The molecules of the air surrounding us do not travel with the same speed. Some molecules move fast, some move at moderate speed, some move slowly while some do not move at all.

The Maxwell distribution of velocities is generally shown in the form of a graph with number of molecules on the Y-axis and the speed of the molecule along the X-axis, as represented above.

The graph is not symmetrical about the peak. On the right hand side, it is slightly longer than the left side indicating that there are more molecules on the high speed right end of the graph. The graph continues to the right to extremely large speeds, but to the left the graph must ends at zero as the molecules cannot have a speed less than zero.

As the graph is not symmetrical, the average speed is not exactly the peak in the graph but slightly shifted towards the right hand side. The average speed of the gas is given by

u_avg = [1/N (u₁ + u₂ +…..+ u_N)]

The speed indicated by the peak value shows the most probable speed which is the speed of most of the molecules in the gas.

The root-mean-square speed is the square root of the mean of the squares of the velocities. Mathematically, it is given by

u_rms = [1/N (u₁² + u₂² +…..+ u_N²)]^1/2

We know that speed is a scalar quantity and velocity is a vector quantity. The average value of velocity of gas molecule can be zero as molecules can move right to left and left to right. Hence, we calculate root mean square velocity. The square of velocity is always positive.

The total area under the entire curve is equal to the total number of molecules in the gas.