Question

What is the difference between the root-mean-squared velocity (????) and the average velocity (?̅) of gas particles?

Answer 1

Root - mean - squared velocity v_rms is the root of mean of all the squared velocites of the gas particles; i.e.,

v_rms = v_i², where, v_i is the velocity of i^th gas particle.

Derivation gives the expression for root - mean - squared velocity as :

v_rms = ( 3kT / m ),

where, k = Boltzmann's constant, T = Absolute temperature of the gas, and m = Molecular mass of the gas.

Average or mean velocity v_avg is the mean of all the velocites of the gas particles; i.e.,

v_avg = ( v_i ) / n where, v_i is the velocity of i^th gas particle, and, there are n particles in the gas.

Derivation gives the expression for average velocity as :

v_avg = ( 8kT / m ),

where, k = Boltzmann's constant, T = Absolute temperature of the gas, and m = Molecular mass of the gas.