First slide

Kinetic theory of ideal gases

Question

Two monatomic gases A and B having atomic masses $M_{A}$ , $M_{B}$ respectively are kept at the same temperature. The ratio of r.m.s. velocity and average velocity of gas A is $R_{A}$ and corresponding value for gas B is $R_{B}$ . Then $R_{A} = R_{B}$

Moderate

A

Only if $M_{A} = M_{B}$
B

Only if $M_{A} > M_{B}$
C

Only if $M_{A} < M_{B}$
D

For any value of $M_{A}$ and $M_{B}$

Solution

$v_{R M S} = \sqrt{\frac{3 R T}{M}}; v_{A V G} = \sqrt{\frac{8 R T}{π M}}$
$\Rightarrow \frac{v_{R M S}}{v_{A V G}} = \sqrt{\frac{3 π}{8}}$ (independent of nature of gas).

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