Kinetic Energy of a Gas ( i ) Average kinetic energy of translation per molecule of a gas is given by E = ( 3 / 2 ) kt where k = Boltzmann ’ s constant . ( ii ) Average kinetic energy of translation per mole of a gas is given by E = ( 3 / 2 ) Rt where R = universal gas constant .
( iii ) For a given gas kinetic energy E ∝ T ⇒ E1 / E2 = T1 / T2
( iv ) Root mean square ( rms ) velocity of the gas molecules is given by ( v ) For a given gas c ∝ √T ( vi ) For different gases c ∝1 / √M ( vii ) Boltzmann ’ s constant k = R / N where R is ideal gas constant and N = Avogadro number . Value of Boltzmann ’ s constant is 1.38 x 10 -28 J / K . ( viii ) The average speed of molecules of a gas is given by ( ix ) The most probable speed of molecules of a gas is given by