Quote:
Originally posted by Sapper
4) according to Archimedes principle, the mass of water displaced by the submerged portion of the ice equals the volume of the ice displacing the water times its density
of interest: this means that as the ice melts (becomes more dense) it will displace less water but its volume also decreases proportionately
Ok - with what we know, the ice cubes will become more dense and thus have a lower volume (by definition) as they melt. We also know that the ice cubes displace a certain amount of water (raising the water level) due to the difference in density. We also know that the amount of water displaced by ice is proportionate to the volume of ice.
Sadly, not enough information is given to choose between a or b as was noted by Peetster.
|
Volume times density is mass. Your first sentence has been greatly obfuscated by you saying "volume of the ice displacing the water times its density" when you could simply have said "mass."
I disagree with your (and
Peetster's) assessment that there is not enough information to choose an answer. I believe that there is, as I have already stated in an earlier post. You are looking so hard for more information to help you with this problem that you have included too much of it. Not everything that you mentioned is relevant to this problem and much of it is too specific.
Then again, this is the mathematician in me talking.
Let's work backwards because I find it easier to think that way.
Say, you have a pitcher of water. The water level will be at some height. Now, suppose that we freeze a portion of the water. This will be our "icecube." This portion of water will expand and the water level will rise as a result.
However, because the icecube is now going to float to the top, a portion of it's volume, that was previously displacing the water and causing the water level to rise, will be floating above the water. Obviously, this portion is
not displacing the water and, so, the water level will go down, again.
The question now becomes, by how much will it go down? This is the difficulty that
Peetster was mentioning and the both of you are convinced that we don't have enough information to know.
I think we
do.
According to
Archimedes, the mass of water displaced by the submerged portion of the icecube equals the mass of the icecube (as paraphrased by
Sapper).
So, what is the mass of the icecube? Well, it's
the same as the portion of water it was made from! I mean, just because you froze some water doesn't mean you changed its mass, does it?
Since the mass is the same, we can safely conclude that the volume of water displaced by the icecube is the same as the volume of the ice cube when it was water!
Therefore, the water level will not change.
QED. (oh, there's that math, again!)