Calculate the rms speed of nitrogen at STP (pressure `=1` atm and temperature `= 0^0 C`. The density of nitrgoen in these conditions is `1.25 kg m^(-3)`

Explanation

At STP, the pr essure is `1.0xx10^(5) N//m^(3)`. The rms speed is
`v_(rms)=sqrt((3P)/P)`
`=sqrt((3xx10^(5)N//M^(2))/(1.25//m^(3))`
`=490m//s`
transltional Kinetic Energy of a gas
The total transltional Kinetic energy of all the molesules of the gas is
` K=sum1/2mv^(2)=1/2mN(sumv^(2))/N=1/2mv_(rms)^(2)....... "(4)"`
The average Kinetic enegry of a molecule is
`K//N=1/2M/Nv_(rms)^(2)=1/2mv_(rms)^(2)`
From equation `(2)`
`pV=(2)/(3).(1)/(2)Mv_(rms)^(2)`
`pV=(2)/(3)K`
`K=(3)/(2)pV`