Question

Define (a) RMS (b) Average and (c) most probable speeds of gas molecules. Give their inter relationship.

Answer 1

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Answer 2

(a) RMS speed : RMS speed or root mean square speed is defined as square root of mean of square square of velocity of gas molecules.

for instance, v1, v2, v3, v4, ...vn are velocities of gaseous molecules present in a container.

then, RMS velocity of gaseous molecule = √{v1² + v2² + v3² + v4² + ....+vn² }/n}

from kinetic theory of gases,

$v_{rms}=\sqrt{\frac{3RT}{M}}$

(b) average speed : average speed of all molecules present within the gas is known as average speed.

average speed is given as $\bar{v}=\sqrt{\frac{8RT}{\pi M}}$

(c) most probable speed : the speed possessed by the maximum number of molecules of gas is known as most probable speed.

most probable speed is given as $v_p=\sqrt{\frac{2RT}{M}}$

now relation between RMS, average and most probable speeds .

$v_{rms}$ : $\bar{v}$ : $v_p$ = $\sqrt{\frac{3RT}{M}}$ : $\sqrt{\frac{8RT}{\pi M}}$ : $\sqrt{\frac{2RT}{M}}$

= 1 : 1.128 : 1.234