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A bartender gets an ice cube weighing 20 grams from an ice bucket and puts it into an insulated cup containing 100 grams of water at 20 degrees Celsius. Will all the ice melt? What will be the final temperature of the water?

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Not really sure how to do this one, but I think that it will melt and the final temperature will be about 16.6 degrees Celcius

StuartR

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You’ve got the first part right. The correct solution requires Heat of Fusion and Specific Heat Capacity et al

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Yes, of course it does, I was being silly.

StuartR

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Silly of me not realising you were being silly. Please carry on.

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(Edited by sdckapr on 30-Nov-06 15:20. Added Work)

I get 3.3

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That’s what I get. Have a cool drink on me, Steve.

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One must presume that the ice is at 0

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Absolutely, Alan. Thanks for pointing that out.

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This begs another puzzle. How cold would the ice have to be to freeze the contents of the glass?

Alan

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As far as I calculate: It is impossible, the ice would have to be < "absolute zero" (I calc about -500

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I concur Steve. It was, in fact, a trick question (

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An excellent point. I think that since the ice was from an ice bucket and not from a freezer that this seems a reasonable presumption.

If the ice had come from a freezer we would first have to warm it 0

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Just to be pedantic (and because I’m not clever/motivated enough to actually do the working out) – since no cup is 100 per cent insulated, the final temperature will (eventually) match the room temperature.

Or, presuming that someone drinks the water, perhaps it will be nearer body temperature…

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Just to be even more pedantic, what if it’s done outdoors?

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To be really pedantic, Waggers should have used “ambient temperature” instead of “room temperature”….

In actuality we could be very, very pedantic, and presume that the final temperature (given a long enough time frame) will be absolute zero when the universe has expanded to such and extent that there is actually no futher motion of any molecules…

I presumed (as did most people) that “final temperature” was the equilibrium temperature (the “immediate final temp”) of the warm water with the ice, not the “moderate-term final temp” of the ambient conditions or the “long-term final temp” of absolute zero.

I suppose that it could have a trick to get people to calcuate when either one of the 2 other answers was the “correct answer”, but either seems a little overly pedantic.

Steve

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> presume that the final temperature (given a long enough time frame) will be absolute zero when the universe has expanded to such and extent that there is actually no futher motion of any molecules

But wouldn’t the problem itself then be irrevevant, since molecules themselves would have long ago dissociated into their more fundamental bits?

Alan

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I don’t understand the point. I presumed since it was only a “problem”, it most likely was not “relevant” to begin with…

Steve

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Only the answer would have to be changed to indicate that water would not exist at “final” equilibrium. Then again, one could argue that the original constituents would still exist in some form, and be at absolute zero along with everything else. I think life would be rather boring at that stage of cosmological evolution.

Alan

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It is still “water” even if we have given a separate name for the solid (ice) and gas (steam) phases. “Liguid” water may just be called “water”, but “ice” and “steam” can also be called “solid water” and “gaseous water”…

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I think life would be rather boring at that stage of cosmological evolution

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I think more “non-existent” than “boring”…

Steve

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But at such levels of cosmological expansion, everything would have been long since pulled apart. It’s not a local absolute zero – it’s a universal one, accompanying an expansion of everything within. The electrons originally orbiting the water’s oxygen nucleus might now be 3 suburbs away. You couldn’t still call that a water molecule, could you?

Alan

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(Edited by sdckapr on 06-Dec-06 12:45. Added PS)

Yes, you are correct, if it is 3 suburbs away, definitely not water, but If it were only 2 suburbs away, then it could still be called water with very long “hydrogen bonding”…

Steve
PS this whole conversation reminds of the Short Story, The Last Question by Isaac Asimov

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Just to throw my tuppenyworth into your entertaining dialogue with Alan, the quantum mechanical model of electrons allows for a minute but finite probability that the bonding electrons of water molecules are 3 suburbs away.

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But the finite probablitly of an oxygen atom is within 3 suburbs of 2 hydrogen atoms while still a finite probability is a much more remote probability [perhaps it is time to turn on our “infinite probability drive” to work it out

Steve

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It makes me think of Hamlet and Horatio! In any even, you’re probably right.

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If you are thinking of more things in heaven and earth, then this seems to not be far enough. We are speaking of way past this time, when there is no heaven and earth…

We have probably already beat this dead horse enough [or is it “half-dead / half-alive” Schr

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I think you are right, Steve. I promise not to open the box if you don’t.

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I promise not to open the box if you don’t.

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But if we don’t open the box, the cat will forever be in the “half-state” neither dead, nor alive….

Steve

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Now you’ve thrown some uncertainty into the mix… probably.

Alan

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Yes, I am quite certain that it is a definite probability that I might have…

Steve

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