# Fluids question!

Hi!
I'm new to the forums and this is the first that I'm posting something :D!

Question: An ice cube is floating in a glass of water that is filled entirely to the brim. When the ice cube melts, the water level will

a. fall
b. stay the same, right at the brim
c. rise, causing the water to spill.

Apparently, the key word is floating which has to do with bouyancy!

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Hey man

It's actually not too hard of a question and yes floating is a key word. Because ice floats it means that it is less dense as a solid than a liquid. This means that the solid ice takes up more space than the liquid water of the same mass. So if the solid melts into a liquid it would take up less space and therefore the water amount would drop.

Side note if interested:
The less dense structure of ice is because of hydrogen bonding that takes place. This hydrogen bonding causes the ice to form octagon structures which have a lot of open spaces between them causing them to be less dense than liquid water.

Borek
Mentor
So if the solid melts into a liquid it would take up less space and therefore the water amount would drop.
What about ice that was sticking above the water?

What is the mass of displaced water? How does it relate to the mass of ice? What volume will be occupied by the water from the melted ice?

stewartcs
Hey man

It's actually not too hard of a question and yes floating is a key word. Because ice floats it means that it is less dense as a solid than a liquid. This means that the solid ice takes up more space than the liquid water of the same mass. So if the solid melts into a liquid it would take up less space and therefore the water amount would drop.
Apparently it is hard since the level would NOT drop.

CS

simple use of archimedes' principle.
When the ice is put in water, it displaces water equal in volume to itself .
Now as it melts, it turns to water, so the level of water should increase, but at the same time, the volume of ice submerged is decreasing, so the volume of water displaced will decrease, and the water level should fall. This increase and decrease effect nullify and the water level remains constant.

Thank you so much!! Indeed, the water level stays the same but I just didn't understand why! I really appreciate it!

Borek
Mentor
Think this way: piece of ice displaced water. Mass of the displaced water was identical with the mass of ice. When the ice melts, mass of the water from melting doesn't change. What changes is the volume - but the volume of the water from melted ice is identical to the volume diplaced (why? because it is water, so one from melting has exactly the same density as the one displaced). So you have removed some volume and then you have added identical volume - and total volume didn't change.

Isn't the density of ice less than the density of water? I thought of it this way, ice is submerged partly in water as it is floating--lets say 3/4. So when that whole ice - 1 ice melts, the volume of melted ice (water) is 3/4 that of one ice, which takes the space of the displaced volume of water, hence level doesn't change. Am I right?