will it take off?

[gizmo]

I always tell people that one of the most important funcions of my tractor is provide me with some good thinking time. I suspect that some of you may feel the same. I also suspect, based on the above, that a lot of you have spent WAY too much time on your tractors lately. Don't be proud, seek help. You can beat this.

 

[SPYDERLK]

Homemade ice cream -- What is making it cold? Fahrenheit knew how cold it gets.

I guess we should actually be phrasing this one in language that reflects the fact that cold is not really quantifiable, but we're talking temperature here, not heat.

It is being cooled by ice being forced to melt without addition of heat. As this is happening, the latent heat of fusion originally taken out of the water to change 32 water to 32 ice must be supplied to the melt. This heat is financed by the ice, reducing its temperature and making it harder to melt. I believe the practical limitation to this cycle when using table salt to force the melt is about 0F. The ice cream will be somewhat above that.
Larry

 

[daTeacha]

Pretty good!

The temperature of water ice and salt is in fact 0 F. This is what Fahrenheit used as the basis of his temperature scale, unlike Celsius who used the freezing point of pure water. jOddly enough, as the salt dissolves the ice, it makes it colder.

A guy could probably win a few bucks betting on whether or not salted and slushy sidewalks are colder than icy ones.

 

[daTeacha]

Hmmm. Addressing the beard thing here.

If the logic of having an infinitesimally small force works for the person leaving the boat, what prevents the aqueduct from being percieved to have a similarly infinitesimally small margin before catastrophic failure? It would seem the same logic prevails.

To use the beard analogy, at what point in the painful process of plucking the hairs from Egons face would there be agreement that he no longer has a beard? When there are 100 hairs left? 50? 10? 1? Or would that have to go to zero? Why doesn't the logic work both ways? And if it does, the aqueduct could indeed be perceived as close enough to failure that a mosquito landing on one of the boat occupants might cause it.

Please bear with me. I am calculus deficient. Thanks to several things, among them a dread fear of counselors, weeder courses, and my own ignorance, as a college freshman I found myself enduring interesting quarters such as one in which I was simultaneously enrolled in Chemisty, Physics, Calculus, Statistics, and Probability. My Calc classes were taught by: 1) A woman with a thick German accent and a speech impediment. 2) A blind guy who literally erased with his left hand as he wrote with his right, moving carefully from one side of the board to the other and talking (mumbling) at the board all the while and, oh yeah, blocking our view of what he wrote. 3) The German lady again. I didn't know about varioius other courses unrelated to my major that I had to take and was wondering why people spent 4 years finishing college. Then I found out about such things as History, Psych, English, etc. being required in college.

Anyways, as a result of my ignorance, I flunked the third calc class way back in '66, and changed majors to Biology. So when you guys start incrementalizing things, I understand the basics of what you're saying, but miss some of the details.

On the coffee problem, why is it that adding the cream early keeps things warmer longer? The specific heat of the cream is close to that of water, and adding it will absorb a fair amount of heat from the coffee, thus reducing the overall temperature while not transmitting any joules of heat energy to the air. So you have used the heat of the coffee to warm the cream while cooling the coffee to a certain extent. This reduces the difference in temperature between the coffee and the air and thus reduces the rate of heat transfer. I understand that easily enough. There is X amount of heat energy in the coffee and you want to reduce the rate of transfer of that heat from the coffee to the surrounding air, napkin fires notwithstanding, by reducing the temperature difference.

However, transferring the heat to cream also increases the warm mass in contact with the cup and indirectly, the air. It increases the surface area at which the heat exchange takes place -- the cup is filled higher, more side area and top of the coffee area are now in contact with the air. Does not the increase in heat transferring area compensate for the reduction in temperature difference? There are going to be convection microcurrents inside the cup, air motion outside the cup, and radiation from the cup, all of which are increased by the increased amount of coffee/cream in the cup.

Your responses almost begin to sound like the old tale that hot water placed in an ice cube tray will freeze sooner than an equal amount of cold water in the same tray in the same freezer.

Point of definition Egon -- talking in third person is fine, but it is twelve that is divisible by 3 and 4 rather than 3 and 4 being divisible by twelve. One presumes you are restricting the question to integers. Might this also mean that you like 6 and 2, but not 5 or 8?

Patrick, we haven't heard from you on the billiard ball problem. Egon says he knows. I know I know. I don't know how many others know. Do you know?

 

[SPYDERLK]

daTeacha. Good point about coffee cup, exposed surface area, cup contact etc. These factors - not the radiation factor - may carry the day with certain aspect ratios of the vessel [like if it were a saucer], but with standard cup shape and conductivity, the lower T differential would win out. Im sure this could be proven mathematically, but Im not gonna try.
Larry

 

[patrick_g]

Larry, Thanks for the support on the coffee thing. Da Teacha, I'm not sure but it sounds a bit like first you proclaim ignorance and then make claims that those of us who use concepts with which you admit no knowlege are wrong because of some (what seems to me to be) pretty skimpy arguments. YOu can't have it both ways.

Good ole Farenheit. He use the lowest temperature able to be created in a laboratory to be the zero for his thermometer (salt and water was as high tech as they could mannage) and body temperature to be the other calibration point of 100 degrees. OK there is a small misunderstanding and we say 98.6 so maybe he had a fever. 212 just happened as a result of linear extrapolation of the scale. Celcius got it right with zero and 100 as easily reproducible numbers, boiling and freezing points of water at sea level.

Of course the beard thing can argue the delta of the safety margin on the aquaduct to be arbitrarily small but didn't a previous post of yours say one pound from destruction?

The heat loss per unit time of the cup falls exponentially from its greatest value toward zero as the coffee temp falls from its max to the asymptote of room temp (considerably less.) By adding the cream immediately you are using up heat from the coffee that was going to be lost anyway fairly quickly to the environment through conduction, radiation, convection and the faster evaporation at the elevated temp. You are going to take a "HIT" whenever you add the cream but the way I explain pays this penalty with heat that would have been quickly lost anyway.

In a regular car lets say you are driving 100MPH and only have just a little braking power and then the brakes refuse to operate. What do you do? You let the aerodynamic drag take as much energy as practical and reserve braking until later. Same essential strategy as the coffee example.

Larry, Modeling this problem with math is not so tough if you don't mind not solving for a numeric answer (qualitative solution not quantitative.)

Brief digression: If a qualitative solution finds one value to be larger than another, say, x<y then a numerical solution will show the same relationship. IN our case we do not need to know the numbers ony which is larger (hotter.)

Sketch a rough approximation of an exponential decay where the inititial value of the curve on the Y axis is the 210 F coffee. and the curve asymptotically approaches rooom temp (70F) In 5 time constants the temp will have fallen close to the final value (room temp.) The area under the curve per unit time is the heat loss per unit time. Sketch a similar curve for the temp of the coffee starting at the temp you'd get when not adding cream until some reasonble time later (it doesn't matter how long later as any time later is a poorer solution) It should be pretty clear from your sketches that the final temp of the coffee-cream mixture is not the same in the two cases and that the add-cream-immediately strategy preserves a higher temperature longer.

Since a qualitative solution proves the contention then a quantitative solution will do the same but with values. I didn't ask for values just which method ended up with hotter coffee.

This is absobloominglutely NOT similar to the hot water freezes faster myth. I shall not waste your time trying to explain why the two are so very different in the face of self procalimed innumeracy.

My current interest in Billiard Balls is in having a pocket billiard (pool) table to install in my basement fairly soon. I did see reference to a billiard ball problem but have not read the problem so can't have a reasoned comment.

Pat

 

[SPYDERLK]

Hot water freezes faster because you dont get as much ice. Vapor pressure rises with temperature. The hot water evaporates quickly taking 540calories/gm with it. This along with the fast conduction from the larger delta T causes the hot water to cool extremetly rapidly. The evaporation is the telling factor tho because there is less water left to freeze.
Pat, I get the coffee thing easy, but I dont follow your example. I think theres atypo.
Larry

 

[Egon]

Egon is talking in third person because he likes numbers divisible by twelve

What Egon meant to say is " Egon likes numbers that 12 is divisible by."

Combine that with the number of fingers on one hand and you should get the idea.

For the icecream temperature you must also assume sufficient ice was originally provided.

 

[daTeacha]

Patrick -- I sense a tone of some sort in some of your comments. Do not take my quest for understanding as trying to have it both ways. I admit to a comparitive lack of training and educational opportunity in some of the higher levels of math but that doesn't mean I don't grasp the concepts involved.

Taking the coffee cup as an example, the use of the cream as a heat sink of sorts to store the heat at a lower temperature makes sense, but you failed to account for the increase in radiant surface area, which also makes sense. I pointed that out as a question for which I was seeking an answer. If you're going to interpret any question about your answers as some kind of a challenge to the accuracy of your comments, it makes it pretty hard for us ignorant types to learn anything.

Why is it okay for you to split hairs, grasp at straws, or add details to the problem but you seem offended when someone else does the same? The napkin thing is an example. After you mentioned burning the napkin as a way to keep the coffee hot, I pointed out that doing so would cause a certain amount of commotion which the problem specifically mentioned as something to be avoided. You replied with a tone of superiority that you could burn the napkin with sufficient surreptiousness that the waitress wouldn't notice. Perhaps you could with all your survival and backwoods training, but I could also spray the thing with my handy aerosol can of expanding weatherstripping that just happened to be in my briefcase for use in classroom demonstration later that day.

Keep in mind that you are not the only here who can engage in mental exercises. Also, there are probably a few left following this thread who are lurking and not commenting since some of these posts have gotten pretty deep. A simple question about a complex issue followed by a simple answer for all to see will go a long ways to help everyone understand. Please treat my questions as questions, not insults or challenges to your authority. You're the guy who said you just like to debate things, so debate, but don't be offended.

 

[Egon]

I say, pour in the cream slowly but do not stir!

But if you do stir, stir lots, and really muck up the boundary layers and calculations.

And yes there may be a very definitive danger point when making an attempt at plucking Egon's Beard

 

[daTeacha]

Egon -- I have picked a number of the ball and I know if it is light or heavy. Would you like to tell me what is on the left side and right side of the balance so I can tell you what happens? Presuming your method works, you will know what ball I picked and the nature of its discrepancy in a very few posts.

Patrick -- I fear I was a bit harsh yesterday in my comments. Sorry. I just think we need to more exactly define the parameters of a problem when we address it rather than leaving the door open for factors not mentioned originally.

 

[Egon]

daTeacha:

Couldn't answer that question but as for finding one out of twelve balls that is a different weight than the others by using a scale three times has at least three different approaches that will result in finding the off weight ball. There may be more but these have eluded me!

 

[BillyP]

daTeacha:

Couldn't answer that question but as for finding one out of twelve balls that is a different weight than the others by using a scale three times has at least three different approaches that will result in finding the off weight ball. There may be more but these have eluded me!

Egon, you gave the hint of solving the problem several posts ago, 4

 

[Egon]

{4-4-4} {5-5-2} {6-6} will all work.

This would be perfect for a flow diagram for FORTRAN programing.

 

[SPYDERLK]

Quote --Taking the coffee cup as an example, the use of the cream as a heat sink of sorts to store the heat at a lower temperature makes sense, but you failed to account for the increase in radiant surface area, which also makes sense. I pointed that out as a question for which I was seeking an answer. If you're going to interpret any question about your answers as some kind of a challenge to the accuracy of your comments, it makes it pretty hard for us ignorant types to learn anything.--

So, are we competing? Bad us. --- daTeacha, you have a good education and raise good questions. Some have an intuitive feel that instantly bypasses some of these questions. This may cause a certain aura of impatience and each may view the other as splitting hairs. A communication problem. -- It is very difficult to explain what one sees as intuitively obvious to another who hasnt to same feel for the problem definition. Adding the cream first is the way to go. I am an intuitive physicist and it is intuitively obvious to me. However, following your thot, there is a good possibility that with the introduction of a bit of intuitive tedium, a "cup" could be designed and filled to just the right level with coffee, such that adding the cream early would be the wrong choice. It would be a strange cup. It wouldnt suit lips. Youd have to drink it with a straw I think.
Larry

 

[daTeacha]

Puzzling over the billiard balls -- Are Egon's solutions all going to result in not only the identification of the odd ball, but also tell whether it is lighter or heavier than the rest? I think Egon thought he was told if the ball was light or if it was heavy. He was told it was different, but not in which way.

I ask because 6 vs 6 simply tells that one side goes down and the other goes up, which is foregone given that one of the balls is different, and useful only if you know ahead of time whether it is light or heavy.

Also, given that the problem involves the use of a basic 2 pan balance and not some exotic 3 pan design, I'm thinking the 4 - 4 - 4 solution is also based on knowing in advance if the ball is light or heavy. The same probably holds true for the 5 - 5 - 2solution.

The thing that makes this problem interesting is that you only know the ball is different. If you accept the challenge of the problem, you are to not only identify the odd ball, but also to tell if it is light or heavy.

If all three of your solutions will work when you don't know the nature of the difference, I would very much like to see them here. The only one I know does not start with 6 vs 6.

 

[patrick_g]

Da Teacha, I just checked the back of my lisc and confirmed that I was liscensed to do all of the things you suggest I do and MORE! You probably are too. I regret not being able to chat with you face to face as I am more that just sure we would have fun and part friends. Unfortunately there are certain difficulties in this sort of communications (especially with my meager skills) that interferes. Let me assure you I am not at all distressed and enjoy the exchange.

If we were always in agreement there would be little fun. I sometimes alter the circumstances dymanically and adaptively to increase the fun. After convincing someone of my position I have been known to take up their original position and make a case for it trying to refute my previous argument. We aren't being graded. This isn't even pass/fail, this is RECESS.

Now as to the coffee, I assert that your argument is flawed and that apparently you don't understand the exponential decay of the coffee temp toward the room temp. The heat loss of the coffee per unit time is way faster when the differential is the greatest and rapidly drops over time (an exponential decay, not linear.) That is why adding the cream immediately is the superior strategy. Lets forget the spray foam (got a chuckle on that, great idea... deux ex machina) and the burning napkins. I thought about a large Fresnel lense but that requires dining al fresco or a window seat as concentrating fluorescent light output is too puny.

If neither of us has a Gilbert chemistry set or Erector set or any special "Inspector Gadget" surgical implants then of the original choices the "stir in the cream immediatley strategy" is the winner by a good margin.

I gather from the latest posts that the billiard ball thingy is a rehash of the counterfit coin problem where one coin is different but we don't know if it is heavier or lighter and we are using just 12 of the balls. This is as old as the Fox, Goose, and Grain problem (or older.)

Larry, I can't think of a cup design that would favor delaying the addition of the cream. Can you give an example? Even a spherical vacuum bottle filled with a fine gauge needle would favor the early addition since it still has finite heat loss which is in the form of exponential decay. The heat loss by evaporation from a "regular" cup follows the form of exponential decay but would be elliminated by the above "special" spherical vaxcuum cup. The answer would remain the same although of less importance since the coffeee in a vacuum cup (spherical mini-dewar) would stay hot so well the loss during a quick lunch would probably not matter.

Now, about the hot water freezing faster than cold. That is an assertion that needs defense. It is like saying why is it that black cows fly faster that red cows. It is not established that either black or red cows can fly.

Lets take an example where the wind speed is essentially zero and the RH is 50% and we have two ice cube trays suspended on well insulated holders in identical domestic freezers. One ice cube tray is filled with hot water and the other with cold, from the tap. The hot is 125 F and the cold is 50 F. (typical household values in winter.)

Insert trays into the freezers and start the clock. The remote reading thermometer on the cold sample starts to fall. The temp of the hot samoplke starts to fall. At some point the hot water will have cooled to 50 F.

Why is it not reasonable to expect the time to freeze the hot water after it has fallen to 50F to be didfferent from the water that started at 50F?

I assert that with no evidence to counter the assumptioin that the time to freeze from 50 F on down to be thte same. Since it took time to get from 125 F to 50 F the time to freeze hot water is greater.

Pat

 

[SPYDERLK]

Pat, daTeacha - - Ok heres a "cup" with dubious potential. It is normal up to near the top, then has an extreme flair outward on the lip that close to doubles its diameter with little change in depth. The coffee fill would be to the top of the normal classic cup shape. The addition of cream would result in a solution that now extended well out onto the flaired lip to the extent that the surface exposed to air was increased 2 to 4 times normal. Evaporation would be favored - and heat of vaporization is high. Now intuitive tedium... The solution on the lip is somewhat isolated from the well of the cup and w/o some optimization favoring a natural convective flow, it will not cool the well well. In order to provide convective flow the lip would incorporate radial channels sloping downward back to rejoin the well. These would serve to collect the denser cooled fluid and provide a flowpath back to the well. This would in turn favor warm surface flow back out onto the lip.

As for the ice. Pls re read post 647 and add the following contributory factors. Most would fill an ice tray with equal volumes of hot vs cold water. The hot cube already starts with less water. Then there is evaporation. Then there is a higher surface area to volume ratio. The key point is there is less ice from the hot water. See what I mean?
Larry

 

[daTeacha]

Well, let's see here. I graduated from high school in '63, so I heard the billiard ball problem in '62. That makes it fairly old, but it's still an interesting problem. As you said, Pat, about like the Fox, Goose, and Grain. Or the town on the island with seven bridges.

If we want to pursue a cup design that would bring about faster radiation than the traditional cup shape as the cream is added, consider something like an old fashioned "Yard Glass" as used in British Pubs to serve up a yard of ale. These containers, if you are not familiar with them, resemble nothing quite so much as an Florence flask with a very long neck. If you minimize the size of globe at the bottom and the diameter of the neck, while maximizing the flare at the top, is it conceivable the increase in surface area resulting from increasing volume would offset the heat sink characteristics of the cream? This would in effect be the opposite of your sherical DeWar flask with the tiny opening.

Oh yeah, if you've never tried drinking ale or whatever out of a yard glass, you owe it to yourself to do it at least once, preferably in the company of good friends in a room that can put up with a spill or two.

 

[daTeacha]

On the water -- I see what you mean, but the density of water doesn't increase by a lot while it's still a liquid. The temperature of maximum density is 4C. At 100C, the density is 95.8% of that, so you're dealing with only a 5% or so decrease in the mass of water to be frozen.

The specific heat of water is 4.18 kj / kg C degree. The heat of fusion is 333 kj / kg , more or less. The heat of vaporization is about 2200 kj / kg.

I have no idea how much water is in a typical ice cube tray, but if I had to guess, I'd go with about 600 ml or .6 kg.

To cool .6kg of water from 100C to 50C would mean the freezer needs to remove about 10 000 kj of heat by my calculations. How much heat would be lost due to vaporization during the cooling process would depend on the humidity of the air in the freezer.

At this point, your exponential rate of heat loss based on temperature differences takes over, so you guys can take it from here.