The top of a lake gets frozen at a place where the surrounding air is at a temperature of `-20^(@)C` . Then :

Options

A. The temperature of the layer of water in contact with the lower surface of the ice block will be at `0^(@)C` and that at the bottom of the lake will be `4^(@)C`
B. The temperature of water below the lower surface of ice will be `4^(@)C` right up to the bottom of the lake
C. The temperature of the water below the lower surface of ice will be `0^(@)C` right up to the bottom of the lake
D. The temperature of the layer of water immediately in contact with the lower surface of ice will be `-20^(@)C` and that of water at the bottom will be `0^(@)C`

Explanation

To solve the problem regarding the freezing of the top layer of a lake when the surrounding air temperature is at -20°C, we can break down the situation step by step.

### Step 1: Understanding the Situation
The top of the lake is frozen, which indicates that the temperature of the water at the surface has dropped to 0°C, the freezing point of water. The surrounding air temperature is -20°C, which is significantly colder than the freezing point of water.

**Hint:** Consider the relationship between temperature and the state of water (liquid vs. solid).

### Step 2: Temperature of the Ice
Since the ice forms at the top of the lake, the temperature of the ice must be at or below 0°C. Therefore, the ice layer will be at 0°C.

**Hint:** Remember that ice forms when water reaches 0°C or below.

### Step 3: Density of Water
Water has its maximum density at 4°C. As the temperature of water decreases below 4°C, its density decreases, which means that water at temperatures lower than 4°C will rise to the surface.

**Hint:** Recall that the density of water changes with temperature, and that ice is less dense than liquid water.

### Step 4: Temperature Distribution in the Lake
The water just below the ice (the layer in contact with the ice) will be at 0°C, as it is freezing. The water below this layer will be at 4°C, since that is the temperature at which water is densest.

**Hint:** Think about how temperature gradients form in a body of water when the surface freezes.

### Step 5: Conclusion About the Bottom Layer
The bottom layer of the lake will remain at 4°C as long as the freezing process continues at the top. This is because the colder water (below 4°C) will rise to the surface and freeze, while the denser, warmer water (4°C) will stay at the bottom.

**Hint:** Consider how the properties of water affect its behavior in a freezing environment.

### Final Answer
The temperature of the water in contact with the lower surface of the ice block will be 0°C, while the temperature of the water at the bottom of the lake will be 4°C.