Explain the speed of molecules of a gas and the average speed $(u_{av})$.

(N/A) Speed of molecules and energy: Molecules are the constituent particles of a substance in the gaseous state. These particles are far apart and occupy a large volume. They are in continuous motion in all directions.
These moving particles collide with each other and with the walls of the container.
During these collisions,their speeds and directions change. Consequently,not all particles in a container have the same speed; they possess different speeds that are continuously changing. However,at a constant temperature,the distribution of molecular speeds remains constant.
Average molecular speed $(u_{av})$: Suppose there are $n$ molecules of a gas with individual speeds $u_{1}, u_{2}, \dots, u_{n}$.
The average speed $(u_{av})$ is defined as the arithmetic mean of the speeds of all the molecules:
$u_{av} = \frac{u_{1} + u_{2} + \dots + u_{n}}{n}$