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If you fill a glass with ice cubes to the top, then fill the same glass with water until one more drop and it will over flow. When the ice melts will the glass over flow the sides of the glass?
80-89, M
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SomeMichGuy · M
No. The density of ice is less than the density of water
ρ_{ice} < ρ_{water}
so, as the ice melts, it decreases in volume. Even if you fill the glass entirely with ice, the melted ice will not overflow the glass.
It might be easier to see if one considers it in reverse: if the glass were full of water, then frozen, the ice would expand and go over the upper edge of the glass. So the quantity "water frozen in ice which is only to the edge of the glass" is clearly less than the quantity "water up to the edge of the glass which is then frozen in ice".
ρ_{ice} < ρ_{water}
so, as the ice melts, it decreases in volume. Even if you fill the glass entirely with ice, the melted ice will not overflow the glass.
It might be easier to see if one considers it in reverse: if the glass were full of water, then frozen, the ice would expand and go over the upper edge of the glass. So the quantity "water frozen in ice which is only to the edge of the glass" is clearly less than the quantity "water up to the edge of the glass which is then frozen in ice".