The Flying Circus of Physics

By: Lee Grenci , 7:19 PM GMT on December 21, 2012

Beell asked me to follow up on my tuna-can experiment using RO water (reverse osmosis). As I mentioned, my wife put a hold on Lee's experiments until after Christmas.

If the truth be told, she probably remembers my last freezer experiment when, after a hailstorm after dark, I took a flashlight and crawled around on my hands and knees in the front yard looking for hailstones with an insect entombed at its core (updrafts in strong thunderstorms can sweep insects to high altitudes, where water deposits onto bugs and freezes). Needless to say, she was not very enthusiastic about frozen insects being stored in her freezer (she said it "bugged" her). :-) The bottom line is that my freezer experiments are not very popular in the Grenci household.

As you might have read in the comments section below my tuna-can blog, I told beell that I'm expecting more drops to remain unfrozen after several tens of minutes in my freezer. I'll let you know what happens.

Beell's interest in my experiments reminded me of one of my all-time favorite books, Jearl Walker's The Flying Circus of Physics. I just love this book!

One of Walker's experiments has always intrigued me. I bought his book at least 20 years ago, but, alas, I confess that I've never had the time or drive to try the experiment. To my credit, I've always had it on my list of fun things to do (at 65, I better get my rear in gear). My procrastination aside, Walker's experiment goes something like this...

Grab two identical containers (cups, etc.). By identical, I mean they both must have exactly the same thermal characteristics. Fill one with cool water (I think the temperature matters here, but I'll have to look this up) and the other with boiling water. Great care must be taken to insure that both containers have exactly the same amount of water, so measure, measure, measure! Now place both containers outside on your porch on a cold winter night. You must pay close attention because you want to determine the time it takes for the water in one of the containers to freeze. So you just can't walk away and watch a movie or order a pizza. In other words, you must check your experiment frequently.

Which container freezes first? You might be surprised to learn that the boiling water should freeze first. Can anybody explain why?

Lee Grenci

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17. DelWeather
6:54 PM GMT on December 24, 2012
I tried to model the cooling of water including mass loss due to evaporation. I decided the Newton's Law of Cooling constant should be multiplied by a linear factor based on the ratio of initial mass over current mass (so that, as mass decreases, the cooling constant increases). Why linear? Because thermal conductivity has units that are linear in mass. And volume goes as the first power of mass. Not sophisticated or based on much, but easy to model. Then I looked at the graph for how the number of molecules with enough energy to evaporate from a surface depends on temperature (using the Maxwell-Boltzmann distribution, integrating above some arbitrary energy and seeing how that function depended on temperature) and the result (which involved an exponential and the Error Function... eww) looked for all the world like a linear function that crosses the horizontal axis at some temperature... which must be something like the temperature where the evaporation rate heads to zero. So maybe that is the dew point, or something like it. I then used my initial and final masses and temperatures from yesterday's experiment to make a rough guess at the proportionality constant.

Then I performed a simple numerical integration using Python. After tweaking the proportionality constants for cooling and evaporation, I got this:



Mass Graph 1

Temp Graph 1

Red is starting with boiling water, white is for room temperature water. You can see that I got the mass decrease close, and this shows the initially boiling water cooling faster due to mass loss. But still, the model is poor, since I know the temperature of the initially boiling water was much closer to that of the room temperature water by the time the latter started to freeze.

One thing that neither my explanation nor the one proposed in the original post takes into account is this: Newton's Law of Cooling assumes that the temperature of the water in the cup is uniform at all times. That is, it doesn't take into account energy transport through the volume of the water. The thermal conductivity of water is quite a bit higher at boiling than it is at room temperature (about 10%!). Thus, the improved efficiency of moving energy out of the bulk and towards the surface at higher temperatures means the hotter water temperature will catch up with the cooler water temperature even faster than what I modelled here.

I'm starting to believe that if I were in Fairbanks (-30 C this morning and -35 C dewpoint), and I did this experiment on my porch instead of my refrigerator, I might actually see the boiling water start to freeze first... maybe. Anybody up in Fairbanks want to give it a try?
Member Since: October 9, 2012 Posts: 0 Comments: 52
16. WunderAlertBot (Admin)
4:47 PM GMT on December 24, 2012
24hourprof has created a new entry.
15. LowerCal
11:56 PM GMT on December 23, 2012
When I first heard the claim from my Jr. High School science teacher that hot water would freeze first it seemed unlikely yet intriguing and I had try it for myself.

I used two virtually identical containers - aluminum ice cube trays (it was the Preicemaker Era). I thought frequent opening of the freezer might introduce too much variability in conditions so I used cool tap water a few times to establish the approximate time interval until ice crystals would first appear.

Then I filled each tray to the same level marking, one from cool tap water and one from cool tap water raised to boiling temperature. There was no discernible difference in the onset or progression of freezing. I performed the experiment again with the same trays in the same position but switching which I filled with tap and boiling temperature water. Again there was no discernible difference in freezing timing.

To this day I remain skeptical of the effect and per your link the effect is still not reliably reproducible with identical samples of water. At the very least the difference in water temperature is not the determing factor.
Member Since: July 26, 2006 Posts: 59 Comments: 10288
14. Lee Grenci , Retired Senior Lecturer and Forecaster
10:08 PM GMT on December 23, 2012
Quoting Barefootontherocks:
Hello Lee,
I thought it might be because the elevated kinetic energy levels of hot water molecules make them quicker to react, so to speak.

Thanks for your blogs. Happy you are blogging at wu. Must admit I have some Ketchup reading to do - which is kinda like reading tea leaves. :)

To you and yours,
Merry Christmas and Happy New Year



And to you, my friend. And thanks for the welcome. Everyone has been so kind.
Member Since: October 24, 2012 Posts: 128 Comments: 1063
13. Barefootontherocks
4:41 PM GMT on December 23, 2012
Hello Lee,
I thought it might be because the elevated kinetic energy levels of hot water molecules make them quicker to react, so to speak.

Thanks for your blogs. Happy you are blogging at wu. Must admit I have some Ketchup reading to do - which is kinda like reading tea leaves. :)

To you and yours,
Merry Christmas and Happy New Year

Member Since: April 29, 2006 Posts: 173 Comments: 21589
12. Lee Grenci , Retired Senior Lecturer and Forecaster
2:02 PM GMT on December 23, 2012
Quoting DelWeather:
The experimental results are in. The room temperature water formed ice first. Myth busted? Maybe?

I used identical paper cups with 206 g of water each (starting instead with equal VOLUMES of water would be comparing... well, more water to less water). In my freezer (-11.5 C... but the door kept getting opened both by the main experimenter and his lab partner who was doing other, more applied, development... like dinner), it took 90 minutes to form a skim of ice on the cooler water. The final mass of the water in each cup was 196 g for the water that started hot, and 204 g for the room temperature water. Given my quick and dirty initial evaporation experiments, I was surprised by the amount of evaporation that actually occurred.

I didn't wait until the water froze completely for several reasons: 1) I figured that would be very hard to judge, 2) the better, more testable question seems to me to be "which cup of water reaches 0 C first?" and 3) I don't want to wait that long. Perhaps, even starting with a few degrees "behind" as the initially cooler water started to freeze, the initially boiling water, having about 4% less mass, might end up completely freezing sooner.

Questions: What if we started with equal volumes of water? What if I had waited until the water froze completely? What if we had put the water outdoors at sub-freezing temperatures (a slight breeze and increased volumes of cool air could lead to lower humidities above the water samples)?

Interesting side note. My predictions of freezing time were way off. It seems my cooling constant was too large by a factor of two or so. I had bumped UP my constant, based on the thermal mass of the thermometer. Perhaps, instead of slowing the cooling of the water, the big thermometer sped that cooling up. Maybe it was acting like a big cooling fin. Now that I think about it, this latter explanation makes more sense.


Very nice. I'm not surprised by your results, given the scientific debate over this issue. I think starting with the same mass was the way to go. A colleague of mine told me that he, too, had mixed results with this experiment. Many, many thanks for your time and effort. You reminded me that this experiment is not set in stone. Much appreciated and it's nice for me to learn from you.
Member Since: October 24, 2012 Posts: 128 Comments: 1063
11. DelWeather
10:22 PM GMT on December 22, 2012
The experimental results are in. The room temperature water formed ice first. Myth busted? Maybe?

I used identical paper cups with 206 g of water each (starting instead with equal VOLUMES of water would be comparing... well, more water to less water). In my freezer (-11.5 C... but the door kept getting opened both by the main experimenter and his lab partner who was doing other, more applied, development... like dinner), it took 90 minutes to form a skim of ice on the cooler water. The final mass of the water in each cup was 196 g for the water that started hot, and 204 g for the room temperature water. Given my quick and dirty initial evaporation experiments, I was surprised by the amount of evaporation that actually occurred.

I didn't wait until the water froze completely for several reasons: 1) I figured that would be very hard to judge, 2) the better, more testable question seems to me to be "which cup of water reaches 0 C first?" and 3) I don't want to wait that long. Perhaps, even starting with a few degrees "behind" as the initially cooler water started to freeze, the initially boiling water, having about 4% less mass, might end up completely freezing sooner.

Questions: What if we started with equal volumes of water? What if I had waited until the water froze completely? What if we had put the water outdoors at sub-freezing temperatures (a slight breeze and increased volumes of cool air could lead to lower humidities above the water samples)?

Interesting side note. My predictions of freezing time were way off. It seems my cooling constant was too large by a factor of two or so. I had bumped UP my constant, based on the thermal mass of the thermometer. Perhaps, instead of slowing the cooling of the water, the big thermometer sped that cooling up. Maybe it was acting like a big cooling fin. Now that I think about it, this latter explanation makes more sense.
Member Since: October 9, 2012 Posts: 0 Comments: 52
10. Lee Grenci , Retired Senior Lecturer and Forecaster
8:46 PM GMT on December 22, 2012
Quoting DelWeather:
I'm not sold on the explanation. Since school is out, I think I'll model it in Mathematica, as I'm waiting for the water to freeze in my freezer (since the winter refuses to be winter, I can't do the experiment on my porch!).

Here's why I doubt the above explanation: the evaporation rate must be substantially high in order to let the hotter water "catch up" to the cooler water. While it's true that the warmer the water, the quicker it will cool (aka Newton's Law of Cooling, dT/dt=kT), the warmer water should never catch up to the cooler water, neglecting evaporation. Is the evaporation rate enough to lower the mass of water enough to let the hotter water catch up to the cooler water? Doesn't seem likely.

So I'm going to do this the hard way. I've now got some water in the freezer so I can estimate the constant k in Newton's Law of Cooling. Then I'll get an evaporation rate of boiling water, using my wife's food scale. Then I'll model the situation (have to determine how to model evaporation rate... ideas? exponential in temperature difference between water and air?) THEN, when maximum fun has been extracted from the modeling angle, I'll do the experiment.



It's good that you are skeptical...see this piece from Science News. I haven't kept up with this problem (obviously), but apparently it can be reproduced under very special circumstances.

I have Walker's first edition (1977), and I finally found it in a very old and musty box in my basement...(I haven't read it in 30+ years, so thanks for prodding me to search my basement). On page 243, Walker writes:

"The critical feature is the increased evaporation from the initially warmer water. If equal masses of warmer and cooler water are set outside in freezing weather and in open-topped containers, the evaporation from the warmer water will reduce the mass remaining in that container. With less mass to cool, the water in that container can overtake the cooling of the initially cooler water and reach the freezing point sooner. The actual cooling rate can depend somewhat on the composition of the containers, the circulation above the containers, and the circulation of the water. Although Bacon (Sir Francis) commented on the effect and although the result is well known in Canada, people in warmer countries find it mysterious. The physics journals rediscovered it recently only after a high school student in Tanzania convinced his skeptical teacher of the result."

Good luck. Let me know what happens.
Member Since: October 24, 2012 Posts: 128 Comments: 1063
9. DelWeather
8:44 PM GMT on December 22, 2012
Hey Rookie, I've never lived anywhere where winter behaved like THAT. Minus 41 C... whew.
Member Since: October 9, 2012 Posts: 0 Comments: 52
8. DelWeather
8:32 PM GMT on December 22, 2012
Well finding the constant in Newton's Law of Cooling wasn't as easy here at home as it would have been in the lab. The only thermometer I could find is the big one I use for keeping track of wort temperature while brewing. The thermal mass of that thing is huge! So after several trials, I settled for a constant of 0.00067 per second.

Next, I tried to measure the decrease in mass of water put into the freezer at near boiling temperature. I found no change in the mass down to a temperature of about 30 C, so I doubt that I'm losing much mass at all going all the way to 0 C.

I modeled the cooling curve and found that I will need about 1800 to 2000 seconds to cool my water to 0 C. It's time to do the experiment.
Member Since: October 9, 2012 Posts: 0 Comments: 52
7. Some1Has2BtheRookie
7:55 PM GMT on December 22, 2012
Should winter start behaving as winter should, you can try this experiment: Link :-)
Member Since: August 24, 2010 Posts: 0 Comments: 5222
6. DelWeather
6:29 PM GMT on December 22, 2012
I'm not sold on the explanation. Since school is out, I think I'll model it in Mathematica, as I'm waiting for the water to freeze in my freezer (since the winter refuses to be winter, I can't do the experiment on my porch!).

Here's why I doubt the above explanation: the evaporation rate must be substantially high in order to let the hotter water "catch up" to the cooler water. While it's true that the warmer the water, the quicker it will cool (aka Newton's Law of Cooling, dT/dt=kT), the warmer water should never catch up to the cooler water, neglecting evaporation. Is the evaporation rate enough to lower the mass of water enough to let the hotter water catch up to the cooler water? Doesn't seem likely.

So I'm going to do this the hard way. I've now got some water in the freezer so I can estimate the constant k in Newton's Law of Cooling. Then I'll get an evaporation rate of boiling water, using my wife's food scale. Then I'll model the situation (have to determine how to model evaporation rate... ideas? exponential in temperature difference between water and air?) THEN, when maximum fun has been extracted from the modeling angle, I'll do the experiment.

Member Since: October 9, 2012 Posts: 0 Comments: 52
5. Lee Grenci , Retired Senior Lecturer and Forecaster
12:56 PM GMT on December 22, 2012
Folks,

Here's my answer...

The cooling rate is a function of the difference in temperature between the air and the water. So the initial cooling rate of the boiling water is much higher than the initial cooling rate of the cold water (cooling rates decrease thereafter). Moreover, more water is lost to evaporation over the boiling water (rate of evaporation is a function of temperature).

Eventually, the cooling rate over the initially hot water reaches the cooling rate over the initially cold water. But because the volume of water of the initially hot water is less than the volume of the initially cold water, the initially hot water freezes first. Or, at least it should. Like I stated before, it's important to start with exactly the same amount of water in both thermally identical containers.
Member Since: October 24, 2012 Posts: 128 Comments: 1063
4. bappit
3:17 AM GMT on December 22, 2012
The wikipedia article is interesting. Details, details.

Ricky Rood's recent blog hits on the same general topic but in the reverse direction. The lesson I think is that details matter.

"In 2007 I started this blog with the release of the Intergovernmental Panel on Climate Change Fourth Assessment Report. At the time of that report, the evolving scientific understanding made it clear that the melting of sea ice and ice sheets had been underestimated in the papers that were used in the 2007 report. A major reason for that underestimation was due to the simplicity of the way the freezing and thawing of large masses of ice were represented in the climate models. Freezing and thawing of large masses of ice on Earth is not like an ice cube melting away on the kitchen counter at normal room temperature. Rather, it is a far more dynamic process, with, for example, water from the ice melt collecting on top of an ice sheet, then flowing through the ice in a way that accelerates melting. In the ocean, the seawater accelerates sea ice melting through essentially stirring the ice in warmer water. If you go back to the ice sitting on the kitchen counter, you can speed up its melting by fanning it with warm air or by placing it in a glass of water and stirring it. In all of these cases heat is being carried to the ice more effectively than in the case of the static cube sitting on the counter."
Member Since: May 18, 2006 Posts: 17 Comments: 6830
3. Lee Grenci , Retired Senior Lecturer and Forecaster
9:00 PM GMT on December 21, 2012
Quoting beell:
The hot water freezes first-because your wife, possessing more kinetic energy than you (or I), could freeze the boiling water with just a single look at it, and you, out there on the front porch on a cold winter night.

Some things cannot be explained by science/physics.



LOL!!!!
Member Since: October 24, 2012 Posts: 128 Comments: 1063
2. beell
8:09 PM GMT on December 21, 2012
The hot water freezes first-because your wife, possessing more kinetic energy than you (or I), could freeze the boiling water with just a single look at it, and you, out there on the front porch on a cold winter night.

Some things cannot be explained by science/physics.

Member Since: September 11, 2007 Posts: 158 Comments: 19317
1. Skyepony (Mod)
7:39 PM GMT on December 21, 2012
Mpemba..

I want to try the tuna can freezing experiment with some ozonated water. Something only found naturally around alot of lightning.

After the Holidays.
Member Since: August 10, 2005 Posts: 396 Comments: 43348

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About 24hourprof

Retired senior lecturer in the Department of Meteorology at Penn State, where he was lead faculty for PSU's online certificate in forecasting.