Explain following terms :
(i) `u_(mp)`
(ii) `u_(av)`
(iii) `u^(2)`
(iv) `u_(rms)`

Explanation

(i) Most probable speed `(u_(mp))` : At fixed temperature, maximum number of molecule of gas.
`u_(mp)=sqrt((2RT)/(M))=0.816xx u_(rms) " "` …..(Eq. -i)
(ii) Average speed `(u_(av))` : Different velocity average at molecules of gas is known as average speed.
`u_(av)=(u_(1)+u_(2)+u_(3)+.....u_(n))/(n)`
where, `u_(1), u_(2), u_(3)` .... = speed of different molecule and n = number of molecules of gas.
`u_(av)=sqrt((8RT)/(M))`
(iii) Square of average speed of molecules `(u^(2))` : Square of average speed of molecule is kinetic energy of molecules of gas.
`bar(u)^(2)=(u_(1)^(2)+u_(2)^(2)+.......u_(n)^(2))/(n) " "` ....(Eq. -ii)
`u^(2)=(3RT)/(M) " "` ......(Eq. - iii)
`(u_(rms))` : 1 root `(bar(u)^(2))` average speed square speed is known as `(u_(rms))`.
`u_(rms)=sqrt(bar(u)^(2))=sqrt((u_(1)^(2)+u_(2)^(2)+u_(3)^(2)+......)/(n)) " "` ......(Eq. - iv)