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QPages 34-37: Q44: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q44 Solution: An ideal gas is kept in a long cylindrical vessel fitted with a …

An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm210 \text{ cm}^2 and weight 1 kg. The length of the gas column in the vessel is 20 cm. The atmospheric pressure is 100 kPa. The vessel is now taken into a spaceship revolving round the earth as a satellite. The air pressure in the spaceship is maintained at 100 kPa. Find the length of the gas column in the cylinder. Use R=8.3 J K−1 mol−1R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** L2=20 cmL_2 = 20 \text{ cm} **Step-by-Step Explanation:** In the spaceship (free fall), effective gravity is zero. The piston has no weight force. The chamber is maintained at P=100P = 100 kPa = atmospheric pressure. The gas inside is also at 100 kPa. Since P1=P2P_1 = P_2, volume is unchanged: L2=20L_2 = 20 cm.

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