If we make a deep well, and fill it with fresh cold water, at what depth will ice sink?

Question

Phase diagram of water can be found here:

http://www.lsbu.ac.uk/water/phase.html

Answer 1

All materials, including water and ice, are compressible to some degree. Ice will sink if, at its given pressure and temperature, it is more dense than water. Ice having a density of 1.1 at high pressure vs. water's 1 at normal pressure is not enough, as floodtl implies; we need to know water's density at that pressure too.

From basic considerations of work and heat, ice's density is greater than water's if an isothermal increase in pressure causes water to solidify into ice. This is because the work done on the medium must equal the heat of fusion that diffuses into the isothermal reservoir assumed. Since heat of fusion is invariably positive, PdV must decrease during the pressure increase (ie, it contracts). Focusing on the second phase diagram (detail), this corresponds to the boundary between ice III, V, or VI, and the liquid phase. For example, if the temperature is 0 C, the pressure must be 600 MPa for ice to sink. At -20C, it must be 200 MPa. From the diagram we see that the latter is the lowest pressure that ice will sink at any temperature.

Answer 2

Not clear why the "deep well" is specified. Are you thinking reaaaaaly deep; so that air pressure (on the cube and on the water surface) will somehow make a difference? If that's your supposition, it should be specified up front. Or, perhaps, the water is reaaaly cold, super cooled to less than 0 deg C, so that when the ice is dropped in, the entire surface of the well water freezes over...and the ice does not sink much, if any, at all. Discounting all these rare conditions, here's the solution.

Ice will sink to a depth (d) where W = w; the weight of the ice w equals the weight of the displaced water W, which is also the buoyancy. It will sink no farther because the weight of the ice and the buoyancy are equal but opposite forces. So there is no acceleration in any direction.

Since mass density rho of ice is less than mass density Rho of water, the volume of water displaced (v) will be less than the volume of the ice (V). W = Rho v g = rho V g = w; where g is the acceleration of mass acted on by gravity alone. Thus, Rho v = rho V and v = (rho/Rho) V, which says the volume of the displaced water (v) will be less than V the volume of the ice when it is floating in the water.

If we assume an ice cube of V = L^3, where L is the length of all sides, and displaced water of v = dl^2, where l = L where the cube sides carve out the non vertical sides in the water and d is the depth (vertical) of the displaced water on the cube, then dl^2 = (rho/Rho) l^2 L because the area of the cube and water displaced are both l^2. Then d = (rho/Rho) L; where L is the length of the cube side sticking up from the water. d = depth of the cube in the water and L - d = the height of the vertical cube sides above the water. That is, as you put it, it will "sink" so that d of its L sides is submerged.

Answer 3

I don't understand why floodtl got 2 thumbs down, He got the gist of the problem, true ice II can not exist if the "cold water" is above 0c, but that is nitpicking

I'd have to say good luck Keeping the water cold at that depth. Actualy I have to ask, is the water at depth the same temperature as the "cold" water poured in at the surface? if so we will have to go a bit deeper to get the pressure up to about 626MPa to get ice VI. Of course at that depth (assuming we are on earth) there is a fair bit of the planet above us, so the pressure isn't increasing with depth as much as near the surface. But I don't really want to calculate that. This might be another one of Alexander's quasi unanswerable questions. Anyway, floodtl was the first to realise that at high pressure denser forms of ice can exist.

Answer 4

Water becomes more dense as pressure increases at depth. Since ice is less dense already than water at the surface, it will always float at any depth.

The same is not true for compressible substances, like gases. A balloon with air will float at the surface, but below a certain depth, the pressure will compress the gas to a density that is near water density, and the weight of the balloon will cause it to sink.

Answer 5

Why do you think the ice would sink? Have you ever put ice in a cold glass of water? No different. Depth of the well makes no difference.

Answer 6

Ice will not sink at any depth. (Unless you have something on top of it, forcing it down.)

Answer 7

it will float ice floats its slighty lighter than fresh water.

Answer 8

im probable going to sound stupid, but doesnt ice float??? i kno it does in my cup.