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Thermodynamic Processes

A big contain...

Question

A big container having ideal gas at pressure $P_{0}$ and of volume $V_{0}$ is being evacuated by using vacuum pump of cylinder volume $V$ . Find the pressure in the big container after n strokes. (Assume the whole process to be isothermal)

P_{n} = P_{0} {(\frac{v_{0}}{v_{0} - v})}^{n}

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P_{n} = P_{0} {(\frac{v_{0}}{v_{0} + v})}^{n}

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P_{n} = P_{0} {(\frac{v_{0} - v}{v_{0} + v})}^{n}

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P_{n} = P_{0} {(\frac{v_{0} + v}{v_{0} - v})}^{n}

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Solution

The correct option is B $P_{n} = P_{0} {(\frac{v_{0}}{v_{0} + v})}^{n}$

Say pressure before and after stroke to be $P_{0}, P_{1}$ respectively.

$P_{i} v_{i} = P_{f} v_{f}$

$P_{0} v_{0} = P_{1} (v_{0} + v)$

$P_{1} = \frac{P_{0} v_{0}}{v_{0} + v}$

For the next stroke $P_{i} = P_{1}$ and $P_{f} = P_{2}$

$P_{1} v_{0} = P_{2} (v_{0} + v)$

$P_{2} = \frac{P_{1} v_{0}}{v_{0} + v}$

Similarly
$P_{3} = \frac{P_{2} v_{0}}{v_{0} + v}$

$P_{2} = P_{0} {(\frac{v_{0}}{v_{0} + v})}^{2}$

$P_{3} = P_{0} {(\frac{v_{0}}{v_{0} + v})}^{3}$

$P_{n} = P_{0} {(\frac{v_{0}}{v_{0} + v})}^{n}$

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