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Two identical containers A and B have friction less pistons. They contain the same volume of an ideal gas at the same temperature. The mass of the gas in A is mA and that in B is mB. The gas in each cylinder is now allowed to expand isotherm ally to double the initial volume. The changes in the pressure in A and B are found to be Δp and 1.5 Δp respectively(a) 4mA = 9mB (b) 2mA = 3mB (c) 3mA = 2mB (d) 9mA = 4mB |
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Answer» Correct Answer is: (c) 3mA = 2mB Let pA, pB be the initial pressures in A and B respectively. When the gases double their volumes at constant temperature, their pressures fall to PA/2 and PB/2 ∴ for A, pA - pA/2 = Δp or pA = 2Δp for B, pB - pB/2 = 1.5Δp or pB = 3Δp ∴ pA/pB = 3/2. Also, pAV = mA/M RT and pBV = mB/M RT. ∴ pA/pB = mA/mB ∴ mA/mB = 2/3 or 3mA = 2mB. |
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