You will be astonished to know that this was actually the title for a paper published by The Institute of Physics and The Physical Society. But maybe after understanding the content discussed, you would also agree that there would be no more appropriate title than this. Personally, I would have said ‘Cool?!’, but as always, I digress. Let’s discuss this ‘cool’ idea, today known as the Mpemba effect.
The Mpemba effect states that, under certain circumstances, boiling water freezes faster than cold water. The history is fascinating- a 13 year old Erasto Mpemba from Tanzania (1969) was making ice cream with his buddies, but there was limited fridge space. He had bought boiling milk to make ice cream, but his friend saw this and rapidly put his cold milk in the freezer to freeze. There was limited space in this fridge, so to not miss his chance, Mpemba had no choice but to place the boiling milk in the freezer to freeze. What he discovered was shocking- his boiling milk had frozen in an hour and a half while his friend’s wasn’t even close.
Unfortunately for Mpemba, none of his teachers could believe his theory (as generally is the case for new scientific discoveries). And as also is the case, common (non-scientific) people had known about this idea for a while. It got to the point where others would rib the poor Mpemba: “We do not wonder, for that is Mpemba physics.” However, no one could come up with an explanation!
Luckily for Mpemba, a visiting professor Dr. Osborne caught on to the young innovator’s idea, and tested it further. What he found was interesting:
- An oil film on surface of water delayed freezing by several hours, which means that surface evaporation is important for system cooling.
- Evaporation only causes small changes in volume
- Latent heat of vaporization cannot account for more than 30% of system cooling
- A temperature gradient within the fluid was established
The first bullet is the key- a lot of the cooling occurs from the surface. Heat is transferred within the water via convection and wicked away from the surface by convection as well. This makes sense as air is a poor heat conductor, therefore having a lower convection coefficient than water. Another conclusion from this hypothesis is that a ‘hot top’ and ‘cool bottom’ is maintained during cooling to allow for a temperature gradient to drive cooling.
Ok, you certainly must be thinking that the verbal explanation is decent. How about some equations? Here are two key equations for heat transfer via transport processes:
Conduction: q” = k∇T; q” = heat flux, k = thermal conductivity, T = temperature
Convection: q” = hΔT; h = convective heat transfer coefficient
So a temperature difference is definitely the key to maximizing heat output, with conduction dependent on the spatial temperature distribution while convection is dependent on the surface-bulk temperature difference. And in comparison, for water the thermal conductivity is roughly 0.6 W/m²K vs the convective heat transfer coefficient, which is anywhere from 10-100 W/m²K. What does this mean? Convective heat transfer is generally more powerful for a means of heat transfer. This gives us some insight to the above explanation. In addition, it also explains a key idea: if the initial bulk temperature is hotter, the ‘hot top’ of the solution develops convection currents within the fluid, along with air convection current to wick away the heat of the solution (represented in below diagram)
So this is one potential explanation- let’s explore two others. First, warmer water can lose heat to evaporation. If we run the numbers, the enthalpy of vaporization (ΔHvap) of water is between 40-44 kJ/mol, which is a lot. That means that a lot of energy is potentially lost when water boils. This could also be a potential explanation for why the warmer water loses energy faster than the cold water does when freezing, especially when boiling.
Finally, we consider the effects of supercooling. Supercooling occurs when a liquid freezes below its melting point, without become a solid. How does this occur? Remember that when a liquid changes phases, it undergoes a structural change- i.e. a crystal lattice must form for the solid to exist. In addition, nucleation must occur- liquid nuclei must attract others in order to start to form a lattice. It is known that both of these events are preferred at temperatures below 0 C for water, and when the average mean velocity of the liquid is low. Therefore the rate of temperature cooling will have an impact on how much supercooling occurs- this is seen in the graph above and the video below:
In summary, evaporation, supercooling, and convection currents play a large role in explaining the Mpemba effect. I would like to caution the reader, however, that none of these results are conclusive. It is difficult to replicate this experiment exactly from one time to the next, because even the smallest impurity in the liquid will affect the cooling/freezing time. This even causes the Mpemba effect to not occur sometimes, the conditions of which are also unclear. What should be taken away from this story, however, is that science can be discovered/explored by anyone at anytime. We don’t know all the answers, and the persistence of 13 year old Erasto Mpemba has led to a huge ongoing discussion even today. Or cool pictures like these: