First slide

Molecular velocities

Question

6 x 10²²gas molecules each of mass 10^-24kg are taken in a vessel of 10 liter. what is the pressure exerted by gas molecules? The root mean square speed of gas molecules is 100 m/s.

Moderate

A

20 Pa
B

2 x 10⁴Pa
C

2 x 10⁵Pa
D

2 x 10⁷ Pa

Solution

$\begin{array}{l} P = \frac{1}{3} \frac{{nmc}^{2}}{V} \\ = \frac{1}{3} \times \frac{6 \times 10^{22} \times 10^{- 24} \times (100)^{2}}{10 \times 10^{- 3}} \\ = 2 \times 10^{4} Pa \end{array}$

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