First slide

Maxwell speed distribution law

Question

For a gas at a temperature T the root mean square velocity v_rms, the most probable speed v_mp, and the average speed v_av obey the relationship

Moderate

A

${\nu _{av}} > {\nu _{rms}} > {\nu _{mp}}$
B

${\nu _{rms}} > {\nu _{av}} > {\nu _{mp}}$
C

${\nu _{mp}} > {\nu _{av}} > {\nu _{rms}}$
D

${\nu _{mp}} > {\nu _{rms}} > {\nu _{av}}$

Solution

${V_{av}} = \sqrt {\frac{{8KT}}{{\pi m}}} ,\,\,{V_{rms}} = \sqrt {\frac{{3KT}}{m}} ,{V_{mp}} = \sqrt {\frac{{2KT}}{m}}$
$\therefore {V_{rms}} > {V_{av}} > {V_{mp}}.$

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