A long metallic bar of length 0.5 m is placed in such a way that its one end is in ice and other end is in steam at `100^@C` . What will be the thermal conductivity of the metal if amount of ice melt in 1 minute is 20 g, Cross sectional area of the bar `= 4 xx 10^(-4) m^2` and latent heat of ice `= 80 cal g^(-1)` .

Explanation

To solve the problem of finding the thermal conductivity of the metallic bar, we will follow these steps:

### Step 1: Identify the given data
- Length of the bar, \( L = 0.5 \, \text{m} \)
- Cross-sectional area, \( A = 4 \times 10^{-4} \, \text{m}^2 \)
- Mass of ice melted, \( m = 20 \, \text{g} = 0.02 \, \text{kg} \)
- Latent heat of ice, \( L_f = 80 \, \text{cal/g} = 80 \times 10^{-3} \, \text{kcal/g} = 80 \times 10^3 \, \text{cal/kg} \)
- Time, \( t = 1 \, \text{minute} = 60 \, \text{s} \)
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