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Question
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 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-1
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Solution
P1V1 = P2V2
⇒ `((mg)/A + P_0)Al = P_0Al``
⇒ `((1 xx 98)/(10 xx 10^-4) + 10^5)0.2 = 10^5 I``
⇒ (9.8 × 103 + 105) × 0.2 = 105I`
= 109.8 × 103 × 0.2 = 105I`
⇒ I' = `(109.8 xx 0.2)10^2`
= 0.2196 m
= 0.22 m ≈ 22 cm
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