Ice starts forming in lake with water at `0^(@)C` and when the atmospheric temperature is `-10^(@)C`. If the time taken for `1 cm` of ice be `7` hours. Find the time taken for the thickness of ice to change from `1 cm` to `2 cm`

Options

A. `11 hours`
B. `6 hours`
C. `16 hours`
D. `21 hours`

Explanation

To solve the problem, we need to understand the relationship between the thickness of ice formed and the time taken for that formation. The process of ice formation can be modeled using the concept of heat transfer.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We know that the temperature of the water is at `0°C` and the atmospheric temperature is `-10°C`.
- The time taken for `1 cm` of ice to form is `7 hours`.

2. **Assumption of Linear Growth**:
- We can assume that the thickness of the ice formed is directly proportional to the time taken for its formation. This means if it takes `7 hours` to form `1 cm` of ice, it will take longer to form `2 cm` of ice.

3. **Calculate the Time for 2 cm of Ice**:
- Since it takes `7 hours` to form `1 cm`, to form `2 cm`, we can use the proportionality:
\[ \text{Time for 2 cm} = 2 \times \text{Time for 1 cm} = 2 \times 7 \text{ hours} = 14 \text{ hours} \]

4. **Conclusion**:
- Therefore, the time taken for the thickness of ice to change from `1 cm` to `2 cm` is `14 hours`.

### Final Answer:
The time taken for the thickness of ice to change from `1 cm` to `2 cm` is **14 hours**.