Two identical containers A and B with frictionless piston contain the same ideal gas at the same temperature and the same volume V. The mass of the gas in A is m A and that in B in m B . The gas i

Question

Two identical containers A and B with frictionless piston contain the same ideal gas at the same temperature and the same volume V. The mass of the gas in A is m A ​ and that in B in m B ​ . The gas in each cylinder is now allowed to expand isothermally to the same final volume 2 V . The changes in the pressure in A and B are found to be Δ p and 1.5Δ p respectively. Then,

TestHub · Accepted Answer

Process is isothermal, so T = constant ( p ∝ V 1 ​ ) ; volume is increasing, therefore pressure will decrease. In chamber A: Δ p = p i ​ − p f ​ = [ V μ A ​ RT ​ − 2 V μ A ​ RT ​ ] = 2 V μ A ​ RT ​ . In chamber B: 1.5Δ p = 2 V μ B ​ RT ​ . From the two equations: μ B ​ μ A ​ ​ = 1.5 1 ​ = 3 2 ​ ⇒ m B ​ / M m A ​ / M ​ = 3 2 ​ ⇒ 3 m A ​ = 2 m B ​ .

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