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  4. Let vrms, vmp and vavg represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, (vrms)2: (vmp)2: (vavg)2 is

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Q. Let $v_{rms}, v_{mp}$ and $v_{avg}$ represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, $(v_{rms})^2 : (v_{mp})^2 : (v_{avg})^2$ is

JIPMERJIPMER 2013Kinetic Theory

Solution:

$ \because \:\: v_{rms} = \sqrt{\frac{3RT}{M}} , v_{mp} = \sqrt{\frac{2RT}{M}}$ and $v_{avg} = \sqrt{\frac{8RT}{ \pi M}}$
$ \therefore \:\:\: (v_{rms})^2 : (v_{mp})^2 : (v_{avg})^2 = \frac{3RT}{M} : \frac{2RT}{M} : \frac{8RT}{\pi M}$
= $3 \pi : 2 \pi : 8$