(1) Mean (or average) speed of molecules of a gas : The mean speed of gas molecules is defined as the arithmetic mean of the speeds of all molecules of the gas at a given temperature.
(2) Mean square speed of molecules of a gas : The mean square speed of gas molecules is defined as the arithmetic mean of the squares of the speeds of all molecules of the gas at a given temperature.
(3) Root-mean-square speed of molecules of a gas : The root-mean-square (rms) speed of gas molecules is defined as the square root of the arithmetic mean of the squares of the speeds of all molecules of the gas at a given temperature.
If there are N molecules in an enclosed pure gas and v1 , v2 , v3 , …, vN are the speeds of different molecules,
1. the mean speed, \(\bar v\) = \(\frac{v_1+v_2+,,,+v_N}N\)
2. the mean square speed,
\(\overline {v^2}\) = \(\frac{v_1^2+v_2^2+,,,+v_N^2}N\)
3. the rms speed, vrms = \(\sqrt{\overline{v^2}}\)
[Note : The mean square velocity is numerically equal to the mean square speed. Similarly, the rms velocity is numerically equal to the rms speed. But in random motion, the mean velocity would be statistically zero, but the mean speed cannot be zero. ]
