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Infinite number of flask are connected to one another as shown.
The volumes and pressure in each flask vary as shown above.The stop-cocks are intially closed. Then find the common pressure in atm when all the stop-cocks are opened if (P = 30 atm)

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answer is 40.

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Detailed Solution

For, the infinite number of flask;

$P_{f} \times (V + \frac{V}{2} + \frac{V}{4} \dots \infty)$

$= 2 P \cdot V + P \cdot \frac{V}{2} + \frac{P}{2} \cdot \frac{V}{4} + \dots \infty$

$= 2 P \cdot V (1 + \frac{1}{2^{2}} + \frac{1}{2^{4}} + \dots \infty)$

$\Rightarrow P_{f} \times V (\frac{1}{1 - \frac{1}{2}}) = 2 P V (\frac{1}{1 - \frac{1}{2^{2}}})$

$P_{f} = \frac{4}{3} P = \frac{4}{3} \times 30 = 40$

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