If barv, vrms and vp represent the mean speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature T and if m is mass of the molecule, then

Question

If barv, vrms and vp represent the mean speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature T and if m is mass of the molecule, then (A) vp < v < vrms (B) no molecule can have a speed greater than √2 vrms (C) no molecule can have a speed less than vp / √2 (D) None of the above

Tardigrade Admin · Accepted Answer

Mean speed, barv=√(8 k T/π m)=0.92 v rms rms speed, v rms =√(3 k T/m) Most probable speed, vp=√(2 k T/m)=0.816 v rms So, vp < barv < v rms

Q. If $\overset{v}{ˉ}, v_{r m s}$ and $v_{p}$ represent the mean speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature $T$ and if $m$ is mass of the molecule, then

$v_{p} < v < v_{r m s}$

no molecule can have a speed greater than $2 v_{r m s}$

no molecule can have a speed less than $v_{p} / 2$

None of the above

Mean speed, $\overset{v}{ˉ} = \frac{8 k T}{πm} = 0.92 v_{r m s}$
rms speed, $v_{r m s} = \frac{3 k T}{m}$
Most probable speed,
$v_{p} = \frac{2 k T}{m} = 0.816 v_{r m s}$
So, $v_{p} < \overset{v}{ˉ} < v_{r m s}$

Q. If vˉ,vrms​ and vp​ represent the mean speed, root mean square and most probable speed of the molecules in an ideal monoatomic gas at temperature T and if m is mass of the molecule, then

vp​<v<vrms​

no molecule can have a speed greater than 2vrms​​

no molecule can have a speed less than vp​/2​