At 20°C, two balloons of equal volumes and porosity are filled to a pressure of 2 atm, one with 14 kg N₂ and other with 1 kg of H₂. The N₂ balloon leaks to a pressure of 1 atm in 2 hr. How long will i

Question

At 20°C, two balloons of equal volumes and porosity are filled to a pressure of 2 atm, one with 14 kg N₂ and other with 1 kg of H₂. The N₂ balloon leaks to a pressure of 1 atm in 2 hr. How long will it take for the H₂ balloon to reach a pressure of 1 atm?

TestHub · Accepted Answer

At fixed V and T, dP/dt ∝ P/√(M), so the time for a given pressure ratio scales as t ∝ √(M). For the same ratio 2 → 1 atm: t(H₂) = 2 h × √(2/28) = 0.535 h = 32 min. Confirms Ans: (d) 32 min.

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