Does Archimedes' Principle mean that Melting ice will not cause water rise?

Question

I'm not sure if I understand the principal.

if you fill a bath tub with water say a foot deep then add several blocks of ice such that they are floating in the water. Next mark the level of the water in the bath tub. When the ice melts will the level be the same?

Additional Details

Scorpio9...

Please read more thoroughly next time before you vote other's responses down. I specifically said that you measure the level of the water "after" the ice is added.

Answer 1

Best Answer - Chosen by Voters

yes, the level of water remains the same. When ice is added to water, 1/5 th of the ice is visible above water and 4/5ht is below the water level.
As the volume of ice is more than that of water(due to anomalous expansion of water),when the ice melts, it occupies the space previously occupied by 4/5 th the ice,and thus the water level remains same.

Answer 2

Yes, the level will remain the same

Answer 3

It should remain the same.

Answer 4

Yes, the level will remain same. There is an easy way to experiment. Fill a glass with some ice cubes. Then pour water in it till glass fills up to brim. Entire ice will melt but not a drop of water will spill. Principle is simple. The volume of ice was equal to volume of water it displaced. Hence melted ice will occupy same volume what it had displaced.

Answer 5

The water will RISE instantly upon adding with the ice. Because Archimedes Principle states that "the volume of solid submerged is equal to the volume of liquid displaced". The water will rise due to the volume of solid ice.

But assuming that water being used for making ice has the same density with the bath tub water, then the ice will be covered by water on the top. Now, when the ice melts, the level of water will REMAIN THE SAME with the level after putting/adding the ice.

Answer 6

What you don’t understand is that the water’s density as a solid ice is different from its density as liquid water. When it’s solid it’s more compressed.
When it becomes liquid its molecules become more distant from each other and of course the total volume occupied by the water changes.
Anyone who thought it remains the same should not have answered your questions they’re idiots!

Answer 7

in terms of archimedes principle, the reasoning is correct, the ice displaces water equal to it's own mass, and when it melts the water has that mass and that volume. However, if the water in the bath was 4C and the ice melting cooled it to 1C then all the water would have expanded slightly, so I think it might be slightly higher. (water expands from 4C to 1C)