Kinetic Theory of Gases

Kinetic Theory of Gases: What is it?
It is a theoretical model which describes the molecular composition of gas with respect to the number of submicroscopic particles such as atoms and molecules. This theory also defines properties such as volume, temperature, pressure, thermal conductivity, viscosity and mass diffusivity. The elements of kinetic theory were developed between the years 1860-1880’s by Boltzmann, Clausius and Maxwell. This theory was developed for gas, solid and liquid, however, over here we will only discuss the Kinetic Theory of Gases.

 

Kinetic Theory of Gases Assumptions
The theory of gases assumes that the atoms or molecules of a gas have huge-inter particle distance and are constantly on the move undergoing perfectly elastic collisions. These assumptions lead it to the following conclusion:
 

What are particles?
Gas is a collection of a large number of atoms or molecules.
 

Point masses
Gas is made up of atoms or molecules which are very small particles, similar to a dot on a paper having small mass.
 

Negligible particle volume
Gas particles are far apart from each other and there is a lot of free space in the container. The volume of the particle in comparison to the volume of the container is negligible.
 

Zero interaction
The particles are independent of each other. They exert no force and do not have any attractive or repulsive interactions among them.
 

Constant motion
Due to lack of interaction and availability of free space, the particles in a gas are always in constant motion. Though in constant motion, these particles don’t have any fixed direction and move about randomly but in a straight line.
 

Gas volume
Gas occupies the total volume of the container, irrespective of it being big or small. Therefore, the volume of the container is also said to be the volume of the gases.
 

Mean free path
This is the average distance a particle travels to meet another particle.
 

Kinetic energy of the particle
The particles of gas are always in motion, hence their average kinetic energy is proportional to the temperature of the gas.
 

Energy is constant
As the particles of gas are in motion they collide with other particles or the container. These collisions are perfectly elastic in nature, hence they do not change the energy or momentum of the particle.
 

Pressure of gas
The collision of the particles on the container walls exerts a force on them. Pressure is calculated by force per unit area. The pressure of the gas is thereby proportional to the number of particles colliding in unit time per unit area on the wall of the container.

 

Postulates of Kinetic Theory of Gases

• Gas consist of large number of molecules which are perfectly elastic, identical and hard sphere
• Gas molecules do not move in a preferred direction, in fact their motion is completely random
• The molecules of gas travel in a straight line
• When collision between two gas molecules occur, the time interval is very small
• There is a perfectly elastic collision between gas molecules and walls of the container. Therefore, kinetic energy and momentum in such collision is conserved
• The motion of gas molecules is governed by Newton's laws of motion
• There is negligible effect of gravity on the motion of gas molecules

 

Understanding Behavior of Gases

Ideal gas behavior:
An ideal gas is defined as the one in which collisions between atoms or molecules are perfectly elastic and independent of each other with absence of attractive forces. It can be visualized as a collection of perfectly hard spheres that collide but do not interact with each other. In this case, internal energy is in the form of kinetic energy and any change in that is accompanied by a change in temperature.
An ideal gas is characterized by variables such as volume (V), absolute pressure (P) and absolute temperature (T).
 

Non-ideal gas behavior:
Ideal gas laws are followed by all gas molecules under conditions of low pressure and high temperatures. However, deviation in real gases from the ideal behavior is brought on due to wrong or incorrect assumptions in the postulates. These assumptions are as follows:
• Gas particles are small and often compared to a dot on a paper and said to have no volume. If this is the case, then it should be possible to compress gases to zero volume. But as we know, gases cannot be compressed to zero volume indicating that they have volume and cannot be neglected.
• Particles in a gas and are independent of each other. This assumption is incorrect as the particles interact depending on their nature and their interactions affect pressure of the gas.
• It is said that particle collisions in a gas are perfectly elastic. However, this is untrue as collisions are elastic and exchange of energy takes place. All particles do not have the same energy and distribution of energy also happens.
 

Maxwell and Boltzmann Distribution of Energy and Velocity
The Kinetic Theory of Gases predicts that the gas particles are always in motion and their kinetic energy is proportional to the temperature of the gas. The Maxwell and Boltzmann Distribution of Energy and Velocity defines the distribution of speeds for a gas at a certain temperature. It can be used to calculate the most probable speed, the average speed and the root-mean square speed.