At normal pressure (p = 1013.25 hPa ) corresponds to the freezing point T = 0,000 ° C or T = 273.150 K. The freezing point of water is at the condition p = 611.657 Pa (about 6 hPa ) at T = 0.010 ° C and T = 273.160 K. for other pressures, the freezing point is above or below this value may be for freezing. This fact is independent of freezing point depressions due to dissolved impurities and undercooled melts due to lack of crystallization nuclei.

Microscopic structure of liquid

The Mpemba effect is completely within the framework of classical thermodynamics to explain. Microscopic properties such as the structure of liquids, apart from its importance for the caloric data of the actual substance, without influence.

Other liquids

The Mpemba effect is not limited to water, so no anomaly of water. Whether it occurs, is mainly determined by the caloric data of a substance. So also have other substances such as ethanol, acetic acid, benzene or hexane in a similar exponential dependence of the vapor pressure of the temperature. However, the freezing points of these substances are either substantially lower than that of water, so that the practical test has higher experimental requirements for the necessary cooling, or they are toxic or flammable, so that the evaporation bans in open systems without special protective measures.

Use of the Mpemba effect

Correctly, you would have to call the Mpemba effect than the effect in which a smaller amount of hot water freezes faster than a larger amount of cold water. This is the reason why use of the effect is useless both for reasons of energy balance as well as for reasons of kinetics.

Energy balance

The energy balance when using the Mpemba effect adjusts itself so is that first energy is used to heat a system, and then to cool it down again. The amount of energy that is spent on heating above the starting temperature outside and then cooling to the starting temperature back is wasted in terms of energy, regardless of whether it is an open system ( a part of the applied energy is used for evaporation of water at constant pressure used) or a closed system ( a part of the applied energy is used for evaporation of water under pressure increase) is. Energetically is a priori only the cooling optimally.

Kinetics

But even under kinetic point of view is the use of the Mpemba effect meaningless if one assumes that the goal in this case is an arbitrary initial amount ( mass) of water should be brought as soon as possible to crystallize a precisely defined quantity ( mass ) to produce ice. In this case you will choose the appropriate initial water and cools it. This is always the absolute fastest method. If a sufficient initial amount of hot water used, which create the same amount of ice leaves after crystallization as in the former case, the Mpemba effect occurs not because the icing needs now total more. However, the same initial amount of water is used as in the first case, the Mpemba effect can indeed occur faster and produce ice, but in a lesser amount. But even in this case it would have been faster in absolute terms, cool reduced the initial amount of water directly and without detours.

For these reasons, a useful technical use of the Mpemba effect is excluded, because there is always a more energy efficient and faster solution for each crystallization problem.

Use by Mpemba

Of course, this fact does not exclude that there are practical applications, where the Mpemba effect occurs. Mpemba itself has such discovered by he could freeze his ice cream faster. However, the effect in such cases ( thermodynamically considered ) undesirable side effect dar. This consisted in Mpembas case is that he has produced less ice cream than would have been possible under optimal conditions. He also had to defrost the fridge more often.

Conclusion

The Mpemba effect is the result of a surprising and counterintuitive speaking show effect whose physico- chemical basis is essentially the well-known since the 19th century August 's formula to see.

Mpembas merit is to have rediscovered the effect and made ​​known to a wider scientific audience interested.

The consideration of the effect is suitable to train the knowledge of the principles of classical thermodynamics based on a philosophical as well as amazing experiment in the real world and deepen.

Mention in the media

On 28 March 1999, the Mpemba effect was in the ARD science program header demonstrates understandable and explained.

On 21 January 2010 the WDR reported in The Small request as part of the radio broadcast Leonardo about the Mpemba effect, with some sound bites were recorded by Mpemba.

In the sat.1 infotainment TV show Clever! - The show that knowledge creates dated 13 March 2006 ( broadcast 39 ), the Mpemba effect by cooling of different non- specific output quantities of water of different, not a specific composition (mineral water, distilled water, tap water) and different temperature in an open system demonstrated. As we have seen, made ​​experimental set-up and execution so under largely undefined initial and end conditions. The specified in the program explain the effect is incorrect.

On 26 June 2012, the Royal Society of London praised from 1000 British pounds in order to promote the further explanation of the effect. Nikola Bregovic, a chemist at the University of Zagreb, was announced in January 2013 as the winner: He had come to the conclusion that he could not find a final solution, and noted: "Once again, surprised and intrigued us this small, simple molecule with his magic. "