Find the time during which a layer of ice of thickness 2.0 cm on the surfaceof a poind will have itsthickness increasedby 2 mm when temperature of the surrounding air is `-20^(@)` and latent heat of fusion `=80"cal"g^(-1)`, density of ice `0.91g//cm^(3)`, coefficient of thermal conductivity of ice `=5xx10^(-3)"cal"//cm//s-^(@)C`

Explanation

To solve the problem of finding the time during which a layer of ice of thickness 2.0 cm on the surface of a pond will have its thickness increased by 2 mm when the temperature of the surrounding air is -20°C, we will follow these steps:

### Step 1: Understand the Problem
We need to calculate the time required for the thickness of ice to increase from 2.0 cm to 2.2 cm (which is an increase of 2 mm). We will use the concepts of heat transfer and phase change.

### Step 2: Identify Given Data
- Initial thickness of ice, \( x_1 = 2.0 \, \text{cm} = 20 \, \text{mm} \)
- Final thickness of ice, \( x_2 = 2.2 \, \text{cm} = 22 \, \text{mm} \)
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