An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area `10cm^(2)`and weight 1kg. The length of the gas column in the vessel now taken into a spaceship revolving round the earth as satellite. The air pressure in the spaceship is maintained at 100kPa. Find the length of the gas column in the cylinder.

Explanation

To solve the problem step-by-step, we will follow the reasoning provided in the video transcript and apply the principles of the kinetic theory of gases and the ideal gas law.

### Step 1: Understand the Given Information
We have a cylindrical vessel with:
- Cross-sectional area \( A = 10 \, \text{cm}^2 = 10 \times 10^{-4} \, \text{m}^2 = 10^{-3} \, \text{m}^2 \)
- Weight of the piston \( m = 1 \, \text{kg} \)
- Gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \)
- Atmospheric pressure \( P_{\text{atm}} = 1 \times 10^5 \, \text{Pa} \)
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