At a constant temperature, a vessel of 1 litre capacity contains `10^(23)N_(2)` molecules. If the rms velocity of the molecules be `10^(3)m//s`, then determine the total kinetic energy of the molecules and the temperature of the gas.

Explanation

Average kinetic energy per molecule
`=(1)/(2)mc_(rms)^(2)=(1)/(2)xx(28)/(6.023xx10^(23))xx(10^(3))^(2)g*m^(2)*s^(-2)`
`=2.324xx10^(-17)g*m^(2)*s^(-2)=2.324xx10^(-20)J`
Average kinetic energy per molecule `=(3)/(2)kT`
or, `(3)/(2)xx(8.314)/(6.023xx10^(23))xxT=2.324xx10^(-20)J=2.324xx10^(3)J`