russ_watters said:
Disagree. If "everything else is equal" is not at least implied, then there is no mystery/paradox to resolve. I could easily just say "hot water freezes faster than cold water if I put the hot water in the freezer and drink the cold water." That's not just unsurprising and not a paradox, it's just plain stupid. To put a finer point on it, the OP says "identical" and the wiki on the subject in different descriptions uses "identical" and "similar" and in folk tales if a difference were known one would do better to directly exploit the actual difference rather than indirectly exploit it by using hot water.
I was thinking about the following: if you boil water for a while, the freezing temperature of the water will change, so the initial composition of the water is different. Is this violating the conditions of 'all else equal'? The two water samples were the same before you started boiling one sample.
Actually, if boiling the water would
add nucleation agents to the water, then the freezing temperature would be higher than the non-boiled water and the Mpemba effect could be due to this. But the opposite (less nucleation agents when you boil the water) is happening as shown in the paper, so boiling for a long period of time and cooling a sample of this water should even increase the time of freezing compared to a sample that was not boiled!
russ_watters said:
That isn't true. In the first experiment in the article, he sealed the water in a glass vial and repeated the experiment dozens of times (both with tap water and de-ionized water) in order to make all other conditions besides starting temperature exactly identical. As should be expected, the effect did not manifest.
Yes. My point was that something (a boundary condition, the composition of the water, the convection current in the water) must be different (at the moment that the hot water reaches the temperature of the cold water) or else the effect cannot occur. I think that the experiment with the copper containers in Brownbridge fulfills the requirement 'all else equal at the start of the measurement'.
The convection currents in the water might also play a dominant role under certain circumstances, but I haven't seen many studies on this, only this one on the royal society of chemistry website:
http://www.rsc.org/images/adam-smith-paper-entry_tcm18-225152.pdf
According to these measurements, if your initial temperature is around 5 C then no convection currents will be formed. When you start with a higher temperature (20,40,60,80,100), the convection currents will result in a stronger cooling rate. There is then a trade-off between the time it takes to cool down from the initial temperature and the increase in cooling rate that you will (eventually) get. Also, the exact moment that the water starts to freeze is a statistical event and they show quite some spread in their measurements for the 5 C samples.