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Molecular Speeds - Vrms, Vavg, Vmps

The RMS spe...

Question

The $R M S$ speed of the molecules of a gas of density $4 k g m^{3}$ and pressure $1.2 \times 10^{5} N m^{2}$ is:

120 m s^{1}

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300 m s^{1}

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600 m s^{1}

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900 m s^{1}

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Solution

The correct option is A $300 m s^{1}$
As we know,

$U_{r m s} = \sqrt{\frac{3 R T}{M}}$

$∵ P V = n R T$

$R T = \frac{P V}{n}$

$U_{r m s} = \sqrt{\frac{3 R T}{M}} = \sqrt{3 P \frac{V}{M}}$

$U_{r m s} = \sqrt{\frac{3 P}{d}}$
$= \sqrt{\frac{3 \times 1.2 \times 10^{5}}{4}} = 300 m / s e c .$

Hence, the correct option is $B$

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