Re: [math-fun] 177 million tons of ice???
Yes, I think that this is on purpose, since the original defn of a ton was used for the displacement of water in a ship. According to www.thefreedictionary.com/ton , a "ton" is also a unit of _volume_ in shipping -- either 35, 40 or 100 cubic feet. 35 cubic feet is approx one cubic meter. I recall from high school chemistry that a cubic foot of water is 64#, so 64*35 = 2240#, which is the definition of a "long ton". At 10:04 AM 9/20/2005, wrote:
Henry wrote:
<< 177 million tons should be the weight of a small comet or a decent size meteor (see <http://www.meteorcrater.com/eventsfun/exptheimp.htm>www.meteorcrater.com/eventsfun/exptheimp.htm). I'm not sure that whether the meteor was iron or water would make much difference in the resulting crater.
In discussions about this, a surprising factoid I learned is that the volume of 1 ton of ice is almost exactly 1 cubic meter. This is an easy rough estimate, but I'd never thought of doing it before. At first blush, that a ton of ice should be a mere cubic meter was amazing to me. (Either a ton is a lot smaller than it seems, or a cubic meter is much bigger.)
--Dan
Henry Baker wrote:
According to www.thefreedictionary.com/ton , a "ton" is also a unit of _volume_ in shipping -- either 35, 40 or 100 cubic feet. 35 cubic feet is approx one cubic meter. I recall from high school chemistry that a cubic foot of water is 64#, so 64*35 = 2240#, which is the definition of a "long ton".
But isn't the good ton to use here the metric ton? 1 metric ton = 10^3 kilos = 10^6 grams; 1 cubic yard = 10^6 cubic cm. The original definition of the gram was the weight of one cc of water. As Google calculator will happily tell you, "one metric ton per cubic meter in pounds per cubic foot" is 62.4279606. Up to the minor variation in density due to temperature, this is the actual weight of a cubic foot of water -- the 64 lbs, ie "a pint's a pound," is a fine approximation, but not exact. And one metric ton = 2204.62262 pounds. --Michael -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
On Tuesday 20 September 2005 18:32, Henry Baker quoted Dan (the original doesn't seem to have reached me):
In discussions about this, a surprising factoid I learned is that the volume of 1 ton of ice is almost exactly 1 cubic meter. This is an easy rough estimate, but I'd never thought of doing it before. At first blush, that a ton of ice should be a mere cubic meter was amazing to me. (Either a ton is a lot smaller than it seems, or a cubic meter is much bigger.)
The latter. This is a special case of a general phenomemon: 3-space is bigger than we tend to think. (And space in dimensions higher than 3, more so.) -- g
Some years ago, RWG thought up the clever question: does heavy ice (frozen heavy water) float in ordinary water? Gene __________________________________ Yahoo! Mail - PC Magazine Editors' Choice 2005 http://mail.yahoo.com
On Tuesday 20 September 2005 20:24, Eugene Salamin wrote:
Some years ago, RWG thought up the clever question: does heavy ice (frozen heavy water) float in ordinary water?
Regular ice's density is 0.914. Heavy ice (D2O) has two extra nucleons on top of 18 (16 for the O, 1 for each H), so it's 20/18 heavier than 0.914, or about 1.016. Therefore it should sink. The site jchemed.chem.wisc.edu/JCESoft/CCA/CCA2/MAIN/ICECUBE/CD2R1.HTM says that D2O ice sinks, confirming this simple reasoning. Steve Gray
I just ordered some D2O; it should arrive in a few days, and I'll let you know. On Sep 20, 2005, at 5:54 PM, Steve Gray wrote:
On Tuesday 20 September 2005 20:24, Eugene Salamin wrote:
Some years ago, RWG thought up the clever question: does heavy ice (frozen heavy water) float in ordinary water?
Regular ice's density is 0.914. Heavy ice (D2O) has two extra nucleons on top of 18 (16 for the O, 1 for each H), so it's 20/18 heavier than 0.914, or about 1.016. Therefore it should sink. The site jchemed.chem.wisc.edu/JCESoft/CCA/CCA2/MAIN/ICECUBE/CD2R1.HTM says that D2O ice sinks, confirming this simple reasoning.
Steve Gray
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So how come we haven't been mining D2O ice from the sea/lake floor? :-) :-) At 02:54 PM 9/20/2005, Steve Gray wrote:
On Tuesday 20 September 2005 20:24, Eugene Salamin wrote:
Some years ago, RWG thought up the clever question: does heavy ice (frozen heavy water) float in ordinary water?
Regular ice's density is 0.914. Heavy ice (D2O) has two extra nucleons on top of 18 (16 for the O, 1 for each H), so it's 20/18 heavier than 0.914, or about 1.016. Therefore it should sink. The site jchemed.chem.wisc.edu/JCESoft/CCA/CCA2/MAIN/ICECUBE/CD2R1.HTM says that D2O ice sinks, confirming this simple reasoning.
Steve Gray
The molecular size and charge distribution is almost identical, so the crystals form without distinguishing between H2O and DH2O. It would be rare to find any significant number of molecules of D2O. DH2O ice does not sink, in any case. On Sep 20, 2005, at 6:29 PM, Henry Baker wrote:
So how come we haven't been mining D2O ice from the sea/lake floor? :-) :-)
At 02:54 PM 9/20/2005, Steve Gray wrote:
On Tuesday 20 September 2005 20:24, Eugene Salamin wrote:
Some years ago, RWG thought up the clever question: does heavy ice (frozen heavy water) float in ordinary water?
Regular ice's density is 0.914. Heavy ice (D2O) has two extra nucleons on top of 18 (16 for the O, 1 for each H), so it's 20/18 heavier than 0.914, or about 1.016. Therefore it should sink. The site jchemed.chem.wisc.edu/JCESoft/CCA/CCA2/MAIN/ICECUBE/CD2R1.HTM says that D2O ice sinks, confirming this simple reasoning.
Steve Gray
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On Tuesday 20 September 2005 23:36, Tom Knight wrote:
The molecular size and charge distribution is almost identical, so the crystals form without distinguishing between H2O and DH2O. It would be rare to find any significant number of molecules of D2O.
I think all the above was why Henry added those smileys...
DH2O ice does not sink, in any case.
So, why not, given that (1) the naive calculations suggest it should and (2) electrostatically D2O looks just like H2O? -- g
On 9/20/05, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
DH2O ice does not sink, in any case.
Do you mean DHO? -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
On 9/20/05, Mike Stay <metaweta@gmail.com> wrote:
On 9/20/05, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
DH2O ice does not sink, in any case.
Sorry, attribution out of context. Tom Knight said it, not Gareth. -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
Yes, sorry, that's what I meant. Old numeric habits die hard. Quoting Mike Stay <metaweta@gmail.com>:
On 9/20/05, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
DH2O ice does not sink, in any case.
Do you mean DHO?
-- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
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On Wednesday 21 September 2005 00:13, Mike Stay wrote:
On 9/20/05, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
DH2O ice does not sink, in any case.
Do you mean DHO?
*I* don't; those words were Tom Knight's, not mine. I'd been assuming he meant D2O. I'm sure DHO ice doesn't sink. -- g
I found a great web site on water: http://www.lsbu.ac.uk/water/ . There is so much good stuff here; I'll just mention a few tidbits. According to data from this source Density of H2O ice = 0.9168 Density of D2O ice = 1.0175 So we might expect HDO ice to have density 0.967, i.e. floats. Note that HDO does not exist as a pure substance; it is a mixture of H2O, HDO, and D2O molecules. Furthermore, in equilibrium at 25 C, H2O + D2O <==> 2 HDO, Keq = 3.85, not the value 4 one would expect from total randomization. This is attributed to D2O having stronger hydrogen bonds than H2O. In addition to the isotopic molecular species due to H, D, and the radioactive T, and also the stable O-16, O-17, and O-18, there is another class of distinct molecules that differ in the alignment of their nuclear spins. Considering only H2O, the H nuclei (protons) have spin 1/2. In ortho-water, the two spins are parallel, resulting in total nuclear spin 1, while in para-water, the spins are antiparallel, resulting in total nuclear spin 0. The equilibrium ratio is all para at 0 K, and 3:1 ortho:para at high temperatures (> 50 K). The equilibration time is about 1 hour in liquid water and several months in ice. It appears possible to separate ortho and para-water, but I can't say more because I don't have access to the journal articles from here. Similar considerations apply to the hydrogen molecule H2. When hydrogen gas is liquified, it retains the 3:1 ratio. As ortho-hydrogen slowly converts to para-hydrogen at cryogenic temperatures, the energy released causes a substantial evaporization of the liquid. For this reason, a catalyst is used to quickly convert the hydrogen to para form. This can double the storage lifetime of the liquid. Occurring in conjunction with ordinary water is the extremely dangerous chemical dihydrogen monoxide (DHMO). Learn about it at http://www.dhmo.org/ . Gene ______________________________________________________ Yahoo! for Good Donate to the Hurricane Katrina relief effort. http://store.yahoo.com/redcross-donate3/
I see a market opportunity. Think about the ad campaign for *pure* ortho water. You *do* want all of your water be straight, don't you! On Sep 21, 2005, at 1:53 PM, Eugene Salamin wrote:
I found a great web site on water: http://www.lsbu.ac.uk/water/ . There is so much good stuff here; I'll just mention a few tidbits.
According to data from this source
Density of H2O ice = 0.9168 Density of D2O ice = 1.0175
So we might expect HDO ice to have density 0.967, i.e. floats.
Note that HDO does not exist as a pure substance; it is a mixture of H2O, HDO, and D2O molecules. Furthermore, in equilibrium at 25 C,
H2O + D2O <==> 2 HDO, Keq = 3.85,
not the value 4 one would expect from total randomization. This is attributed to D2O having stronger hydrogen bonds than H2O.
In addition to the isotopic molecular species due to H, D, and the radioactive T, and also the stable O-16, O-17, and O-18, there is another class of distinct molecules that differ in the alignment of their nuclear spins. Considering only H2O, the H nuclei (protons) have spin 1/2. In ortho-water, the two spins are parallel, resulting in total nuclear spin 1, while in para-water, the spins are antiparallel, resulting in total nuclear spin 0. The equilibrium ratio is all para at 0 K, and 3:1 ortho:para at high temperatures (> 50 K). The equilibration time is about 1 hour in liquid water and several months in ice. It appears possible to separate ortho and para-water, but I can't say more because I don't have access to the journal articles from here.
Similar considerations apply to the hydrogen molecule H2. When hydrogen gas is liquified, it retains the 3:1 ratio. As ortho-hydrogen slowly converts to para-hydrogen at cryogenic temperatures, the energy released causes a substantial evaporization of the liquid. For this reason, a catalyst is used to quickly convert the hydrogen to para form. This can double the storage lifetime of the liquid.
Occurring in conjunction with ordinary water is the extremely dangerous chemical dihydrogen monoxide (DHMO). Learn about it at http://www.dhmo.org/ .
Gene
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Tom Knight meant to write:
The molecular size and charge distribution is almost identical, so the crystals form without distinguishing between H2O and DHO. It would be rare to find any significant number of molecules of D2O.
[I corrected a DH2O to DHO, per later conversation.] Let's be clear here: heavy water is indeed D2O. You can't have a sample of pure, um, welterweight water, DHO: the hydrogen atoms are exchanged between water molecules all the time, so you'd really have a sample with half DHO and a quarter each H2O and D2O. Per Steve Gray's density calculation, you would need about (1/.914 - 1)/(20/18 - 1) = "85% heavy" water to make ice the density of normal liquid water. -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
So how come we haven't been mining D2O ice from the sea/lake floor?-) Similarly, do thermal neutrons dribble out the bottoms of reactors, creating a column of chemical and isotopic peculiarities below? (Do submariners bunk under the powerplant??) --rwg
--- "R. William Gosper" <rwg@osots.com> wrote:
So how come we haven't been mining D2O ice from the sea/lake floor?-)
Someone has already posted an answer to this. Ice contains nearly, but not exactly, the same fraction of deuterium as the water from which it freezes.
Similarly, do thermal neutrons dribble out the bottoms of reactors, creating a column of chemical and isotopic peculiarities below?
They dribble out in all directions. Neutrons have mass 1, compared to N2 mass 28 and O2 mass 32. A neutron atmosphere would be about 30 times thicker than the normal one.
(Do submariners bunk under the powerplant??) --rwg
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participants (9)
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Eugene Salamin -
Gareth McCaughan -
Henry Baker -
Michael Kleber -
Mike Stay -
R. William Gosper -
Steve Gray -
tk＠csail.mit.edu -
Tom Knight