An astronaut carries with him a cylinder of capacity 10 litre filled with nitrogen gas at temperature 27 $^{o}$ C and pressure 50 atmosphere. He makes a hole of area 1 cm $^{2}$ in it. In how much time will it be emptied?

575 s

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1.312 s

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0.513 s

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0.387 s

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Solution

The correct option is D 0.387 s
$t = \frac{d}{V_{r m s}} = \frac{2 V}{A V_{r m s}}$
$= \frac{2 V}{A \sqrt{\frac{3 R T}{M}}}$
$= \frac{2 \times 10^{- 2}}{10^{- 4} \sqrt{\frac{3 \times 8.3 \times 300}{28 \times 10^{- 3}}}} = 0.387 s$

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An astronaut carries with him a cylinder of capacity 10 litre filled with nitrogen gas at temperature 27oC and pressure 50 atmosphere. He makes a hole of area 1 cm2 in it. In how much time will it be emptied?

The correct option is D 0.387 st=dVrms=2VAVrms =2VA√3RTM=2×10−210−4√3×8.3×30028×10−3=0.387s

An astronaut carries with him a cylinder of capacity 10 litre filled with nitrogen gas at temperature 27 $^{o}$ C and pressure 50 atmosphere. He makes a hole of area 1 cm $^{2}$ in it. In how much time will it be emptied?

The correct option is D 0.387 s
$t = \frac{d}{V_{r m s}} = \frac{2 V}{A V_{r m s}}$
$= \frac{2 V}{A \sqrt{\frac{3 R T}{M}}}$
$= \frac{2 \times 10^{- 2}}{10^{- 4} \sqrt{\frac{3 \times 8.3 \times 300}{28 \times 10^{- 3}}}} = 0.387 s$