Physics

Observing the Mpemba effect over a range of initial temperatures of bodies of water.

Abstract:

This study was conducted in an effort to confirm or deny the existence of the Mpemba effect. The Mpemba effect states that when identical bodies of water at two different temperatures are exposed to a physical cooling agent, the body with a higher starting temperature will cool faster than its counterpart. The experiment was conducted by heating identical bodies of water to different temperatures and measuring the point at which they freeze when placed inside a commercial freezer. If the bodies of water with a higher starting temperature freeze at a faster rate than cooler bodies, then the experiment would give weight to the argument that the Mpemba effect exists. The results of the experiment proved unreliable as there were clear signs of equipment malfunction, providing results that do not accurately represent reality.

Introduction:

The experiment described in this article was developed to measure the Mpemba effect over a range of temperatures for bodies of water. The Mpemba effect describes the phenomena by which if two bodies of water at different temperatures are introduced to the same cooling agent under identical conditions, the body with a higher starting temperature should cool faster (Phys, 2010)[1]. Since its formal discovery in 1963, the existence of the phenomena has been divisive within the scientific community, as some researchers claim the phenomena doesn’t exist (Nature, 2016)[2]. Given the fact that the verification of this phenomena could change humanity’s understanding of thermal physics, this experiment was conducted for the purpose of providing evidence for or against its existence.

Literature Review:

The Mpemba effect has remained a divisive topic within the scientific community with sources including Nature [2] claiming to disprove its existence and the National Academy of Sciences [3] claiming to confirm it. Discrepancies between pieces of literature on the Mpemba effect may be due to a lack of a clear scientific definition according to one report by Nature [2], with the report using this statement of obscurity to make an argument against its existence. Despite the lack of a formal definition, papers that work with a chosen definition of the effect do supply evidence proving a hotter body of water cools faster when exposed to a cooling agent. A theory against this evidence is the assertion that those experiments don’t take into account how hotter bodies of water may produce more vapour out of its own mass. This phenomenon would decrease the mass of water the cooling agent needs to freeze the entire body, giving a misleading result.

Method:

To investigate the validity of the Mpemba effect and measure the time when bodies of water at different temperatures freeze when exposed to a cooling agent, the following methodology was used. First, four beakers were filled with 250ml of tap water. One was kept at room temperature while the other three were placed on a tripod above a Bunsen burner and heated to approximately 10, 20, and 30 degrees Celsius above room temperature. Next, four digital thermometers set to record temperature data for an extended period of time were each submerged in one of the beakers. The tray containing the four beakers was then placed in a standard commercial freezer over a period of a day. The thermometers were then removed, and their data was recorded. The point at which the water had completely frozen was considered to be the point at which the temperature measured below and not at . This method allowed the confirmation or denial of the Mpemba effect, as it would identify the point in time at which each body of water achieved a full phase change into a solid. Freezing points could then be compared to see if the bodies with higher starting temperatures froze faster.

Potential sources of error include the accuracy of the measuring equipment. The Pasco PS-3201 digital thermometer used during the experiment is stated to have an accuracy up to by the manufacturer; this deviation was accounted for in the results. Other sources of error include variable temperatures within the freezer as some bodies might be closer to the cooling agent and freeze faster. This variance was to be quantified by measuring the minimum temperature achieved by each body of water as any difference would indicate a varying local temperature within the freezer.

Results:

Sample:

Starting Temperature ():

Time until frozen (S):

1

22.9

Unknown

2

38.4

~24,000

3

45.8

~15,500

4

54.2

Unknown

Figure 1: Temperature data for sample 1

Figure 2: Temperature data for sample 2

Figure 3: Temperature data for sample 3

Figure 4: Temperature data for sample 4

Discussion:

The results of the experiment can be considered unreliable based on the fact that there were many anomalous peaks, troughs, and jumps throughout Figures 1 and 2. In addition, no point of solidification was observed. In Figure 1, the temperature jumped down to for a period of approximately 16,000 seconds, far below the temperature inside a commercial freezer. The data for Figure 3 cut out for an unknown reason before a point of freezing could be observed. As these anomalies occurred at different points between the four data sets and no visible damage could be seen on the four digital thermometers, there was no evidence of equipment malfunction. Therefore, the anomalies could not be accounted for to extract accurate data. The severity of anomalies calls the entire experiment into question, and the results cannot be seen as giving any weight towards either argument of the Mpemba effect’s existence. The other data sets (Figures 2 and 4) would seem to have reasonable data, and of what can be interpolated from the results does seem to indicate the validity of the Mpemba effect, but again the unreliability of the measuring equipment means that this data cannot be seen as useful.

Possible improvements to the methodology of this experiment include using a sealed container to hold both the water and digital thermometer, removing the possibility of water vapour escaping from the container and giving a misleading result. Another possible improvement to the experiment could be the use of distilled water, reducing the possibility of particulates altering the results of the experiment. Repeated trials would provide more data which would result in a more accurate result. Lastly, a more precise method of heating the water to a specific temperature would allow for more exact results, allowing for the creation of a model.

Conclusion:

To confirm the existence of the Mpemba effect, the process by which hotter bodies of water cool faster than cooler bodies, an experiment was conducted to measure the point at which bodies of water at different starting temperatures froze when exposed to a cooling agent. Unfortunately, the results of this experiment are extremely anomalous and inaccurate, and no reliable data for the point at which all bodies froze can be observed. Because of this, this article cannot be seen as a reliable source in terms of the Mpemba effect’s existence.

References:

Lin E. “Mpemba effect: why hot water can freeze faster than cold”. Phys, (23/03/10). https://phys.org/news/2010-03-mpemba-effect-hot-faster-cold.html.

Burridge, Henry C. and Paul F. Linden. “Questioning the Mpemba Effect: Hot Water does Not Cool More Quickly than Cold.” Scientific Reports (Nature Publisher Group) 6, (24/11/2016): 37665. https://www.nature.com/articles/srep37665.

Lu, Zhiyue, 卢至悦, and Oren Raz. “Nonequilibrium Thermodynamics of the Markovian Mpemba Effect and Its Inverse.” Proceedings of the National Academy of Sciences of the United States of America 114, no. 20 (16/05/2017): 5083-088. https://www.pnas.org/content/114/20/5083.

Wang, Andrew, Monica Chen, Yanni Vourgourakis, and Antonio Nassar. “On the Paradox of Chilling Water: Crossover Temperature in the Mpemba Effect.” arXiv, (13/01/11). https://www.researchgate.net/publication/48187824_On_the_Paradox_of_Chilling_Water_Crossover_Temperature_in_the_MpembaEffect.

Pankovic, Vladan and Darko V. Kapor. ”Mpemba Effect, Newton Cooling Law and Heat Transfer Equation.” arXiv, 2012. https://www.researchgate.net/publication/45916133_Mpemba_effect_Newton_cooling_law_and_heat_transfer_equation.

About The Author

 Reuben Meyer is a 10th-grade student at Good Shepherd Lutheran College Noosaville. He is currently studying in the Real Application of Maths and Science (RAMS) elective course for which he wrote this article.

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