3 Why a polar lake freezes from the top and fish survive

When the air temperature falls from 4 °C toward 0 °C:

1. The surface water cools, becomes denser (as long as it is above 4 °C) and sinks; warmer water below rises. This mixing continues until all the lake water is at 4 °C.
2. When the surface falls below 4 °C, it becomes less dense and stays on top. The coldest water (0 °C) is at the surface, where it freezes into ice.
3. The floating ice forms an insulating layer (ice and trapped snow are poor conductors) that slows loss of heat from the water below, so the rest of the lake does not freeze.
4. The water near the bottom stays near 4 °C, liquid, and aquatic organisms survive the winter.

• This is another reason why water is called an ideal habitat.
• If ice were denser than water it would sink, lakes would freeze from the bottom upward, and many polar ecosystems could not exist.

• Problem. (a) Find the mass of fresh water at 4 °C in a tank 2.0 m × 1.5 m × 1.0 m.
• (b) Find the mass if the tank holds sea water of density 1025 kg/m³.
• (c) A block of ice of volume 0.50 m³ and density 917 kg/m³ floats in sea water.
• What fraction of its volume is submerged?

Solution. (a) V = 2.0 × 1.5 × 1.0 = 3.0 m³; m = ρV = 1000 × 3.0 = 3000 kg. (b) 1025 × 3.0 = 3075 kg. (c) Floating: ρ_ice V = ρ_sea V_sub → fraction = 917/1025 = 0.895 (about 89.5 % submerged).

• Problem. Four 1 kg samples of water: (A) pure water at 4 °C, (B) pure water at 8 °C, (C) salt water at 4 °C, (D) pure water at 0 °C (liquid).
• Which has the greatest volume?
• Which has the smallest?

Solution. Volume = m/ρ, so the sample with the lowest density has the largest volume. Density order: C (salt, 4 °C) > A (4 °C pure) > D (0 °C) ≈ B (8 °C) (the density of water at 0 °C, 999.84 kg/m³, is very slightly smaller than at 8 °C, 999.85). Greatest volume: D (pure water at 0 °C, 999.84 kg/m³), only just ahead of B (8 °C, 999.85 kg/m³); both are larger than A (1000 kg/m³). Smallest volume: C (salt water at 4 °C). The point of the example: moving away from 4 °C in either direction lowers the density of pure water.