There is the effect of evaporation mentioned above, and also the thermal contact with the freezer shelf will cool the bottom part of the body of water. If water is cold enough, close to four degrees C the temperature at which water is densest , then near-freezing water at the bottom will rise to the top. Convection currents will continue until the entire body of water is 0 degrees C, at which point all the water finally freezes. If the water is initially hot, cooled water at the bottom is denser than the hot water at the top, so no convection will occur and the bottom part will start freezing while the top is still warm.
This effect, combined with the evaporation effect, may make hot water freeze faster than cold water in some cases. In this case, of course, the freezer will have worked harder during the given amount of time, extracting more heat from hot water.
One way [described in Jearl Walker's book The Flying Circus of Physics Wiley, ] depends on the fact that hot water evaporates faster, so that if you started with equal masses of hot and cold water, there would soon be less of the hot water to freeze, and hence it would overtake the cold water and freeze first, because the lesser the mass, the shorter the freezing time.
The other way it could happen in the case of a flat-bottomed dish of water placed in a freezer is if the hot water melts the ice under the bottom of the dish, leading to a better thermal contact when it refreezes. Still feeling skeptical?
Fred W. Decker, a meteorologist at Oregon State University in Corvallis, encourages readers to settle the question for themselves:. Use a given setting on an electric hot plate and clock the time between start and boiling for a given pot containing, say, one quart of water; first start with the water as cold as the tap will provide and then repeat it with the hottest water available from that tap. I'd wager the quart of water initially hot will come to a boil in much less time than the quart of water initially cold.
Take into the chamber two quart-volume milk bottles filled with water, one from a hot tap and the other from a cold tap outside the chamber. The data within each individual dataset exhibit a broadly consistent trend, with the cooling time increasing with Ra T and the datasets are best-fit in a least squares sense by a power law of approximately.
This suggests that the cooling times follow. We note that we scaled the data in Fig. Equation 7. The different definitions of the Rayleigh number that we tested all resulted in the various datasets exhibiting trends well approximated by 1.
Considerations of high Rayleigh number convection, in which the assumption that the heat flux is independent of the depth of the fluid, imply that. The time rate of change of temperature for a given sample is then proportional to the heat flux, i. We note that crucially, in deriving 5 we assumed that the convection exhibited behaviour associated with that of asymptotically high Rayleigh number convection.
The data investigating the Mpemba effect, plotted in Fig. As such, if the data plotted in Fig. The above analysis, although informative as to the physics of cooling water, does not explicitly address when the Mpemba effect has been observed.
In order to establish a single observation of the Mpemba effect, one must compare two experiments which are identical in every manner except for a difference in the initial temperatures of the water samples.
One can then state that the Mpemba effect may be regarded to have been observed if the sample of water initially at the higher temperature reaches the desired cooling temperature first. Hence, any data lying above this line may be reasonably reported as an observation of the Mpemba effect.
The variation in the ratio of mean heat transfer rates with initial temperature or equivalently enthalpy for pairs of otherwise identical samples of hot and cold water. Examining Fig. Data from a number of studies do lie on or just above Mpemba effect line. Notably, these data tend to be towards the left hand end of the horizontal axis, i. This suggests that any inaccuracies in the measurement of temperature may be significant. None of the data of Thomas 14 lie far above the Mpemba effect line.
Indeed, Fig. In addition to our data deduced by comparing temperatures recorded at equal heights within the hotter and cooler samples, Fig. These data show observations which lie above the Mpemba effect line and as such could, quite incorrectly, be described as being observations of the Mpemba effect if sufficient care had not been taken in our experiments.
The vertical and horizontal location of this data within the figure encompasses the region that includes all the data reporting to be observations of the Mpemba effect in other studies. We note that in studies reporting observations of the Mpemba effect the authors are either unable to produce the effect in a repeatable manner or details pertaining to the precise height of the temperature measurements were not reported. The only study which includes observations beyond the region covered by our data shown in Fig.
We have made efforts to contact both of the authors, Mr Erasto B. Mpemba and Dr Denis Osborne. In our attempts to contact Dr Osborne we were saddened to be informed of his death in September It seems that throughout his life, Dr Osborne continued to make extremely positive contributions to both science and politics.
We have so far failed in our attempt to contact Mr Mpemba although we understand he was the principal game officer in the Tanzanian Ministry of Natural Resources and Tourism, Wildlife Division he is now retired. We conclude that despite our best efforts, we were not able to make observations of any physical effects which could reasonably be described as the Mpemba effect. Moreover, we have shown that all data with the only exceptions coming from a single study reporting to be observations of the Mpemba effect within existing studies fall just above the Mpemba effect line, i.
We have shown Fig. Indeed, all the data which lie just above the Mpemba effect line in Fig. To be precise regarding our meaning by this statement, let us now consider the reported observations of the Mpemba effect from, arguably, the two most careful sets of experiments within the literature 28 , However, the variation in notionally identical experiments is significant. As such, the variation in notionally identical experiments is at least large enough to render any conclusion that the Mpemba effect has been observed in the mean data as highly questionable, and so this cannot be regarded as a meaningful observation of the effect.
The only exception to our above statements, the single study in which some data is reported that shows dramatically warmer samples cooling in substantially less time i. If these data could be reproduced in a repeatable fashion and the underlying mechanism understood then it would be of real significance to a multitude of applications relying on the transfer of heat.
For example ref. With the use of modern heat-exchangers such a result would have profound implications for the efficiency of any number of common industrial processes. Despite these efforts, including our own, none have succeeded. We must therefore assert that this particular dataset may be fundamentally flawed and thus, unless it can be shown to be reproducible and repeatable, this dataset must be regarded as erroneous.
We must highlight that our primary focus has been to examine the cooling of water to the freezing point observed under standard atmospheric conditions , i. In so doing we have been able to show that much of the published experimental data exhibit a scaling behaviour associated with asymptotically high Rayleigh number convection. If one extends the definition of the Mpemba effect to include the freezing process then one can examine the experimental evidence presented by a number of scientific studies which have sought to include the effect of freezing, e.
The freezing of water to ice is a thermodynamically intensive process. Intuition, therefore, guides one to expect the time to completely freeze a sample of water could depend only weakly on the initial water temperature. Moreover, freezing is initiated by a nucleation process and as such it is susceptible to variations at the smallest physical scales, e.
Such intuition is entirely born out in the experimental evidence, with no single study able to report repeatable observations of the Mpemba effect when the freezing process is included 9 , 21 , 22 , 28 , Experimental observations of a particular example of warm water cooling and freezing in less time than a particular example of initially cooler water have been made — what is yet to be reported is any experimental evidence that samples of water can be consistently cooled and frozen in less time the time being less by a repeatable and statistically significant amount by simply initiating the cooling from a higher temperature.
As such we can conclude that even with the freezing process included within the definition of the Mpemba effect, the Mpemba effect is not observable in any meaningful way. We are not gladdened by such a conclusion, indeed quite the opposite. The Mpemba effect has proved to be a wonderful puzzle with which to engage and interest people of all ages and backgrounds in the pursuit of scientific understanding.
However, the role of scientists is to objectively examine facts and further knowledge by reporting the conclusions, and as such we feel compelled to disseminate our findings. Finally, we want to give hope to the educators who may have previously relied on the Mpemba effect as a useful tool with which to inspire their students. There are numerous genuine artefacts of science which can continue to provide such inspiration.
For example, try filling two identical glasses, one with fresh water and one with salty water both of equal temperature , place a few cubes of ice in each and observe which melts first — many students will be surprised by the result, finding it counter to their experience and intuition. Equally one could try placing a thin sheet of card on top of a glass of water, turn the glass upside down and then remove your hand from the card — watch as the atmospheric air pressure allows the water to be held in the glass — repeat this, replacing the card by just a rigid gauze with holes of up to a few millimetres and still the water will be held within the glass We hope that these examples serve to act as catalysts for those seeking other examples of genuine science and that these help to inspire scientific interest within future generations.
It is common in both the practical cooling of water e. These three non-dimensional parameters can all be combined within a Rayleigh number for the cooling. Within a fluid heat may be transported either by advection convection or thermal diffusion conduction ; the Rayleigh number can be interpreted as a ratio of the time scales for conduction, t cond , and convection, t conv.
Suitable length scales for the Rayleigh number can be identified by consideration of these time scales. Convection is generated when thermal effects give rise to gravitationally unstable distributions of density and so it is appropriate to consider only the vertical length scale H in the convective time scale.
It is natural to define the buoyancy as the gravitational acceleration scaled by the normalised density difference between two relevant fluids. One might argue that it is appropriate to take the difference between the density of water at the initial temperature and at some other temperature, e.
Furthermore, both the kinematic viscosity and thermal diffusivity of water vary with temperature, in the case of the viscosity by factor of six over the temperature range of cooling We define the temperature averaged Rayleigh number Ra T , for water cooling from an initial temperature T i to a final temperature T 0 , as. For both sets of experiments temperatures were digitally recorded and stored using up to eight thermocouples, with a data-logger connected to a computer running LabVIEW.
The thermocouples were calibrated using a refrigerated circulator providing temperatures accurate to within 0. All three samples were placed inside the freezer at the same time in order to ensure that the samples were exposed to the same cooling from the thermostatically controlled chest-freezer.
Prior to being placed inside the freezer a thermocouple was located and carefully fixed centrally within each sample of water. The water was then cooled by carefully suspending a brass cooling plate such that the cooling plate was in direct contact with the upper surface of the water.
The cooling plate had been carefully machined so that it contained a continuous channel, entirely housed within the plate except for openings at two of its corners which were connected to insulated pipes. The channel meandered within the plate so that by passing ethylene glycol solutions continuously cooled by a Thermo Haake refrigerated circulator, Phoenix-line, model PII-C41P through the channel the entire plate was held at an approximately uniform and constant temperature.
The thermocouples had been calibrated, to an accuracy of 0. The characteristic temperature of the water at any instant was determined by spatially averaging the temperatures recorded at the thermocouples positioned at the carefully measured heights.
Experiments were run until the water within the tank reached a steady temperature which took approximately one day to occur. In order to be able to scale the data published in other studies it was necessary to have sufficient information in order to be able to calculate the Rayleigh number, i.
For certain studies 9 , 17 , 20 , 28 the required information was explicitly provided. Table 1 provides details of information not explicitly provided by the remaining studies for which we report data. In each case, details of our assumptions and the data on which these assumptions was based is provided. It should be noted that the sensitivity of our results to the assumptions detailed in the table is by no means dramatic.
Indeed, any reasonable variations to our assumptions does not alter any of our findings. How to cite this article : Burridge, H. Questioning the Mpemba effect: hot water does not cool more quickly than cold. The New York Times. The claim: Cold water boils more quickly than hot water. The Telegraph. Have scientists worked out why hot water freezes faster than cold water? The Times. The Daily Mail. Zhang, X.
Hydrogen-bond memory and water-skin supersolidity resolving the Mpemba paradox. Jin, J. III Mechanisms underlying the Mpemba effect in water from molecular dynamics simulations.
C, 5 , — Mpemba effect from a viewpoint of an experimental physical chemist. Mpemba, E. Physics Education, 4 3 , They repeated the test over 1, times, dropping the beads in different wells and starting at different temperatures. Under certain forces from the laser, the hottest beads cooled faster than the lower temperature beads.
Theresa Machemer is a freelance writer based in Washington DC. Her work has also appeared in National Geographic and SciShow. Website: tkmach. Photo by Prithviraj Basak The story goes that in , Tanzanian high school student Erasto Mpemba was making ice cream with his class when he impatiently put his sugar and milk concoction into the ice cream churner when it was still hot, instead of letting it cool first.
Post a Comment.
0コメント