will it take off?

[SPYDERLK]

daTeacha. 4.18X50x0.6=10000?
Also freezer air humidity has little effect. That frigid air has very little water in it even tho its RH may be high. The high vapor pressure of hot water will drive water vapor into the freezer air which will in turn convey it to the extremely cold freezer surfaces, where it will condense off and form frost.
Larry

 

[patrick_g]

Rich and Larry, 1. I am familiar with a yard of ale and have considered a context switch in favor of the "whole nine yards!" Drinking from a "yard" can be accomplished without spilling if you have patience and a steady hand, otherwise you could be innundated. It could be worse than the "ice avalanche" when you tip your beverage glass way up to get the last swallow of liquid.

2. Larry, I think Rich pretty well covered my thoughts on the ice. With equal volumes of hot vs cold and equal circumstances of temp, humidity, and air velocity the delta time between respective freezings will depend on several factors but the time for the hot to cool to the temp of the cool is a greater factor than the minor difference in ice mass. First you have to cool the hot to the temp of the cool and then continue to cool it till it freezes. A better chance of freezing the hot quicker would be if the hot was say just warm and the cold was pretty darned cold. (Let me know if you need references to such scientific terminology as "pretty darned cold") Then the trays would melt themselves down into the frost and ice in the freezer bottom making better contact. The hot would sink in much further and faster and promote a faster rate of heat exchange that would continue throughout the time period, even after it caught up with the cool tray. It could catch up with the cool tray and then outrun it to the freezing point with its better thermal transfer. This might require some fine tuning of hot and cold temps, metal not plastic ice cube trays, a sufficiently overdue for defrosting freezer (not self defrosting.)

If the trays were suspended on insulating (plastic) holders I suspect that there would be no pair of temps, hot and cold, that would permit the hot to freeze first. I guess if we push this to the limit we'd have insulated trays open only at the top surface and no air circulatioin in the freezers. Then the "race" would be between the heat loss from a slightly smaller quantity of hot water than cold and the differential rate of freezing equal temp samples varying in mass by the same as the hot vs cold. If the hot could evaporate enough water to catch up with the cooling cold sample then it would pass it and freeze first.

That isn't so simple a setup as to lend itself to solution by inspection and cranking a few calorimetry formulae. Not that it can't be modeled mathematically but it is a good opportunity for an experimentalist. If I had to place my bet with no further thought or experiment I'd bet that the hot water would not cool enough by evaporation, i.e. not loose enough mass through evaporation to reduce its mass sufficiently that it could freeze before the cold sample.

Lets look at this qualitatively instead of quantitatively. If we can establish relationships that sufficiently define the character of the quantitative answer we don't need a numerical answer just a "<" or ">" or "=" sort of thing.

Is this a "race" condition that is NOT deterministic or can we bound the problem into one or more solution spaces?

If the cold sample were sufficiently cold and the hot sufficiently hot as in near freezing and near boiling respectively then it is easily seen that the cold freezes first.

We can then alter the initial conditions: Lets leave the hot temp the same and change the low temp sample. As the cold temp is stepped higher and higher its time to freeze approaches the time of the hot sample until when it is the same temp its time is the same. HMMMM, at no time did the cold take longer!

Now lets use the same cold temp over and over but change the intitial hot temp. (Remember we agreed that if the cold were near freezing and the hot near boiling that the cold would freeze first!) Each time the hot temp is lowered the time to freeze is reduced. Are we in agreement or is there an argument that the the hotter the water the faster it freezes? We assume the laws of thermodynamics that govern calorimetry have not been repealed. As the initial temp of the hot water is reduced the time to freeze is reduced. In the limit as the initial hot temp is lowered to the same temp as the cold sample the time to freeze equals that of the cold sample.

Are we missing something? Isn't the family of curves we are describing continuous, and monotonic? Like at what point is there a whoopdeedoo or a loop the loop in the curve of initial temp vs time to freeze? If it is argued that there is a "special" point at which the hot freezes faster than the cold then there has to be a discontinuity in the curve or a place where it is not continuous like when the "Y" value of the tangent curve jumps from minus infinity to plus infinity with an infintessimally small change in "X" value. A higher order inflection in the curve would suffice but would require a demonstratiion of its cause. All the thermal effects we are discussing are smooth, continuous, and differentiable curves with no discontinuities. An example of this concept is if we add heat to water it gets hotter (or changes state) and there is no temp region where adding heat to water cools it.

My intent was to clarify the problem. My lack of descriptive ability interferes but hopefully did not garble the basic ideas beyond recognition.

Pat

 

[SPYDERLK]

Hi Pat. This is interesting. I will model it and let you know. I will start at what I consider the highest probability for the hot freezing 1st - - 4C cold and HOT hot. I will datalog T vs t. There will be moving air.
Larry

 

[patrick_g]

Well Larry, You are doing the work so you can do whatever you want but I would mention that moving air wasn't part of the original problem statement and sort of artificially distorts the results. It might be interesting to see the effects of different air velocities but at values that wouldn't blow the water out of a "standard" ice cube tray.

The evaporative cooling will reduce the margin between the two but it remains to be seen if it will reduce the margin enough so that the reduction in mass of the hot sample could cool enough faster due to reduced mass to catch up with and pass the cold sample in getting to the freezing point.

Are you applying the chill factor to the entire ice cube tray ala the "flash freezing" process or just considering the air blowing across the tip of the free surface?

I'm sure we can contort the experiment enough to exceed the assumed initial conditions by a considerable margin in excess of "commpon sense", I know I have done it extensively recently but not in the ICE problem.

Pat

 

[SPYDERLK]

Pat, the problem visualizes in my mind as a standard home refrig/freezer with a manual ice tray station. Nowadays anyway, ice stations blow freezer air over the ice trays. The test will be done in an environmental chamber of uniform Tcold with non concentrated moving air. This is less in favor of the hot water. Still air would be even less, but I think would be unrealistic for making ice in todays refrigs.
It may be a couple weeks to gen the proper setup and retest incorporating lessons learned. The whole test group at work is interested in this.
Larry

 

[patrick_g]

Larry, It is an interesting problem. I guess my age and a certain lack of alacrity is showing as I wasn't thinking about a lot of moving air. This is not a problem with the problem or its statement, it is apparently a problem with my visualization. This is how we so easily diverge in our conceptualization of initial coditions.

In still air I think there would be no contest. With moving air it gets more interesting and complicated but I'm not convinced that the small reduction in mass due to expanded hot water and evaporation will reduce the energy required to be removed sufficient to drop the hot-hot water down to the cold water's dropping temp faster and outrun it.

We are in agreement as to the means of cooling faster than the cold water aren't we? At some point if the hot water catches up with the cold water its reduced mass will allow it to freeze faster. The question is, will the hot water catch up with the cold water? Is its evaporative cooling and reduced mass going to make it drop in temp fast enough to make up for the cold water's head start? The answer is, It depends! It depends on RH, wind speed, exposed surface, R-value/conductivity of the icecube tray, i.e. plastic of aluminum, how thick, form factor of the cubes, and such.

When in doubt of the number of angels dancing on the head of a pin, get a loupe and count them! I wish I had a cross top freezer with icecube racks.

Now about the billiard ball problem that I somehow missed out on here when first introduced. I was curious if there were other solutions besides the one I came up with and VOILA... there is a really neat (I like it better than mine) solution. The first solution listed at the site listed below is the MUNDANE one like I came up with. The second solution is, I think, way neater!

Weighing Pool Balls - Solution

Pat

 

[SPYDERLK]

Quote from patrick g: We are in agreement as to the means of cooling faster than the cold water aren't we? At some point if the hot water catches up with the cold water its reduced mass will allow it to freeze faster. The question is, will the hot water catch up with the cold water? Is its evaporative cooling and reduced mass going to make it drop in temp fast enough to make up for the cold water's head start? The answer is, It depends! It depends on RH, wind speed, exposed surface, R-value/conductivity of the icecube tray, i.e. plastic of aluminum, how thick, form factor of the cubes, and such.

Yeah Pat of course were in agreement. The concept of thermal momentum, where the temperature is dropping so fast it cant be stopped quickly enuf to avoid battering down the freeze barrier, is not what Im positing.

I think your set of depending factors is good. I would think that RH would have a negligible effect tho. The frigid air carries very little water because it cant, but to even 0C water it is arid - - and to hot water it might as well be 0%. Evaporation is an equilibrium condition with water molecules going from liquid to air and vice versa. The net change/loss is the evaporation we see. At 100%RH at air T = water T, evaporation would appear to have stopped because water vapor jumping into the liquid balances exacty with liquid water jumping into the gas/vapor phase. The thing about high RH air in a freezer is that the air is so much colder than even cold water. The water vapor it carries has so little energy compared the liquid water molecules that it is extremely rare for the gas to jump into the liquid. Humidity in a closed and stabilized freezer comes out in the 40-60% RH range, but even if higher the net evaporation from the water would change little if there were a non stagnant atmosphere. The evaporant would disperse and frost off on the freezer stabilized contents and the cooling coil, preventing humidity from rising much in response to the evaporation.
Larry

 

[JimParker]

I was talking to my wife about the coffee problem. She had the best answer yet... Ever the practical one, she said "I would tell the waiter to take it away, and bring back a fresh, hot cup when I was ready for it."

Dang. Sometimes the simplest solutions are the hardest to see...

 

[patrick_g]

Larry, I didn't discern the intent of your last post. I read it. I essentially agree with the narative describing the climate in a freezer. I understand the diff between RH and absolute or grams of water/liter of air or whatever. I have been out and about in arctic (-47 F with a wind) conditions and also have a fair laymen's appreciation for how evaporatioin/condensation works (I've build cloud chambers.) I agree that the RH may be about 50% in the freezer (haven't measured but woild have thought it would have been lower) but due to temp that still isn't much absolute humidity.

The moving air is what the flash freeze is based on. Moving air will remove much more heat from the icecube trays than still air at the same temp. Even if the trays had covers over the water to prevent evaporation the moving air would make a vast difference to the thermal transfer. Of course a covered icecube tray, not in contact with any rhime ice or such, would not be so interesting since the hot would absobloominglutely lag the cold in freezing.

There is one area of your post on which I didn't really understand.

Yu said, "The concept of thermal momentum, where the temperature is dropping so fast it cant be stopped quickly enuf to avoid battering down the freeze barrier, is not what Im positing.

I couldn't tell from your statement if you believe that the effect exists but are excluding it from consideration or if you don't believe it exists.

I believe there is no such thing as "inertia" or "momentum" associated with temperature. You can't get the temp dropping really fast and then expect it to "coast" along without a mechanism for removing the heat energy. If you don't believe in that effect we are still in sync. IF you do believe it is possible we have some fundamental educational opportunities that need attention.

Pat

 

[SPYDERLK]

Yeah Pat of course were in agreement. Neither of us would agree to the specious concept of thermal momentum, where the temperature is dropping so fast it cant be stopped quickly enuf to avoid shattering the freeze barrier. -- However, do consider, separate from this, therealistic analogy of latent heat and infinite thermal inertia.
Larry

 

[patrick_g]

JimParker, Note that in the original problem statement a reason was given for not doing that. Of course women don't have trouble breaking the rules for their convenience.

Pat

 

[daTeacha]

I'm just checking in here, haven't read everything since my last post, no time, shouldn't be here now, but you know how addictive this thing is.

Anyways, Pat -- the first solution on that website is the one I came up with. The second one is, as you say neater, but it sort of bows to a different master. The first would not lend itself to mechanization very well, but the second one does. Also the first one leads you directly to the odd ball while the second requires analysis of all your results at the end of the algorithm. I think the first might win if it came down to a time race, but as I said I haven't really had time to read or digest things properly at this writing.

 

[patrick_g]

daTeacha, When I was hanging out around a university computer lab where when workstations were not in use by university students the policy was to allow walk-ins free access, I met Jr Hi and Hi School students who could have programmed the second solution in BASIC or C or whatever almost as fast as they could have read the solution, except maybe for a query/response section to let the user input the number of the "bad" ball and the problem with it, light/heavy.

I taught evening classes there in software engineering and senior projects classes for seniors in the comp sci curriculum. Some of the high school kids were as sharp or sharper than my average student who "on average" was probably near Mensa qualifying.

Pat

 

[daTeacha]

Back when I was in high school and first heard of the problem, our "calculators" were two. We had to get and learn to use an abacus for math as part of the class, and in Chem and Physics we needed a slide rule. The abacus wasn't expected to be used regularly, but we were required to learn how to use it as a math experience. The slide rule, on the other hand, was required as part of the class.

When I was in college, there was this special room in the math building (freshman year), where only specially designated people were allowed. It contained the computer. Every once in while, someone screwed up and locked the thing into an endless loop by accidentally asking it to divide by zero.

A few years after I started teaching, I managed to save up $70 and purchase a device known as the Bowmar Brain. It could add, subtract, multiply, divide, and find square roots in a package not much bigger than 1 1/2 packs of cigarettes.

I wrote the grant that brought the first computers into our district -- a TRS-80 and a Radio Shack Color Computer. They used cassette tapes for memory while I was teaching the kids programming in BASIC. We converted a hallway section to a computer lab.

I never presented the thing as a problem to the computer classes, even when I was teaching BASIC, PASCAL, or COBOL at the local college. It just never occurred to me. Does anyone even teach those languages anymore?

 

[patrick_g]

Rich, I had a Picket in eye saver yellow (mag alloy) in HS and later in college had a Post versalog (bamboo). Of course as a pilot I have used the standard circular slide rules for various calcs in that field.

My first electronic computer (not including the tic tac toe player I built) was a used Trash 80 16 K level 2. I got it and a self teaching program for learning BASIC. My first program was a space alien arcade program and the second was a celestial navigator that reduced your sextant sights to positions.

A friend of mine and I each bought Tandy model 6000 computers (aboiut $5,000). It was 68000 based and had a Z80 for I/O. It ran a port of Unix called Zenix. It had a whopping 15 meg hard drive and used single sided single density 8 inch floppies (IBM 3740 format which gave you 251K per diskette.) Then IBM became thte defacto standard PC and you could buy a Pascal compiler from Philipe Khan (Borland) for $49.95 vs $800 on a half price sale for the Tandy 6000. I donated mine to Goodwill and bought a PC clone.

A few months ago I specked out a s--t hot dual core monster PC with SATARAID disks of 200 gig each and on and on and on (from a major manufacturer it would be nearly $5000) I did it for a tad over $1600.

Pascal was a very good languge, especially for teaching structured programming. It was THE language in my undergrad studies getting computer science degree ('84) We did some assembler but Pascal was the mainstay. Ada was the only language we used in grad school getting MS in software engineering. It was like Pascal without the training wheels and on steroids. I took systems programming classes in "c" and classes in C++ and they have their place but for a real software engineer Ada was THE high level language if yoi wanted relilability or a "trusted" system. If you don't mind the quality level of Microsoft Windows and the number of dificulties and system hangs then C++ can be a pretty exciting language.

My first electronic pocket calculator was a HP45 (retail $400 but got discount at university bookstore) I still have it and it still works perfectly and RPN (Reverse Polish Notation) IS fun! You can buy way more computational power at Wally World for $20.

Pat

 

[Egon]

[tic tac toe player /QUOTE]

Anyone ever win a game?

 

[patrick_g]

Egon, As you may be aware, common chickens have been taught (ref: B.F. Skinner, operant conditioning) to play a perfect game of tic-tac-toe. The best you can do against a skilled player is a draw. Whether it is a chicken or switches and lights and a battery, makes no difference. To lose you have to make mistakes. If you play correctly every game is a draw. Tic-tac-toe tends to lose its attraction once a player gets old enough to understand the game completely.

That time varies per individual.

Of course there are variants with enough difficulty to maintain the interest of Mensans for a time. Consider a 4x4x4 matrix for a playing field where 4 in a row (rectilinearly or diagonally) constitutes a win. You can substitute for a 3D game board by drawing 4 copies of a 2D 4x4 matrix (3 lines horizontal crossed by 3 lines vertical) This 3D version is a tad tougher to hold all combinations in memory so is a bit more fun and gives a pretty fair chance to either player to score 4 in a row.

Reasons To Own a Pet Mensan

This link tickled me.

Pat

 

[Egon]

Think I'll just stick to plain old flat type of X & O's.

Skilled player???

 

[patrick_g]

Egon, for the visualization impaired there are game boards. They are made of clear plastic "flats" and "legs" to hold the 4 parallel flats apart. You can then look down through the parallel flats to see a 4 in a row diagonal develop in 3D. Playing on 4 side by side 2D "flats" challenged visualization and there were certain diagonal patterns that were pretty counter intuitive (sneaky) till you had seen them a couple times. The actual 3D game board makes it way easier.

Pat

 

[daTeacha]

I never got into the HD tic-tac-toe, but true 3d chess on an 8x8x8 grid always seemed intriguing. The closest thing I've seen commercially is an 8x8x3 layout, although I had a kid a few years ago who came up with a spherical chessboard that was pretty neat to play. He made it from a large potato if I remember correctly.

On the HP calculators, that 45 sounds like the one I offered to my second year chem high school class several years ago. I needed something to really motivate them, so I bought the calculator and said the one with highest number of class points would get it. One guy was taking calc at the college while in high school and he borrowed it a lot for that course. It ran RPN and cost about $400, so I'm guessing it was pretty close to the 45 you mentioned. Anyways, I ended up having to buy two of them since he and a girl tied. She is now working for the oil companies doing Biochemical stuff off the oil rigs in the Gulf, showing the EPA that the oil rigs are not harming the fish that live in and around the structure of the rigs. I figure that's pretty typical of government -- worrying about the adverse impact on fish by the very structures that make it possible for the fish to be there in the first place!

The guy had built a computer from off the shelf bits at Radio Shack for his 8th grade science project. When the color computer acted up, he asked if he could open it to see what was wrong. I let him and he pointed to a transistor(?), saying the colors were off. I took it into the store and asked them about fixing it. The guy quoted me a pretty stiff price, and I asked him to just check the transistor the kid picked out. It was bad, I got a new one for about $.50, and the kid put it in and fixed the machine. He went on to OSU, double majoring in EE and Japanese language while working in the library to revamp and update the entire computer system. Then he went to Japan for a year to absorb the culture somewhat, came home and got a job in the silicon valley working for Claris or some one like that. His first assignment was to convert one of their popular programs to Japanese language, which he did ahead of schedule. They were so impressed they boosted him up 2 rankings in the company heirarchy and gave him a small bonus check of $30K.