Hot Water vs Cold Water Freezing

Cecil's Columns/Staff Reports
1

Man , It took a lot of screens to get here and I’m not sure this is the right place but here goes…

A a former physics student I thought I could add to this eternal question. Since freezing entails the transfer of heat, all things being equal the hotter the starting point of water the longer it will take to freeze.

There is however one little quirk which physics students know from caliometry experiments. There is a little additional energy required to change the physical state of water from a liquid to ice. that means at a temperature near the point of freezing a sample chilled from slightly above freezing will freeze more quickly than a sample at the freezing point. It works kind of like a little push over a hill.

This takes precise measurement to demonstrate…see your local college physics lab.

2

It wasn’t quite right, Albert, but it was close enough for practical purposes. I’ve fixed.

The column in question is Which freezes faster, hot water or cold water?

3

One might suspect that citing a weak analogy like “push over the hill” would be considered insufficient verification to merit revising a Cecil article. Especially in an area that’s been extensively studied for over 150 years, and positing something that sounds causationally and thermodynamically very unlikely.

Perhaps if the original poster, albert, could point us to some place where this is explained in more detail…?

4

Hmmm… I’m skeptical of Albert’s claims, but I’m willing to be convinced. In fact, I’d be happy to be convinced – I would learn something interesting. Let me formulate a few questions that will help me understand what you are saying. Please feel free to correct me where I go wrong below, because I will learn from the corrections.

Let’s call the freezing point of water “F”. If I understand you, you are saying that there is some small temperature difference t1, and an even smaller difference t2, so that:

t2 < t1

and that water that starts at (F+t1) will freeze to ice at temperature F faster than water that starts at (F+t2) in the same environment. Have I understood you correctly, or am I wrong already? If I’m correct, let me ask a few more questions.

Isn’t temperature of a substance continuous – that is to say, that before the sample starting at (F+t1) gets to (F), it is at some point at temperature (F+t2)? If not, I see my problem already, but assuming that’s so, let’s get our lab assistant to run this experiment for us:

He puts the sample that’s at (F+t1) in a freezer, with a temperature monitor. When the temperature of that sample reaches (F+t2), he puts the sample at (F+t2) in an identical freezer, with an identical monitor. Now, if I understand you correctly, the first sample (that started at (F+t1) ) not only freezes before the sample at (F+t2), it will do so fast enough that the total time elapsed (including what’s already passed) will be less than the time it takes (F+t2) to freeze. Have I stated this correctly?

Unfortunately, our careless lab assistant isn’t too bright, or we haven’t been specific enough in our instructions. In his efforts to make both samples exactly the same – same ambient temperature, same freezer temperature, same cooling, same container, same volumes at the point they are at F+t2, and so forth – he has neglected to give them different labels, and can’t tell me which sample is which. Now, I want to know before the experiment continues which sample is which, otherwise the results are meaningless. What can I measure about the two systems to tell them apart?

If there is something to measure, in what way is this not a mistake by our lab assistant, whom we told to keep the environments identical?

If there is not, then how do the two samples behave differently?

5

My opinion of Texas has just zoomed out of sight…

“Texan” has gotten to the raw nub of the gist of the objections to the concept of “hot water freezing faster than cold”.

To re-flog this old Equus: at some point in time the hotter water is going to get down to the temperature of the colder sample. At that instant the two samples are identical. Now how does the originally hotter sample “know” it should now continue cooling down faster than the colder sample? It appears you’d have to attribute something like “memory” or “momentum” to the water, so it would know that it was originally hotter, and cooling off at a faster rate, therefore it shoul dkeep up its fast cooling rate. Of course water doesnt have memory or momentum, AFAIK.

Some possible outs:

(1) The water doesnt have a constant temperature throughout, something like convection currents in the hotter water provide the “momentum”.

(2) ???

6

Yes, Texan has elegantly stated what I’ve always seen as an obvious point: the warmer water must match the cooler water’s temperature on its way past it in the race to freezing; the tortoise and the hare, as it were. Unless there’s an actual, measurable momentum in the rate of freezing–that causes water at 33 degrees F that’s been at 33 degrees F to freeze more slowly than water that’s at 33 degrees F but was at 34 degrees F an hour ago–I’m not convinced.

7

There are a few more “outs”, but I don’t see how they apply to Albert’s claim.

NE Texan has indeed hit the nail on the head with his excellent reply. There must be some physical property which one can use to differentiate the two samples. One such property might be mass. Given that density is a function of temperature, one might measure equal volumes of water, but not have equal masses. Unfortunately for Albert, near freezing the density of water actually increases with temperature, which means the warmer cup would likely have more mass and not less.

I have heard my own [biologist] father claim that a warm water pipe in our house froze one winter, while an adjacent and otherwise “identical” cold water pipe did not. I’m sure these kinds of occurances account for the repeated claims that hot water can freeze before cold water. Neglecting the fact proximity does not imply identical conditions - e.g., one pipe could be sitting in a draft - there are properties that can vary between cold water and warm water pipes.

The water where I grew up had a relatively high percentage of dissolved minerals. In the space of two years, we went through three water heaters, before installing a water softner. It is possible that more minerals were disolved into the warm water, and that these minerals built up inside the hot water pipe as the water cooled between uses. Then there would be less water in the pipe, but the (copper + mineral) pipe would seem to better insulate the water. (Or, does a “clean” pipe provide a better thermal contact between the water and the heat source that is the house?) Mineral deposits might also provide a surface on which ice can form, meaning a pipe with build up will freeze faster than one without. Conversely, it is possible that heating the water actually drove out some of the minerals so that the cold water pipes had more build up. (The water heaters presumably dieing from mineral build up.) Again there are the same issues. Without conducting an experiment, or asking a plumber, I couldn’t say which affect tends to dominate, but I can say that “identical” hot and cold water pipes aren’t necessarily identical.

One thing is clear however, given two identical samples of water, the colder one will freeze first.

8

Actually, Albert has a very good and valid point. I’m a Chemical Engineer who specialized in Physical Chemistry.

The problem is that if you look at the phase transition solid -> liquid for water, the change in Gibbs Free Energy when going from liquid to solid is indeed negative, so water should freeze at 0º C (under normal pressure) spontaneously. However, in all non-ideal phase transitions there is something called the “free energy barrier” which has to be crossed for the phase transition to take place. This is what allows water and other substances to become supercooled. If there was no “free energy barrier” there is no possible way you could ever supercool any liquid, because it would have to solidify at the temperature of the phase transition. There is a good explanation of Gibbs Free Energy and the “free energy barrier” here , although they speak of a “free energy barrier” for chemical reactions. Here they explain how supercooling is possible due to the “free energy barrier”. I quote: “The reason that you can supercool or superheat through first-order phase transitions is because there is a free energy barrier separating the two phases.” The phase transition ice -> water is indeed a first-order phase transition.

So Albert is correct in stating that a sample chilled from slightly above freezing will freeze more quickly than a sample at the freezing point. In fact the phenomenon of supercooling and its cause (“free energy barrier”) are given as the most likely reason that warmer water freezes more rapidly than cooler water here. One important thing to note, is that the hot water only “seems” to freeze more rapidly. In the article above it says that much of the ice actually has large inclusions of still liquid water, while the colder water freezes to a complete solid faster than the warmer water.

9

Good, we have someone with credentials participating! But just stating “some scientific words in quotes” doesnt quite satisfy. Perhaps someone can expand:

(1) How does “the gibbs free energy explanation” explain the situation when the two samples reach the same temperature? Is the answer that the hotter water scoots across instantaneously into freezin, avoiding the dreaded freezing point?

(2) What is the magnitude of this difference? If it requires a calorimiter, it’s hard to imagine this effect being visible to us poor slobs with fridges and ice-cube trays.

10

Well, basically the explanation is kind of like Albert said. The slightly warmer water contains enough residual energy that it can cross the “free energy barrier” more easily, and thus begins freezing sooner. The sample of water that is at the exact temperature of the phase transition itself, actually has to take up energy from the outside to cross the “free energy barrier”. That is why Albert likened it to a push over a hill. Once you have reached the top of the hill, the rest is easy, but you need that little push to get over the top. Note that this only applies to when the samples begin to freeze. The colder sample will still contain less energy than the warmer sample, so it will still be the first to freeze completely, through and through.

However, as you mentioned, the actual free energy barrier is very small, and you definitely need to do real calorimetric experiments to determine it.

The only thing you might be able to observe in your freezer is that warm water will begin to freeze before cold water. But this sample of water/ice mix will contain inclusions of still liquid water, etc. The colder sample will actually be the first to freeze completely, through and through. It just might start freezing later than the warmer sample. So, I guess the corrrect formulation is to say that the warm water will start freezing before the colder sample, but the colder sample will be completely frozen before the warmer sample. This is mentioned in the last of my three links, and there is a very nice diagram of how the temperature changes over time for the two samples.

11

You could almost say this is the case. The thing is that the “freezing point” is actually a point of equilibrium in the phase diagram. Technically you can have liquid and solid water in whatever proportion you would like at the freezing point. If you then postulate that this is an ideal closed system (unattainable in our Universe, but this is a thought experiment, so humour me), these proportions will never change. The same amount of H[sub]2[/sub]O molecules will move from the liquid to the solid and from the solid to the liquid phase over any amount of time. What is needed is some kind of influence from outside the system to get the entire system to move across the phase transition. This can be added energy, seeding with ice crystals, etc. In fact the energy needed for the phase transition itself (in other words the “free energy barrier”) is exactly why citrus farmers will spray their fruit with water when a freeze threatens. The water will actually supercool a little, and when it then freezes, it releases energy, which keeps the fruit above freezing! If we had an ideal first-order phase transition, the act of water freezing would never release any energy.

What’s really fun, is that most substances also have a so called tripel point, when all three pases (solid, liquid, gas) are in equilibrium at a certain pressure and temperature. You should see if you can ever get the chance to observe a substance at a triple point. You can have a container with ice, water, and vapor, and the smallest change in temperature or pressure will suddenly make the whole thing solidify, or melt, or sublimate, or … or … or.

12

Sounds like a 1920’s Style Death Substance…

13

Hmmm, it might help if someone would directly answer these questions:
Assuming:

(1) You have bathtub #1 full of 100 degree (F) water.

(2) You have bathtub #2 full of 40 degree (F) water.

Which of the following statements are true?

(3) If the hotter water (#1) is going to freeze FIRST, it must attain a lower temperature than #2.

(4) By some principle of continuity, if #1 is going to get to a lower temperature, at some point it must have the SAME temperature as #2. i.e. at some time both #1 and #2 will be at some intermediate temperature, say 35 degrees.

(5) If they are at the same temperature, how are #1 and #2 different, in that #1 is going to freeze more quickly?

Either hot water doesnt freeze more quickly, or one of the statements above is somehow incorrect, or there’s some other loophole we havent fathomed yet.

14

This is the incorrect assumption. At no point in time will the warmer sample have a lower temperature than the colder sample. Just look at the diagram in my last link again to see how this never happens. The red line (the warmer water) never crosses the blue line, but the red line starts to freeze first. The warmer water will begin to freeze first, because it will actually begin freezing at a higher temperature (but still one that is below the actual melting point of ice) than the colder sample, due to the fact that it can cross the “free energy barrier” more easily. This means the colder sample will “supercool” much more than the warmer sample, and begin freezing last, but finish freezing first.

Is it so hard to understand? :confused:

15

[Dr. Felix Hoenikker]No, zat vould be Ice-Nine.[/Dr. Felix Hoenikker]

Which actually does exist by the way. See
here. But, it is not solid at room temperature under normal pressure, so no worries there.

16

Yes!

Please try to explain: why should the cooler bathtub supercool much more?

If they’re both passing thru the same temperature, how does the hotter one remember it was hotter, and therefore start freezing at a higher temperature?
Also remember, we’re talking about bathtubs at 40 and 100 degrees, not ultra-pure vials at 32.001 and 32.003 degrees (sorry, F).

What may happen under careful laboratory conditions is interesting, but may not be relevant in our kitchen experiment.

Regards,
grg88

17

Ok, I have credentials too, in the form of a physics Ph. D. (Although it, and myself, are kind of old.)

I looks to me like Mycroft Holmes and grg88 are thinking about two different situations. grg88 (and NE Texan) is thinking about a classic thermodynamic process, in which the samples start in a uniform state and continuously, and slowly, transition from thermodynamic state to thermodynamic state. So the entire tub of water cools from 70 F to 70 F -1/infinity on down to freezing. In this case, the warmer sample eventually transitions to the same thermodynamic state as the 40 F sample. The 70 F sample can’t begin to freeze before the 40 F sample, because the 70 F sample becomes identical to the 40 F sample at some time after the 40 F sample has cooled to a lower temperature. You could reword this situation into trying to freeze two identical samples, one later than the other. The laws of physics predict that two identical samples will take the same time to freeze, so the one that starts last loses.

Mycroft Holmes is talking about cooling under conditions in which an entire sample is not in the same state, which is why ice and water simultaneously exist. (In nature, this often happens. How often have you seen a pond freeze solid in an instant? In my example of the water pipes, mineral deposits can form surfaces on which ice forms more quickly than in pure water.) This can happen, for example, if you cool a sample quickly enough that one part of the sample is cooler than another. Given a greater range of molecular speeds, the initially warmer sample might have enough molecules moving slowly enough to initiate the freeze first.

All that said. Take two cups of water, one filled from the hot water tap, and one from the cold. Place them in your freezer, so that both are the same distance from the cooling vents. The cold water cup is going to freeze first.

BTW, microwave ovens make superheating easier to demonstrate at home than supercooling. A very clean measuring cup, some water, and a microwave and you are ready to go. Heat your water long enough to observe boiling. Wait a bit for your sample to cool down, heat it for not quite long enough to boil and drop a tea bag in. If the water erupts, or starts boiling around the tea bag and not elsewhere, you’ve superheated the water. (Of course, you could just measure the temperature, but that is not as much fun, and since I live at 6700 feet, water doesn’t boil at 212 F anyway.) If you can’t superheat the water, either your glass and water aren’t clean enough or your microwave sucks.

18

The way I’ve heard this claim, it was that water which has been heated will freeze first. The heating has driven out gasses which impede the freezing process. I leave the demonstration up to the conscientious student.

19

The thing I am saying that there is no way we can have an ideal phase transition. A phase transition means there is a point with a specific temperature and pressure where the two phases are in perfect equilibrium and there is no energy needed to change phases. In real life this doesn’t happen. you have that extra barrier, the “free energy barrier”, that needs to be crossed before water can begin solidifying into ice. The sample that was initially warmer crosses this “free energy barrier” more easily than the colder sample, so it actually begins freezing first. However, the colder sample will be the first one to freeze completely, and will always have a temperature lower than the sample that was initially warmer. There is no contradiction of any physical or thermodynamic laws anywhere here.

The important thing to note is that the colder sample will indeed be the first one to solidify completely, so I’m not arguing that it won’t be the first one to freeze. The warmer sample will however be the first one to start freezing. In other words, it will be the first one where you will see ice crystals form.

20

This is another way of saying that you must have equal masses of water.