An ice layer of thickness `d_1` is floating on a pond of water. The atmospheric temperature is -`T^@C`. What is the time taken for the thickness of the layer to increase from `d_1` to `d_2` if L, `rho` and K are the latent heat of fusion of water, density of ice and thermal conductivity of ice, respectively?

Explanation

To solve the problem of determining the time taken for the thickness of an ice layer to increase from \(d_1\) to \(d_2\) given the latent heat of fusion \(L\), density of ice \(\rho\), and thermal conductivity of ice \(K\), we can follow these steps:

### Step-by-Step Solution

1. **Understanding Heat Transfer**:
The heat transfer occurs due to the temperature difference between the water (at 0°C) and the surrounding air (at -T°C). The heat flows from the water to the air, causing the water to freeze and the ice layer to thicken.

2. **Heat Transfer Rate**:
...