Re: [math-fun] NYTimes: melting ice cubes cause water to rise ?
Henry Baker wrote that an old SAT question goes like this: << A cube of ice is floating in a glass of water that is filled to the top. (No discussion of meniscus.) When the ice melts, the water in the glass: A. overflows B. stays at the same level C. goes down D. none of the above
(This sounds more like a question from a physics "achievement test" -- but be that as it may.) I would not say ice displaces the same "amount" of water, since "amount" could mean either mass or volume. The floating ice cube has the same weight as a) the water it displaces and b) the water it becomes when it melts. Thus a) and b) have the same volume. So when the cube melts, the water level shouldn't change. (So what's the business about floating ice raising water levels when it melts?) --Dan
That was the point of my original posting -- the NYTimes thought that melting floating ice would raise the water level -- they were obviously wrong. At 04:09 PM 9/29/2005, dasimov@earthlink.net, math-fun wrote:
(So what's the business about floating ice raising water levels when it melts?)
--Dan
You should note that seawater is salty, but the ice is not. So, when the ice melts, some of the salt will move from the seawater to the fresh water until equilibrium is reached. This could have some effect on the volume of water, but I don't have time to research what that might be. In any case, the seawater rise due to global warming is due to non-floating ice melting AND to the warming of the water (which increases its volume). The NYTimes is notoriously poor in reporting on any science or technology. I would take all of it with a grain of salt. --ms Henry Baker wrote:
That was the point of my original posting -- the NYTimes thought that melting floating ice would raise the water level -- they were obviously wrong.
At 04:09 PM 9/29/2005, dasimov@earthlink.net, math-fun wrote:
(So what's the business about floating ice raising water levels when it melts?)
--Dan
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Let's consider this in two steps. I. Put an infinitesimal box around the ice (cube) and let the ice melt. The weight inside the box remains the same, so the box neither rises nor falls. II. Compare the density of the (now liquid) pure water inside the box to the density of the seawater outside the box. The pure water inside is less dense, so it actually has a slightly higher level than the seawater outside the box. Conclusion: If a cube of (pure water) ice melts in our full glass of _sea_ water, then the glass should indeed overflow. This seems like a pretty simple experiment. I'm about 20 miles from the Pacific, so I will try to acquire some seawater to try it out. If anyone here is near the Dead Sea or the Great Salt Lake, their experiment should show a greater effect. So any rising of the ocean is a second order effect due to the differences in salinity of ice v. seawater, rather than the (cancelled out) first order effect of the pure ice v. pure water. As an aside, I recently saw a show on Italian cooking on cable TV, and the cook used the change in density of salt water to approximate the correct salinity for a salt broth. She put a potato into the water, and added enough salt until the potato started to float. That was the correct amount for her recipe. Something tells me that this technique was probably used for thousands of years. At 05:59 AM 9/30/2005, Mike Speciner wrote:
You should note that seawater is salty, but the ice is not. So, when the ice melts, some of the salt will move from the seawater to the fresh water until equilibrium is reached. This could have some effect on the volume of water, but I don't have time to research what that might be. In any case, the seawater rise due to global warming is due to non-floating ice melting AND to the warming of the water (which increases its volume).
The NYTimes is notoriously poor in reporting on any science or technology. I would take all of it with a grain of salt.
--ms
Henry Baker wrote:
That was the point of my original posting -- the NYTimes thought that melting floating ice would raise the water level -- they were obviously wrong. At 04:09 PM 9/29/2005, dasimov@earthlink.net, math-fun wrote:
(So what's the business about floating ice raising water levels when it melts?)
--Dan
On 9/30/05, Henry Baker <hbaker1@pipeline.com> wrote:
As an aside, I recently saw a show on Italian cooking on cable TV, and the cook used the change in density of salt water to approximate the correct salinity for a salt broth. She put a potato into the water, and added enough salt until the potato started to float. That was the correct amount for her recipe. Something tells me that this technique was probably used for thousands of years. Except that the potato is from the New World. Anyone know if Andean indians use salt broths in their traditional cooking? -- Mike Stay metaweta@gmail.com http://math.ucr.edu/~mike
I hope everyone's clear that nothing has been pointed out in the NY Times article that's actually incorrect. The ``offending'' quote is this:
But a host of troubles lie ahead as well. One of the most important consequences of Arctic warming will be increased flows of meltwater and icebergs from glaciers and ice sheets, and thus an accelerated
rise in sea levels,<< threatening coastal areas.
Glaciers and ice sheets are on land, not floating in the water. The concern raised by scientists is that Arctic warming, accelerated by the lower albedo of a smaller ice cap, will melt these, along with the ice cap. The article does say say or imply that the meltwater from the ice cap wil raise the sea levels, even though a careless reading might leave that impression. --Bill Mike Speciner wrote:
The NYTimes is notoriously poor in reporting on any science or technology. I would take all of it with a grain of salt.
--ms
Henry Baker wrote:
That was the point of my original posting -- the NYTimes thought that melting floating ice would raise the water level -- they were obviously wrong. At 04:09 PM 9/29/2005, dasimov@earthlink.net, math-fun wrote:
(So what's the business about floating ice raising water levels when it melts?)
--Dan
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participants (5)
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Bill Thurston -
dasimov＠earthlink.net -
Henry Baker -
Mike Speciner -
Mike Stay