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

Table of Contents

Toggle

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, n₁, n₂, n₃ …etc., molecules possess velocities c₁, c₂, c₃…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, c₃…..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) :

• 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) :

• 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: