**Calculation of Root Mean Square Velocity, Average Velocity and Most Probable Velocity**

** On the basis of kinetic theory of gases**, there are

**three different types**of velocities :

**1. Average velocity (v) **** **:

• The **arithmetic mean** of the **different velocities of all the molecules present in a given gas** is called as **average velocity.**

**We can represent Average Velocity in following ways:**

• Suppose, in that gas, n_{1}, n_{2}, n_{3} …etc., molecules possess velocities c_{1}, c_{2}, c_{3}…etc, respectively, ** then by definition,** the

**average velocity, v, is given by**

•If, in that gas there are **n molecules** present having velocities** c _{1,} c_{2,} c_{3}…..c_{n}** then the average velocity is :

**Average velocity is also given by the expression:**

**where**,**R = gas constant,****m = Mass of one molecule****M = Molar mass of gas****k = Boltzmann’s constant**

**2. Most Probable Velocity (****𝛼****) **** **:

**2. Most Probable Velocity (**

• It is defined as the **velocity possessed by the ****maximum**** number of molecules of the gas.**

• **It is given by the expression:**

**3.Root-mean-square velocity (u) : **

**3.Root-mean-square velocity (u) :**

• It is defined as the **under root of the mean of the squares of all the velocities of the molecules present in the gas. **

** • Then by definition**,

**Root-mean-square velocity (u)**

**is given by:**

**Relation between Most Probable Velocity, Average Velocity and Root Mean Square Velocity :**

**Calculation of Root Mean Square Velocity, Average Velocity and Most Probable Velocity From Maxwell’s Distribution Of Velocities:**

**1. Root mean square velocity: **

**In an actual gas**the velocities of individual molecules**span over a wide range**, and the**collision in the gas continuously redistribute the velocities among the molecules.****Before a collision**, a molecule may be travelling rapidly,**but after collision**it may be**accelerated to a very high velocity**,**only to be slowed again by the next collision.**

**2. Average Velocity:**

**3. Most Probable Velocity:**