# cold water freezes fastest?

Well, as I peruse the archived columns, I noticed a bit about whether cold water freezes faster than hot water.

There were, IMO, fairly lenghty comments on it (and actual field tests? Really now :-).

Anyway, it is fairly simple to reason it through:

Hot water, at 75C, and cold water at 25C. They both need to cool down to 0C. To get from 75C to 0C, you will at some point reach 25C (this will take x seconds).

x > 0, Hence, it will take x seconds longer for the hot water to freeze than it will for the cold water.

Understand that this works for any temperature changes; the closer a substance is to a given mark, the quicker it will reach that mark.

This would imply that the remark about VERY hot water freezing faster than hot water is off the mark.

In addition, there is no “momentum” that would be gained by the hotter substance; a given substance has a specific heat transfer characteristic, and will always cool down or heat up at the same rate given the same conditions (start temp, pressure, etc).

While your logic is mostly correct, there are a few flaws in your argument.

1. While it is true that the 75 C water has to pass through 25 C to get to 0 C, it does not mean that the rate at which the temperature is dropping is the same for both samples. This is the essence of Zeno’s paradox.

2. There are many processes that cool a particular object. Assuming that we have the same amount of water in identical containers, the heat capacity and heat transfer capabilities will be the same with regards to convection and conduction of heat. However, the rate of cooling due to conduction is (IIRC) proportional to the fourth power of the temperature difference between the object and the air. One would therefore expect that the hot water would cool down at a much faster rate (dT/dt), than the cold water.

3. IIRC, the reason Cecil gave for very hot water cooling faster than hot water has to do with heat loss due to evaporation. This is a pretty powerful cooling effect. First, it requires a lot of heat to transform liquid water to water vapor. Second, this process also results in a loss of mass which then accelerates the cooling process further.

TheDude

Assuming that you are correct, then I understand that it would get from 75c to 50c rather quickly, and from 50c to 25c less quickly, and from 25c to 0c rather slowly. But the second one had a headstart, as it was at 25c to start with. Wouldn’t it freeze in the same amount of time as it took the first one to go those last 25 degrees? The first one does not have any momentum built up, does it?

A different argument goes as follows: Remember that the temperature of the water is not uniform. The outside cools down first, and then the inside cools down. The outside freezes before the inside also. The frozen surface will affect the internal pressure and thus the internal freezing point, but I don’t know this stuff well enough to say what the overall effects will be. Anyone want to continue from this point?

Keeves, you are, of course, correct except for the fact that with the case of the really hot water, you are now cooling down a significantly smaller amount of water.

As for your arguments about the internal pressure, I’m afraid I don’t really know enough about those types of effects. The freezing point of water depends very little on pressure (it does, however, decrease with increasing pressure-one of the reasons ice skates work), and I don’t think the pressure effects would be significant.

TheDude

## Keeves, you are, of course, correct except for the fact that with the case of the really hot water, you are now cooling down a significantly smaller amount of water.

Of course, you are also cooling down from a much higher temperature.

In addition, regarding the cooling rate depending on the differences in temperature between the water and the air:
This is a rate, and it changes as the temperature changes. So by the time you reach 25C it is a different rate then before.

In fact, you will have heated the air around slightly, so it will be a slightly slower cooling time (less difference between water and air) for the water cooled from 75C.

I grant you that evaporation will give hotter liquids a smaller mass to cool, but I believe (no tests) that the difference is offset by the amount that it warms the air around, and that both differences are very small compared to the amount of time it takes to cool down from 75C to 0C.

Basically, two substances close in temperature will experience less difference due to air temp differences, and mass loss and as the difference increases, the time taken to cool increases faster (or possibly as fast) as the benefit due to mass loss.

This all seems to come from the fact that some people believe that an ice cube tray of hot water will freeze faster than one of cold water. It may have originated with old refrigerators that were not frost free and the hot water melted the ice on the coils.
The ice cube tray was almost always situated directly above the coils and the frost would prvent (in theory) a rapid cooldown of the ice cube tray.
Having tested this many years ago with a non frost free fridge I can say it doesn’t work

Mr. Empirical to the rescue!

Yesterday I had to refill my ice cube trays, and having just read this thread, I decided to experiment.

I filled one tray with cold water, from the pitcher in the fridge. I filled the other tray with hot water, from the teakettle that had just been heated for tea. (It was too hot to touch comfortably, but no longer boiling.) Unfortunately, I forgot to note the time.

I then went away and started playing video games. Every so often, I came back and checked the freezer to see what had happened. In the time it took for the cold water to freeze solid, the hot water had just started getting a crust of ice on top.

So, cold water definitely freezes faster than hot water. Anyone who wants to convince me otherwise had better have a damn good argument. =B^)

AuraSeer:

Thanks for the comment; actually Cecil also said that he got the same results. However, he used convection heating/cooling arguments, and said that based on that reasoning, VERY hot water would cool faster than hot water.

I say that the colder water will always freeze quicker, regardless of the starting temperature of each.

The question about melting the ice from the coils is interesting, although I still think that the colder water would freeze quicker.

I just went back and reread the column in question http://www.straightdope.com/classics/a2_098b.html . It appears that the “comment” about very hot water freezing faster than hot water is not just a comment, but rather a series of scientific experiments appearing in Scientific American. And he offers the same explanation that I did, namely, that mass and heat loss from evaporation are the primary cause. For the actual numbers, see the link.

TheDude

The main point that I remember on this topic from my physics classes: the RATE of cooling is faster (because of the greater difference in temperatures) in hotter water (via convection) thus the average time per degree of temperature change is less in warmer water. Also, because of said convection currents, the Ice formed from warmer water will form a comparatively clearer, stronger crystalline matrix.

Argh, enough with the rate nonsense!

The rate is dependent on the temperature of the substance in question. The rate changes as the temperature of the substance changes. At 80C a cup of water will be cooling faster than a cup of water at 70C. At 79C that cup will still be cooling faster than the 70C cup, but will not be cooling as fast as it was at 80C…At 70C it will be cooling at the same rate as the other cup was at 70C.

(There will be slight differences: the cooling down from 80-70 would have raised the ambient temperature, which means a lower rate, and the 80C cup would have evaporated some, which would give it a smaller mass and a higher rate).

About the SA study; I didn’t read that closely enough. Apparently (based off the study) at very hot temperatures the amount of evaporation is significant (16%) - I didn’t expect it to be that great, but I can see how being close to the boiling point results in significantly more evaporation.

The rate of cooling is irrelevent here. The SciAm experiment quoted by Cecil only confuses the issue. The question is not “which cools off faster,” but “which reaches the freezing point first,” which is NOT the same question.

All these theories have a falacious assumption: hot water and cold water have the same freezing point (FP). FPs are determined mostly by properties of the substance, but are influenced by impurities in the substance. Zero C is the FP of PURE H20, but mix something else into it (salt, sugar, ethylene glycol (a.k.a automotive anti-freeze)) and the FP goes down. The FP depression is proportional to the amount of impurity present, not any physical property of the impurity.

So what? Just this: most water, but especially tap water, has plenty of air mixed into it. In fact, many taps have an areator attatchment to add air. Stick that water in the freezer, and the mixed-in air depresses the FP. So how does one remove air (or any gas) from water? That’s right! You heat it!
Try this: heat water in an open pan. It looks and sounds like it is boiling while still lukewarm. The heat is driving air molecules out of solution. As the amount of air decreases, so do the bubbles and noise.

Now you have tap water with less air mixed into it than it had before heating. As a result, the FP won’t be AS DEPRESSED AS UNHEATED TAP WATER. Let it cool to room temp, then put it in the freezer alongside some “gassy” tap water. The will cool at the same rate, since the temp differentials are the same, but THEY WON’T FREEZE AT THE SAME TIME - the previously hot water will reach its FP first.

So why the question in the first place? My theory about that involves people waking up on a chilly winter’s morn to find burst pipes in the basement. Keeping the above facts in mind, the hot water pipes would burst first, not because the water was hot, but because the water in them had been heated.

Eddie,
An excellent and well-presented point, but wrong. If you read the article, he states

. I had originally thought that what you say is true, but Cecil has already proved us both wrong.

TheDude

I freely admit, with no reservations, that Ceil Adams is the world’s smartest human being. However, Cecil is human, and (dare I say?) fallable. To wit: He did the wrong experiment.

From Cecil’s lab notebook:
“Then I carefully measured a whole passel of water into the Straight Dope tea kettle and boiled it for about five minutes. This was so I could compare the freezing rate of boiled H20 with that of regular hot
water from the tap. (Somehow I had the idea that water that had been boiled would freeze faster.)…Finally I put equal quantities of each type into trays in the freezer, checked the temp (125 degrees Fahrenheit all around), and sat back to wait…”

So Cecil has taken “hot water from the tap” and boiled water and made ice cubes. But we know that water will “outgass” at temps well below 100 C (see my previous post). Boiling is not necessary, just a short time in the family water heater.

He continues:
"I subsequently did the same with two trays of cold water, which had been chilled down to a starting temperature of 38 degrees.

The results? The cold water froze about 10 or 15 minutes faster than the hot water, and there was no detectable difference
between the boiled water and the other kind."

Unfortunately, “the other kind” may refer to unboiled hot tap water, or cold tap water. In any case, unless the Straight Dope Water Analysis Facility has some expensive lab equipment (which Mrs. Adams would surely not allow in the kitchen), anyone would have a hard time detecting the difference I am discussing, i.e., the presence (or absence) of air molecules in solution.

Since I have already destroyed any chance of grace in the eyes of Our Cecil, I shall now describe the experiment he should have performed:

1. boil some cold tap water in the Straight Dope tea kettle
2. float the teapot in cold tap water until the temperature of the boiled water is equal to freshly tapped cold water. Don’t contaminate the boiled sample with cold tap water, and don’t agitate the teapot or you will dissolve air molecules in the boiled water.
3. place equal volumes of cold tap water and carefully decanted boiled water into the Straight Dope Cryo Chamber. Grab some Cherry Garcia while the door is open.
4. open chamber and observe samples periodically until discovery that (with initial temps, volumes, and environmental temps being equal to ensure that the cooling rates are the same), the outgassed water forms ice crystals first. Since the temps of the samples were the same since step (2), the outgassed water freezes at a slightly higher temp, and may be said to have frozen “first”

As a last and probably vain attempt to redeem myself as a devoted minion wannabe, Cecil gets the last word:

"Another old wives’ tale thus emphatically bites the dust. Science marches on.

Eddie,
As a scientist, I would be highly interested in the results of that experiment. I believe you may be right, although I’m not sure if the quantity of gas dissolved in the water is sufficient to cause a significant freezing point depression. The only way to be sure is to run the experiment. And as we all know, the only accurate way to do so is in the official Straight Dope Research Labs. What say you, Cecil?

TheDude

What about the salts present in the tap water? By boiling it, some of the water evaporates and the concentration of the salts increases. This would also affect the experiment.
I really think we should nab up some grant money for this. We’re up against a barrage of properties here:
[ul][li]Tap water or “pure” water[/li][li]Aerated water or non-aerated water[/li][li]Various hot water temperatures[/li][li]Allowing the water to evaporate or not[/li][li]Humidity of the freezer[/li][li]Sensitivity of the freezer to humidity[/li][li]Spectrum from well insulated containers (i.e. heating nearby air has an effect) to thermally conductive containers[/ul][/li]
This is not to mention the uniformity of the freezer’s temperature, disturbing the frozen water, methods of decanting the water, etc.
To wit, I have three comments: first, it seems pretty complicated, second, under “conventional kitchen conditions” common sense prevails and cold water freezes faster, and finally, who really cares anyway?