# A Curious Question About Freezing

1. Oct 17, 2004

### CollectiveRocker

Here's a question I've been thinking about for a while; maybe you guys could provide some guidance. If the air temperature is below 0 degrees Celsius, the water at the surface freezes to form ice, right. Now the question I have is: why doesn't freezing occur throughout the entire volume of the lake? Is it pressure?

2. Oct 17, 2004

### Tide

There are two parts to this. If the water is being cooled by the air it is because the air is colder than the water so the water at the top will freeze sooner since water is not a perfect thermal conductor. Also, ice is less dense than liquid water so ice will tend to rise and stay at the top.

3. Oct 17, 2004

### Hurkyl

Staff Emeritus
Ice (and snow) are pretty good insulators too, aren't they?

4. Oct 17, 2004

### Bob3141592

There might be several factors working here. Air moving across the surface of the water is very efficient at cooling the water since it's removing heat by convection. Once a thin layer of ice forms, there's no convection currents, and heat can only excape by conduction, a much less efficient process. And the layer of ice acts as an insulator. therefore deeper freezing can take a very long time. Another thing to keep in mind is that water under pressure doesn't freeze as easily. The greater the depth the greater the pressure and so the lower the temperature must be for it to freeze. Also, the layer of water at the top acts as a kind of buffer, making it hard for the bottom water to experience the temperature at the surface. As long as the water is still, warmer subsurface water cannot rise. Even though warm water is less dense and should rise, as long as the cold water is "attached" to the surface by the ice, it won't rise. This is called a temperature inversion. It's an unstable equilibrium, and if something happens to stir the water, a convection current can form which brings warm water up from the bottom while the colder water at the surface falls. This falling water further pushes up the warmer water by displacement. This is called turnover, and can lead to sudden thinning and melting of the ice at the surface, even if the air temperature is very cold. This makes skating on some large ponds in the early winter very dangerous, as the ice can break even if it seems way too cold outside for melting to occur.

Moving water doesn't freeze, so in a river where there's a constant current, the eeper water will remain in motion and so remain liquid. The surface water will freeze first where it's held still by the shore, andf then that ice forms a new shore that keeps water still, and so the ice can spread across the surface of the river. But you can't stop the deeper currents.

Also, if there's salt in the water (my local lake receives runoff from the road so it has significant salt in it), salt water is heavier than fresh water, so it tends to the bottom and won't freeze unless the temperature is much lower than 0 degrees C.

5. Oct 17, 2004

### CollectiveRocker

Here's another part of this question: What is the process to show that the thickness of the ice sheet formed on the surface of the lake is proportional to the square root of the time if the heat of fusion of the water freezing on the underside of the ice sheet is conducted under the sheet?

6. Oct 19, 2004

### Clausius2

If the air above is at temperature To, and water below at Ta:

$$\frac{dQ}{dt}=-k_{ice}\frac{dT}{dx}$$

with $$dQ=L_f \rho_{ice}$$ where Lf is the latent heat of fusion.

Solve for x(t) and you get:

$$x(t)=\sqrt{\frac{k(T_a-T_o)2t}{L_f \rho}}$$

7. Oct 19, 2004

### CollectiveRocker

What is dT/dx?

8. Oct 19, 2004

### MiGUi

Firstly its not very common that the lake begins to freeze from up to down. This occurs due to the anomal dilatation of water. Normally, materials get more voluminous as we heat them, but with water don't happens this between 0 and 4 degrees. As we heat it, it decreases its volume.

So, imagine a lake. The atmosphere is for example at -20 C so the first dS of water begins to freeze and its temperature is set to zero. But, the thermal conductivity of ice is very poor as someones say, so under this tiny layer of ice the temperature is 0 C. Obviously, the layer grows more or less depending on the thermal difference.

When finally we get the lake with a layer of ice, that ice can be at any temperature lower than zero celsius, but the layer of water downwards will be more, will be 4 degrees since water at 4 degrees is denser than water at 3 degrees so (because Archimedes) the water at 3 degrees goes up, and the water at 4 goes down.

This anomalous dilatation let the life continue ... even when outside we freeze.

MiGUi

9. Oct 20, 2004

### Clausius2

Sorry, x is the vertical coordinate. dT/dx is the gradient of the Temperature in x direction. It's only the conservation of Energy applied to the frozen thickness.