First slide

Rms speed

Question

The rms velocity of a gas at a given temperature is 300 m/s. What will be the rms velocity of a gas having twice the molecular weight and half the temperature in K.

Easy

A

300 m/s
B

600 m/s
C

75 m/s
D

150 m/s

Solution

${V_{rms}}\, \propto \,\sqrt {\frac{T}{M}}$
$\frac{{{V_1}}}{{{V_2}}}\, = \sqrt {\frac{{{T_1}}}{{{T_2}}} \times \frac{{{M_2}}}{{{M_1}}}} \, = \,\sqrt {\frac{{2{T_1}}}{{{T_1}}} \times \frac{{2{M_1}}}{{{M_1}}}} \, \Rightarrow \,\frac{{300}}{{{V_2}}}\, = \,2\,$
${V_2}\, = \,150m/\sec$

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