an ice sheet 5m thick covers a lake that is 20m deep. what is the temperature of the water at the buttom of the lake

Answer 1

When a lake is covered by an ice sheet that is 5 meters thick, and the lake itself is 20 meters deep, the temperature of the water at the bottom of the lake is generally around 4°C (39.2°F).

Here's a step-by-step explanation as to why this is the case:

1. **Density and Water Behavior:** Water has a unique property in that it is most dense at 4°C. As water cools down, it becomes denser until it reaches 4°C. If it cools further and starts freezing, it becomes less dense again.

2. **Thermal Stratification:** During winter, when the surface water is cooled by the cold air, it will sink until it reaches 4°C because it becomes denser. As it sinks, it is replaced by warmer water from the bottom, which then cools down and sinks as well. This process continues until the entire water column from top to bottom reaches 4°C.

3. **Formation of Ice:** Once the entire water column is at 4°C, the surface water can cool down even further and eventually freeze. Ice is less dense than liquid water, so it forms on the top.

4. **Insulating Effect of Ice:** The ice sheet then acts as an insulating layer, preventing the water underneath from losing much heat to the colder air above.

As a result, the water below the ice remains at its densest and thus warmest liquid state, which is 4°C, even if the air above is much colder and the ice sheet is quite thick.

Thus, the temperature at the bottom of the lake will be around 4°C.