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Question

There are n containers having volumes V, 2V, ....., nV. Same mass of a gas is filled in all containers connected with stopcock. All containers are at the same temperature if pressure of first container is P then final pressure when all stopcocks are opened is:

A
npn(n+1)
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B
2P(n+1)
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C
3npn(n+1)
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D
np2n(n+1)
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Solution

The correct option is A 2P(n+1)
The number of moles present in one container is PVRT.

Total number of moles present in n containers is nPVRT.

Let Pf be the final pressure. The final volume is n(n+1)2V.

Total number of moles when all the stopcocks are opened is Pfn(n+1)2VRT.

Since the number of moles remains same,

Pfn(n+1)2V=n(PV)

Hence, Pf=2Pn+1. This is the final pressure when all the stopcocks are opened.

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