1 Why hot water freezes faster than cold water By Daniel Muthukrishna Undergraduate Engineering/Physics Student at the University of Queensland Images also produced by Daniel Muthukrishna
2 Some of the main proposed explanations for the Mpemba effect have been that hotter water loses some of its mass to evaporation and that hot and cold water differ in their gas content causing a difference in freezing times. However, although both of these parameters do have an effect, they are not substantial enough to explain the distinct results. According to Osborne (1979) the amount of mass lost to evaporation is insufficient to explain the results. Additionally, Wojciechowski et al. observed the Mpemba effect in a closed container, which suggests that evaporative cooling is not the sole cause of the effect (Wojciechowski, Owczarek & Bednarz 1988). Furthermore, although hot water can hold less dissolved gas than cold water, causing a disparity in the gas content (Jeng 2005) and thus a difference in the enthalpy of freezing, Mpemba and Osborne s original experiments as well as several other experiments observed the Mpemba effect with recently boiled water, to remove dissolved air (Jeng 1998). These experiments suggest that dissolved gasses are not necessary to the Mpemba effect. Therefore, I will argue that the primary cause of the Mpemba effect is the temperature distribution of the water. As the water cools it develops temperature gradients and convection currents. For most temperatures the density of water decreases as the temperature increases. So over time, as the water cools a hot top will develop, where the surface of the water will be warmer than the bottom. Since the water loses heat primarily through the surface, the water should lose heat faster than one would expect based just on looking at the average temperature of the water (Jeng 1998). Therefore, when the hot water cools down to a colder temperature, it will lose heat faster than a body of water uniformly at that colder temperature because of its hot top. This theory is Figure 1 Convection currents supported by the fact that Deeson (1971) found that gentle stirring substantially raised the time of freezing. This could explain the Mpemba effect because the initially hot water will cool rapidly, and quickly develop convection currents and so the temperature of the water will vary greatly from the top of the water to the bottom. On the other hand, the initially cool water will have a slower rate of cooling, and will thus be slower to develop significant convection currents. Thus, if we compare the initially hot water and initially cold water at the same average temperature, it seems reasonable to believe that the initially hot water will have greater convection currents, and thus have a faster rate of cooling (Jeng 1998). It should also be noted that the density of water reaches a maximum at 4 C. Therefore, below 4 C the density of water actually decreases with decreasing temperature, and a cold top is instead formed. The reason that the water is most dense at 4 C (Robson & Marshall 2010) is most simplistically related to the fact that ice has a lower density than water, which is in fact uncommon for solids. The primary reason for this is because of hydrogen bonding. When water becomes solid, the H 2 O molecules spread apart to form a tetrahedral structure because of the hydrogen bonds. This is because it is more energetically favourable for the molecules to spread apart and for the ice to have a lower density than for the molecules to become more compact. When water falls below 4 C the molecules begin to spread out to make best use of the hydrogen bonds, and thus the density decreases. Figure 2 Convection Currents occur in the opposite direct (colder water rises) when the water falls below 4 C
3 As shown in the figure 1 convection currents mean that a cycle is created whereby the hotter water rises and the colder water sinks. This occurs because hot water is less dense and therefore rises. However, one way to limit the convection currents is by placing baffles in the beaker of water. In this case a baffle (figure 3) is made out of a hard plastic or metal that forms a cross section to separate the water into four sections (figure 4). This means that only small convection currents can occur in each of the quarters. These smaller convection currents would not be able to have as great an effect on creating temperature gradients as the full convection currents shown in figure 1. Therefore, if convection currents have an effect on the freezing time of water, when the baffles are put in the freezing times should increase. Figure 3 Baffle I conducted an experiment which limited the other potential parameters such as frosting, evaporation and dissolved gases. I did this by using a frost-free freezer to eliminate frosting, covered a 250mL plastic beaker with a layer of plasticine to limit evaporation and used recently distilled water to ensure both the cold and hot water were identical in every way except for their initial temperature. I made use of a sofware called DataStudio and three temperature probes at different heights (top, middle and bottom) connected to a laptop to record the temperature change over time and the freezing time (An example data set is shown in Appendix A). I compared water at nine different temperatures between 10 C and 90 C one set with full convection currents, and the other set with limited convection currents using baffles. Figure 4 Convection currents in beaker of water with baffles The next four graphs illustrate the results. Figure 5 Diagram of the beaker put to freeze
4 Freezing Time (minutes) Full Convection Limited Convection - Baffles Initial Temperature ( C) Figure 4.2 Final Freezing time of the water The above graph (Figure 4.2) illustrates the time taken for each of the experiments to completely freeze. The final freezing time is the time for the entire body of water to solidify. This was when all of the probes indicated temperatures below 0 C.
5 Freezing Time (minutes) Freezing Time (minutes) 350 Top Full Convection Limited convection - Baffles Initial Temperature ( C) Figure 4.3 Freezing time of the top section of the water 400 Middle Full Convection Limited Convection - Baffles Initial Temperature ( C) Figure 4.4 Freezing time of the middle section of the water
6 Freezing time (minutes) 400 Bottom Full Convection Limited Convection - Baffles Initial Temperature ( C) Figure 4.5 Freezing time of the bottom section of the water The above three graphs indicated the freezing time (the time taken for the probes to fall below 0 C) for the top, middle and bottom section of the water. These indicate that a temperature gradient exists within each of the bodies of water.
7 The results firstly indicated that the Mpemba effect occurs in distilled water. Although it is not simply a linear trend, where higher temperatures have shorter freezing times as evidenced by the highest freezing time occurring at water with an initial temperature of 50 C, it was clear that much higher temperatures had freezing times shorter than or comparable to much lower temperatures. For example, in graph 1 (blue line full convection beaker) it is evident that the water with an initial temperature of 90 C, had a freezing time much shorter than the water starting at room temperature (20 C). This phenomenon can be explained by convection currents. Firstly, by comparing the two sets of data in figure 5.1 (the red line representing the water with baffles that limited the effect of convection currents, and the blue line representing the water with full convection) it is clear that convection currents have a significant impact on the freezing time. This is evidenced by the fact that all of the data points that had limited convection currents had a much higher freezing time when compared with the water with full convection currents of similar temperatures. However, this does not substantiate that convection currents cause hotter water to freeze first, but only that convection currents influence the freezing time of water. To support the hypothesis that they cause hot water to freeze first, there needs to be a clear indication that the water at higher temperatures are affected to a greater extent by the presence of baffles than the water at lower temperatures. The maximum difference in freezing time when comparing full convection to limited convection occurred in water at an initial temperature of 90 C. By examining the freezing times of the top of the water and comparing the beakers with full and limited convection currents, it is clear that the water with full convection currents froze much faster. The red line is clearly always above the blue, indicating that the freezing times of the top of the water are affected by convection currents. But what really supports my point is the fact that the water at higher temperatures was far more affected by the baffles than the water at the lower temperatures. This is evidenced by the hotter temperatures in the full convection beakers such as 90 C, 80 C etc. all having much quicker freezing times than their corresponding limited convection beakers. Moreover, at 10 C and 20 C, it is clear that the effect of convection currents is minimal and barely affects the freezing Figure 5.1 Copy of figure 4.2 Final freezing time of the water Figure 5.2 Copy of figure 4.3 Freezing time of the top of the water times. This means that convection currents greatly influence the fact that hot water freezes faster than cold water at the top of the body of water. Furthermore, the freezing times of the water at the bottom of the beaker (figure 4.5) present the opposite of the freezing times of water at the top (figure 5.2). The graph shows that the water with limited convection currents has a far shorter freezing time than the water with full convection currents in most cases. This is because convection currents cause the bottom to freeze last. When the temperature of water falls below 4 C, the water becomes less dense. Therefore, the colder water begins to rise (as it is less dense) while the slightly hotter water begins to sink. This causes the top to freeze first and the bottom to freeze last. In the water with baffles, this does not occur
8 because the convection currents do not play a large role. In fact, as represented in Table 5.1, in almost every case in the water with full convection the top froze first; while in nearly every case of the water with baffles, the bottom froze first. This explains why the freezing time of the bottom of the water was quicker for the water with limited convection. Additionally, by examining each of the graphs of each experiment it is clear that water maintains a hot top whilst cooling until it reaches about 4 C (see Appendix C). At this point the Bottom and middle sections plateau for a while, but the top appears to increase its gradient, and cool even faster. Before this point the bottom had the steepest gradient and was losing heat the fastest. The reason that the water plateaus at 4 C is because of hydrogen bonding. Unlike most other substances water s solid state is less dense than its liquid state (as seen by the fact that ice floats on water). This is because the water molecules form tetrahedral structures to make best use of the hydrogen bonding in its solid state (Robson & Marshall 2010). It is more energetically favourable for the water molecules to form this structure which actually spreads apart the molecules and causes it to be less dense. When water falls below 4 C, it begins to form these tetrahedral structures and its density decreases. To form these structures, it requires energy. Therefore, while it is cooling, instead of expending its energy on reducing its temperature it expends it on forming these structures. Therefore, it halts at 4 C for a few minutes while this occurs. But it is at this 4 C that the top of the water increases its gradient quite significantly and freezes first. This is because of its hot top. When it falls below 4 C, the density begins to decrease and thus the cold water begins to rise. This means that it must now have a cold top. This cold top means that the top will freeze first. From all of this, it can be concluded that because of the hot top of water, caused by convection currents, hotter water tends to freeze faster than colder water as supported by Deeson s results (Deeson 1971). This is because the hot top and the temperature gradient are most exaggerated in water at higher temperatures. And since heat is lost most readily through the surface (Jeng 2005), these hot tops allow the water to lose heat rapidly upwards, so that the lower layers cool more quickly. In further support of this, according to Deeson (1971) stirring the water while it was cooling significantly increased the freezing time. This was because the convection currents would be disturbed. In conjunction with the convection current explanation of the Mpemba effect it is possible that the difference in internal energy of the hot water and the cold water can explain the effect. Since hot water has more internal energy, it may be able to use that extra energy to create hydrogen bonds quicker and overcome the latent heat of fusion faster in the freezing process. It is clear that convection currents cause water to freeze faster and also that the convection current s effect on the freezing time was much greater for water at initially higher temperatures. Furthermore, the hot top was much more exaggerated in the water at initially higher temperatures. Since the heat is most readily lost through the surface, the exaggerated hot top in the water at initially higher temperatures allowed it to freeze at a faster rate than the water at initially lower temperatures. In many cases this increased rate allowed the hotter water to freeze first.
9 Appendix A
10 Appendix B Water with full convection currents Initial Temperature ( C) Freezing Time (minutes) Steepest gradient Time to reach 0C Top Middle Bottom Average Top Middle Bottom Order of Freezing Final Freezing time Order before 5 C Top Middle Bottom Max time to reach 0 C Order to hit 0C Top, Bot, Mid 241 bot, mid, top top, mid, bot Top, Mid, Bot 309 bot, mid, top top, mid, bot Top, Bot, Mid 285 bot, mid, top top, bot, mid Bot, Top, Mid 279 bot, mid, top top, bot, mid Top, Bot, Mid 357 bot, mid, top top, mid,bot Top, Mid, Bot 300 bot, mid, top top, mid, bot Top, Bot, Mid 328 bot, mid, top top, mid, bot Top, Bot, Mid 295 bot, mid, top top, mid, bot Top, Mid, Bot 278 bot, mid, top top, mid, bot Water with baffles - Limited Convection Currents Initial Temperature ( C) Freezing Time (minutes) Steepest gradient Time to reach 0 C Top Middle Bottom Average Top Middle Bottom Order of Freezing Final Freezing time Order before 5 C Top Middle Bottom Max time to reach 0 Order to reach 0 C Top, Bot, Mid 263 bot, mid, top top, mid, bot Bot, Top, Mid 341 bot, mid, top top, mid, bot Bot, Top, Mid 308 bot, mid, top top, mid, bot bot, mid, top 289 bot, top, mid top, bot, mid Bot, Top, Mid 328 bot, mid, top top, bot, mid mid, top, bot 322 bot, top, mid top, mid, bot Bot, Top, Mid 354 bot, mid, top bot, mid, top bot, mid, top 300 bot, top, mid top, mid, bot top,mid,bot 351 bot, top, mid top, mid, bot Figure 4.1 Data from all experiments This table provides a comprehensive display of most of the important elements of each of the experiments. The top section shows relevant data for the beakers without baffles and therefore full convection currents, while the bottom section displays the relevant data for the beakers of water with the baffles and therefore limited convection currents. The table firstly states the initial temperatures of each of the experiments therefore each row is a different experiment. It then displays the freezing time for the top, middle and bottom section of the beakers. The next column illustrates the order of freezing. It can be seen that in the Water with full convection currents, the top almost always froze first, while in the water with limited convection currents the bottom mostly froze first. It then displays the final freezing time, which is taken as the time for all of the probes to indicate temperatures below 0 C therefore implying that they had all frozen. The next column indicates that before 5 C that is before water reaches its most dense state the bottom is always cooling the fastest, followed by the middle and then the top in almost all cases. The next columns illustrate the time taken for each section of the beaker to reach 0 C. The max time to reach 0 C is the time taken for all the probes to be at 0 C at the same time. The last column indicates that for all experiments, the top reached 0 C first, followed by the middle and then the top in almost all cases.
11 Appendix C Example of hot top The above graph is an example of water maintain a hot top whereby the top of the beaker cools at the slowest rate until about 4 C, where the hotter water is no longer less dense than the cooler water
12 Bibliography Concetto, G 2007, 'An easy classroom experiment on', Phys. Educ., vol 42, no. 3, pp Deeson, E 1971, 'Cooler-lower down', Phys. Educ., vol 6, pp Freeman, M 1979, 'Cooler still - an answer?', Phys. Educ., vol 14, pp Jeng, M 1998, Can hot water freeze faster than cold water?, viewed 10 July 2011, <http://www.desy.de/user/projects/physics/general/hot_water.html>. Jeng, M 2005, Hot water can freeze faster than cold??, viewed 20 May 2011, <http://www.vnc.qld.edu.au/physics/physproj/mpemba/jeng.pdf>. Mpemba, E & Osborne, D 1969, 'Cool?', Phys. Educ., vol 4, pp Nave, C 2010, Hot Water Freezing?, viewed 18 August 2011, <http://hyperphysics.phyastr.gsu.edu/hbase/thermo/freezhot.html#c1>. Olson, A 2007, Investigating the 'Mpemba Effect': Can Hot Water Freeze Faster than Cold Water?, viewed 5 June 2011, <http://www.sciencebuddies.org/science-fairprojects/project_ideas/phys_p032.shtml?fave=no&isb=cmlkojewmta0odi0lhnpzdowlha6nsxpytpqa Hlz&from=TSW>. Osborne, D 1979, 'Mind on Ice', Phys. Educ, vol 14, pp Robson, D & Marshall, M 2010, The many mysteries of water, viewed 5 June 2011, <http://www.newscientist.com/article/dn18473-the-many-mysteries-of-water.html?full=true>. Wojciechowski, B, Owczarek, I & Bednarz, G 1988, 'Freezing of Aqeous Solutions Containing Gases', Cryst. Res. Technol., vol 23, no. 7, pp
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