An ice layer of thickness 3 cm is formed on a lake. How much time will it take to increase the thickness of ice by 2 mm if temperature of air is `-30^@C` ? Take, Density of ice `= 1 g cm^(-3) ` , Latent heat of ice `= 80 cal g^(-1) ` , Conductivity of ice `= 0.008 cal s^(-1) cm^(-1) ""^@C^(-1)`

Explanation

To solve the problem of how long it will take to increase the thickness of ice by 2 mm (0.2 cm) on a lake with the given conditions, we can follow these steps:

### Step 1: Understand the problem
We need to calculate the time required to increase the thickness of ice from 3 cm to 3.2 cm at an air temperature of -30°C.

### Step 2: Identify the relevant parameters
- Thickness of ice to be increased, \( \Delta x = 0.2 \, \text{cm} \)
- Temperature of air, \( T_a = -30^\circ C \)
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