An ideal gas is held within a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 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 subsequently transported into a spaceship orbiting the earth as a satellite. The air pressure inside the spaceship is kept at 100 kPa . Determine the length of the gas column

Step-by-step solution

Initial pressure of the gas on Earth is given by P₁ = P_ atm + mg A Substituting the given values, P_ atm = 100 kPa = 10^5 Pa , m = 1 kg , A = 10 cm ^2 = 10⁻³ m ^2 , and taking g = 10 m/s ^2 : mg A = 1 10 10⁻³ = 10^4 Pa = 10 kPa P₁ = 100 kPa + 10 kPa = 110 kPa Initial volume of the gas is V₁ = A L₁ , where L₁ = 20 cm . In the orbiting spaceship, the system experiences weightlessness, so the effective weight of the piston is zero. Final pressure of the gas is P₂ = P_ atm = 100 kPa Assuming the temperature remains co