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Main Question or Discussion Point
Whar happens to the level of water when ice melts in a beaker
Is the ice floating?Harshatalla said:Whar happens to the level of water when ice melts in a beaker
Is there any reason to think it wouldn't be?Doc Al said:Is the ice floating?
Could be a trick question involving the other stages of ice (frozen under high pressure), which I assume are more dense.DaveC426913 said:Is there any reason to think it wouldn't be?Is the ice floating
Is there a reason to think it is?Hootenanny said:Or the ice could be physically held underneath the water.
Your mistake is assuming that the ice floats yet is totally submerged. Yes, the volume of ice is greater than the volume of an equal mass of water--but only part of the ice is submerged and thus displacing water. (See SGT's post for a simple argument.)cyrusabdollahi said:I just wrote this proof down myself, so if its got a mistake point it out!
Error in the last line, on the RHS.cyrusabdollahi said:Ok, I will take a crack at it. Correct me if I am wrong Folks.
Let's take a differential element of water, where the top cube of the water lies at the free surface of the water. (i.e. the cube is just under the water).
This cube has dimensions, dx, dy, dz.
The volume of this cube is:
[tex] dV = dx dy dz [/tex]
the associated mass is:
[tex] m = \rho_w dx dy dz [/tex]
when water expands to ice, it increases by volume at about 9%, but the mass remains constant, therefore:
[tex] m = \rho_w dx dy dz = \rho_{ice}( 1.09 dx dy dz )[/tex]
So that means:
[tex] \rho_w = 1.09 \rho_{ice} [/tex]
We can now do a simple force balance to see our result: (weight of ice must balance buoyancy force)
[tex] F_b = \rho_w g dV' = \frac {\rho_w}{1.09} g dx dy dz [/tex]
I think my revision thanks to Gokul has put into equations what you have put into text. Though I think there is need of more equations to back up these arguments at the start of the thread. You guys were right, but it was too informal for my taste.DaveC426913 said:Simply put, the ice will float at a height where it displaces an amount of water exactly equal to its mass. If the volume of that block of ice happened to increase (for whatever reason), or even decrease (for whatever reason), without changing it mass, it is the volume above the waterline that will grow or shrink. The volume below the water line will not change, and thus the displaced amount of beaker water will not change. (It couldn't change! The volume displaced in the beaker water is directly created by the displacement from the mass of the block of ice, which hasn't changed in mass!) Since the amount of wtaer displaced in the beaker does not change, it has no effect on the water level.
(Hm. Inb retrospect, my post may have sounded almost patronizing. I didn't mean to suggest it's simple to understand, merely that the diagram is simple.)cyrusabdollahi said:Not to idiots like me
Thanks, but does it make its point?cyrusabdollahi said:That is a nice drawing.
Nono. Not proof. Simply answers the question intuitively. i.e. enough to make us all agree that the water level doesn't change. The proof can follow.cyrusabdollahi said:Well......I can't see that in and of itself as a valid proof. But I do see what you're getting at.