A metal rod of length 20 cm and diamter 2 cm is convered with a non conducting substance. One of its ends is maintained at `100^(@)C` , while the other end is put at `0^(@)C`. It is found that 25 g ice melts in 5 min. calculate the coefficient of thermal conductivity of the metal. Latent that of ice = `80 cal g^(-1)`.

Explanation

To solve the problem, we need to calculate the coefficient of thermal conductivity (K) of the metal rod using the given information. We will use the formula for heat conduction, which is derived from Fourier's law of heat conduction.

### Step-by-step Solution:

1. **Identify the given data:**
- Length of the rod, \( L = 20 \, \text{cm} = 20 \times 10^{-2} \, \text{m} = 0.2 \, \text{m} \)
- Diameter of the rod, \( d = 2 \, \text{cm} = 2 \times 10^{-2} \, \text{m} \)
- Radius of the rod, \( r = \frac{d}{2} = 1 \times 10^{-2} \, \text{m} \)
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