Question

Show that R.M.S. velocity of gas molecules is directly proportional to square root of its absolute temperature.

Answer 1

We know that,
`P=(1)/(3)(mm)/(V)xxv^(2)`
`implies" "PV=(1)/(3)xxMxxv^(2)(because" mn"=M)`
But `" ""PV"="RT"" "("By Gas equation")`
`:." "v^(2)=(3RT)/(M)`
But `" "v_("rms")=sqrt(v^(2))`
`=sqrt((3RT)/(M))`
`:." "v_("ems")prop sqrt(T)`