When a cube of ice floats on water and it melts what will be the level of water after melting?

Question

Will it remain the same?
increase?
decrease?
increase and then decrease?

Answer 1

will be the same

Answer 2

A floating object displaces an amount of water that weighs the same as the object's mass.

Since an ice cube is less dense than water, some of it is sticking up out of the surface; and the volume of that piece of the ice cube that sticks out is the same as the difference between the volume of the water as solid and the water as liquid.

When the ice melts, its volume will be the same as the part of the ice cube that is below the surface.

Therefore, the level of water remains the same.

There's a fact that I've neglected, though, which has a very small effect: Water, after it melts, first contracts until it reaches 4 degrees Celsius and after that, it expands (this is negligible, but does exist).

The volume of the ice has no effect on the water for the abovementioned reason; but the temperature of the water does have an effect on its volume and thus its level. If the glass is small enough so that the ice cools the water to 0 degrees before it melts (absorbing the amount of energy necessary to liquefy it), then the process goes like this:

--The ice melts, and the water cools down. The volume of the water decreases until it reaches 4 degrees Celsius.
--When the water reaches 4 degrees Celsius, it begins to expand until it reaches zero degrees--the freezing point. At this point, the temperature stays there until the ice cube melts.
--However, the water does not freeze because it still has too much energy; and when the energy in the water equalizes, it is liquid at zero degrees. Then, because (I assume) the room temperature is higher, the water begins to warm.
--As the water warms towards 4 degrees again, it contracts, dropping the level.
--When it hits 4 degrees, the water level rises again until the water reaches room temperature and its volume is the same as just after the ice was dropped into the glass.

So the graph of water level over time should look somewhat like a wavy "W".

If the ice cube doesn't cool all the water to zero degrees, the "W" shape is still there, but less pronounced; because less of the water is going past the 4 degree boundary.

If you assume that no water evaporates, then the water level should be the same after melting as before.

Answer 3

Oct.30/ 06
This depends on the size of container. the amount of definate
increase is volume related. If you put the ice cube in a coffee
cup filled all most to the rim with water, The ice cube when
completely melted, will Over-fill the edge of the cup, causing
a mess for either mum or the wife to clean up.
On the other end of the table, you have an Ice cream
Bucket full of water to say 1 inch from the Top edge of this
bucket. The ice cube is totally melted,however, ( we are
assuming this cube of ice is from a regular kitchen ice tray.)
so,--- the ice cube is like 1" sq. compared to the bucket
which is 12" across, & maybe 10 " deep? The water will
rise maybe 1/32nd of a M/m. You will need a microscope
or magnifying glass to see the difference.
R. [e-mail]

Answer 4

It should stay the same if no other outside forces are acting upon the water or ice(other than the heat melting the ice, but this should matter much).

Its the Conservation of Mass theory.

But if you want the play by play, then it technically increases, but then decrease back to original levels, neglecting evaporation and condesation from the ambient air.

Answer 5

The floating ice cube displaces a mass of water equal to it's own mass. Visualize taking the ice cube out of the water. The water level will drop by Δh = M/ρA. now visualize meltting the ice and pouring it back in . the volume of the melted ice will be AΔh, so the water level will return to its original level. this holds for any size ice cube, so the level remains the same as the ice melts.

Answer 6

It remains the same. The ice floats on the water; the weight of the water displaced by the ice is the total weight of the ice. The combined volume of the water and the volume of ice below water determines the initial level. Let the volume of water be V_w, the combined volume is V_w + V_u, where V_u is the underwater volume of ice. V_u is [d(ice)/d(water)]*V_ice, where d(ice) is the density of ice, d(water) is the density of water and V_ice is the volume of the cube of ice. (Equate the weight of water displaced to the weight of the ice cube to get this.) The resultant formula for combined volume is then

V_c = V_w + [d(ice)/d(water)]*V_ice.

After the ice melts there is only water. The total volume is the initial volume outside the ice V_w, plus the volume of water produced by the melted ice, V_melt. Since mass is conserved, V_ice*d(ice) = V_melt*d(water), or V_melt = [d(ice)/d(water)]*V_ice. The new volume of water is then V_w + V_melt or

V_c' = V_w + [d(ice)/d(water]*V_ice

same as before it melted.

Answer 7

Water level will increase until the Ice is fully melted. If the water volume is great, you will see a significat level increase even after the ice is fully melted due to the expansion of water molecue to achieve equilibrium condition with the surrounding.

Water level increase because your Ice is FLOATING and is not Submerge inside the water.

Well, you need to do an experiment with a glass of water eventually. If you compare to a Lake, then will be insignificant of change in the level because of the conservation of Mass Theory

Answer 8

are you measuring the level before you put the ice in?
is the ice being kept at the level of water?
what is the temperature of the water in the class?
will there be any possibility of evaporation?
what is the ambient temperature?

any one of the above (and more) will have an effect on the outcome

Answer 9

It will increase by a little less then the volume of the ice cube which was above the surface of the water....a negligable increase.

Answer 10

I think it will remain the same because the amount of mass does not change just because it goes from solid to liquid.

Answer 11

It will remain the same.