I have a love-hate relationship with brain-tickling physics problems like this. I've seen them on the Veritasium Youtube channel, and they take a predictable path: state a problem that's...
I have a love-hate relationship with brain-tickling physics problems like this. I've seen them on the Veritasium Youtube channel, and they take a predictable path: state a problem that's counterintuitive, let the community fight about it, then come back with a crucial nugget that makes the problem statement clearer. We don't really have the nugget for this one.
I'm not an expert in material science or kinetics, though I have some background in it. This problem feels like something similar the Veritasium videos (infinitely long wires, can a car with a propeller go faster than the wind). At face value, it seems easy. Can a cup of hot water freeze faster than cold water? Well, no, if you interpret that to mean "If system A has more energy than system B and both are placed in a cold environment that removes energy at roughly the same rate, which will reach equilibrium with the cold environment?" So if you have to remove twice as much energy from system A, it should take ~twice as long (and there are a lot of assumptions made by the observer about each system if that's the answer). At it's most basic level, freezing is removing enough energy to reach a phase change. How you reach that phase change is now the difficult topic, as discussed in the article.
And so I have to wonder if there would be less controversy with a statement like this, "Is there a kinetic pathway that allows system A to reach equilibrium faster than system B, if the state of system A is farther from equilibrium than system B is."
And I think that comes down entirely to experimental setup. I thought the notion that frost forming on a cold cup of water could be melted by the hot cup of water was interesting. And there are lots of questions that arise regarding the experimental method.
How would these two cups freeze if they were insulated vessels? Does the hot vessel reject enough energy to the freezer space that it becomes harder for the cold vessel to reject heat at the same rate?
So should separate freezers be used?
Does the hot water undergo more natural convection when placed into the freezer, and thereby more mixing, and experience a more uniform freezing rate (if so, could this be solved by insulated vessels)?
How does the size scale affect the freezing? That is, if we use a huge freezer with a tiny cup, versus a large cup in a small freezer.
Does the vessel shape matter when doing this experiment? Different shapes will affect heat transfer, but does it matter?
Is the cup suspended in the freezer or is it placed against one of the freezer's cold walls?
Anyway, you can see that just the experimental setup yields questions that could have fascinating answers. I'm sure many of these have been answered already. But at its core, the question posed makes it difficult to answer in a way that gives a satisfactory thermodynamic explanation.
I'll leave it here with this quote:
Science continues to spring from his insistence about the effect that bears [Mpemba's] name. Osborne, discussing the results of their investigations together, took a lesson from the initial skepticism and dismissal that the schoolboy’s counterintuitive claim had faced: “It points to the danger of an authoritarian physics.”
I have a love-hate relationship with brain-tickling physics problems like this. I've seen them on the Veritasium Youtube channel, and they take a predictable path: state a problem that's counterintuitive, let the community fight about it, then come back with a crucial nugget that makes the problem statement clearer. We don't really have the nugget for this one.
I'm not an expert in material science or kinetics, though I have some background in it. This problem feels like something similar the Veritasium videos (infinitely long wires, can a car with a propeller go faster than the wind). At face value, it seems easy. Can a cup of hot water freeze faster than cold water? Well, no, if you interpret that to mean "If system A has more energy than system B and both are placed in a cold environment that removes energy at roughly the same rate, which will reach equilibrium with the cold environment?" So if you have to remove twice as much energy from system A, it should take ~twice as long (and there are a lot of assumptions made by the observer about each system if that's the answer). At it's most basic level, freezing is removing enough energy to reach a phase change. How you reach that phase change is now the difficult topic, as discussed in the article.
And so I have to wonder if there would be less controversy with a statement like this, "Is there a kinetic pathway that allows system A to reach equilibrium faster than system B, if the state of system A is farther from equilibrium than system B is."
And I think that comes down entirely to experimental setup. I thought the notion that frost forming on a cold cup of water could be melted by the hot cup of water was interesting. And there are lots of questions that arise regarding the experimental method.
Anyway, you can see that just the experimental setup yields questions that could have fascinating answers. I'm sure many of these have been answered already. But at its core, the question posed makes it difficult to answer in a way that gives a satisfactory thermodynamic explanation.
I'll leave it here with this quote: