Infinite number of flasks are connected to each other as shown above. The volumes and the pressures in each flask vary as shown. The stopcocks are initially closed. Find the value of $x$ when all the stopcocks are opened and the final common pressure is observed to be $x P$ .

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TestHub · Accepted Answer

n T ​ = n 1 ​ + n 2 ​ + n 3 ​ + … ​ RT P T ​ V T ​ ​ = RT P 1 ​ V 1 ​ ​ + RT P 2 ​ V 2 ​ ​ + RT P 3 ​ V 3 ​ ​ + ⋯ = ∑ RT P i ​ V i ​ ​ ∴ P T ​ V T ​ = ∑ P i ​ V i ​ = 2 P V + 2 P V ​ + 2 P ​ ⋅ 4 V ​ + 4 P ​ ⋅ 8 V ​ + … = 2 P V ( 1 + 4 1 ​ + 16 1 ​ + 64 1 ​ + … ) P T ​ V T ​ = 2 P V 1 − 4 1 ​ 1 ​ = 2 P V ⋅ 3 4 ​ V T ​ = V 1 ​ + V 2 ​ + V 3 ​ + … = V + 2 V ​ + 4 V ​ + 8 V ​ + … = V ( 1 + 2 1 ​ + … ) = V 1 − 2 1 ​ 1 ​ = 2 V ∴ P T ​ ⋅ 2 V = 2 P V ( 3 4 ​ ) P T ​ = 3 4 ​ P = 1.33 P ​

Chemistry - Ideal Gas Question with Solution | TestHub

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