One mode of an ideal monatomic gas is kept in a rigid vessel. The vessel is kept inside a steam chamber whose temperature is `97^(@)C` . Initially, the temperature of the gas is `5.0^(@)C` . The walls of the vessel have an inner surface of area `800cm^(2)` and thickness `1.0cm` If the temperature of the gas increases to `9.0^(@)C` in `5.0` second, find the thermal conductivity of the material of the walls.

Explanation

To solve the problem of finding the thermal conductivity of the material of the walls of the rigid vessel containing one mole of an ideal monatomic gas, we will follow these steps:

### Step 1: Identify Given Data
- Initial temperature of the gas, \( T_1 = 5.0^\circ C \)
- Final temperature of the gas, \( T_2 = 9.0^\circ C \)
- Temperature of the steam chamber, \( T_{outside} = 97.0^\circ C \)
- Area of the inner surface of the vessel, \( A = 800 \, cm^2 = 800 \times 10^{-4} \, m^2 = 0.08 \, m^2 \)
- Thickness of the vessel, \( x = 1.0 \, cm = 0.01 \, m \)
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