A 1 m3 vessel containing 1023 particles have an orifice of area 10–2 mm2. If the average velocity of particle is 103 m/sec, the time taken when initial pressure in the container drop to half of initial value is

Engineering

Chemistry

Collision Frequency and Mean Free Path

Question

A 1 m³ vessel containing 10²³ particles have an orifice of area 10^–2 mm². If the average velocity of particle is 10³ m/sec, the time taken when initial pressure in the container drop to half of initial value is

27720 sec

277200 sec

2772 sec

477200 sec

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$- \frac{dn}{dt} = \frac{1}{4} \bar{c} \times \frac{n}{V} \times A$

$\Rightarrow In \frac{n_{0}}{n_{t}} = (\frac{1}{4} \bar{c} \times \frac{Α}{V}) t$

$t_{1 / 2} = \frac{0 .693}{(1 / 4) \vec{c} \times (A / V)} = \frac{0 .693 \times 4 \times 10^{3} \times 1}{10^{- 2} \times 10^{- 6}} 0 .693 \times 4 \times 10^{5} = 277200 \sec$