I had a mild argument with my friends the other day, while we were drinking at a bar. Someone was commenting on how I was drinking my vodka cranberry drink so slowly that the ice had already all melted. Somehow this become a debate on whether melting ice affects the water level. My friends argued that it did, because water shrinks as it passes from solid to liquid. I was pretty sure that it didn’t, but wasn’t sure how to explain it clearly. The best I could come up with was that the part of the ice that didn’t affect the water level (ie, the part above water) would, as the ice melted, replace the mass lost as the part of the ice below water passed from solid to liquid. Am I correct?
PS - we are a bunch of humanities grad students, so you’ll have to excuse our ignorance.
Someone will likely give you a more scientific answer, but I think you’re essentially correct. The ice floats, w/ a small portion above the liquid level, because it contains entrained air. As the ice melts the liquid level remains the same as he entrained air is released, sans the amount you consumed.
Assuming the ice floats in your drink. Archimedes’s law applies.
Meaning the level of the fluid in your glass isn’t affected by the ice being molten or not.
Archimede’s law is that the amount of water displaced by an object is equal to the volume of said object, correct? But the volume of ice will shrink as it turns into water, no? My question is why doesn’t that affect the water level, and if the explanation I gave in my OP makes any kind of sense.
ETA: Thanks, K364! Your reply wasn’t there when I posted this originally.
And before we get into the global warming rising water level dispute in GQ, let me note that we are talking about ice floating in water in this thread. The melting of the Arctic Ocean Icecap, in isolation, would affect world water level not at all, because it’s floating. Rising water levels would derive from the melting of the Greenland and Antarctic Ice Caps (and the “continental” glaciers on Baffin and Ellesmere Islands and perhaps a couple of others) because they are on land, not displacing liquid water.
Water crystalizes as it freezes into ice, making ice less dense than water (it’s not trapped air). Ice floating in water is going to raise the water level according to the weight of the ice. If the ice was floating in water, then when it melted, you would end up with exactly the same water level afterwards.
The only trick here is that the ice isn’t sitting in water.
If the ice is in a liquid with a higher density, then you’ll end up raising the “liquid” level when the ice melts. An extreme example of this would be if the ice was sitting in a puddle of mercury. The ice would sink very little into the mercury, and when the ice melted, you’d have a layer of water on top of the mercury that has much more volume than the volume of the mercury that was displaced by the ice.
On the other extreme, consider a liquid that is much less dense than ice, so that the ice cube sinks to the bottom in it. Ice takes up more volume than water, so it’s easy to see that when the ice turns into water, you’ll end up with less volume of liquid.
Your vodka-cranberry drink has a close enough density to water that you’d have to take some very careful measurements to notice the difference. You could nitpick your way into either position to win the bar bet (that’s the great thing about bar bets). If you say effectively the density of your drink is the same as water then you win. If your friends say the density is a little different, then they win.
Okay, I just thought of something else. Some of the ice in the glass was not exactly floating - some of the ice was submereged under because there was so much of it. What happens to the ice cubes that are complete below the water(vodka) level?
The density of ethanol is 0.789 g/cm³, liquid. Assuming this isn’t a pussy-ass drink, it’s at least 25% ethanol by volume. That would give us the average density of about 0.94 g/cm³ (I hope I didn’t fuck that up) — significant enough to be noticeable even if drunk with no measuring equipment.
Good lord this is the straightdope message board. Does nobody have an ice cube? I just stuck my tray in the freezer for the first time in five years so it’ll be a while for me, but damnit I’m gonna find out for sure.
You could regard them that way if you choose. But then you must account for the fact that the fully submerged ice cubes cause the ones above to float higher. At the end of your “individual masses” analysis, you’ll arrive at the same conclusion as if you’d treated all the ice as one.
The only thing that matters regarding the whole ‘floating’ thing: If you fill a BIG glass to the rim with ice cubes and add a drop of water the water level will rise when the ice melts. This only happens when the ice is stacked on the bottom of the glass, the moment you add enough water to let the ice float–> you know the waterlevel after meltdown.
For this experiment it is unpractical to consider the difference in specific weight between water and alcohol. (as in: your drinking buddy’s won’t notice the difference)
false: equal to the weight/mass
Consider all ice in your glass as ONE icecube, if one individual cube is pushed up a bit by three friends submerged beneath, it makes no difference for the endresult.
[/bar-physicist]
K364, **Xema **, Polycarp (while leaving the bar to step on some soapbox), engineer_comp_geek(right, but that only happens if your friends bring their slide-rules to the bar), groman(see the thing about the slide-rule), boytyperanma (did I mention a slide-rule?) Christopher,flex727 and Xema are all correct.
[/bar-physicist]
Word-searching the thread, it appears no one mentioned that some water is dissolved into the alcohol. But, I do not mean to imply that ALL the melted ice (per the OP) is dissolved into the alcohol…otherwise, how would bars water down drinks, right?
Sorry to all participating. From past experience with melting ice/sealevel global warming topics, I figured it would be only a matter of time before this nicely erudite discussion of melting ice in a glass got hijacked, and resolved to “head it off at the pass,” so to speak. I should have had more confidence in my fellow GQsters’ capacity to stay on topic. Mea culpa!
Well, once it melts, all the water formerly known as ice would dissolve into the alcohol. I’m not sure how this would hamper a bar watering down drinks, since that’s also a process of adding more water to the solution.
There is, though, a complication that a solution of alcohol and water will have a smaller volume than the volumes of the same amount of each separately. I’m not sure what proportion gives the highest density, though, nor what the percentage of each is already in the drink, so it’s hard to say what net effect this would have on the question.
