Kinetic Theory of an Ideal Gas

Can you imagine a collection of spheres that collide with each other but they do not interact which each other. Here the internal energy is the kinetic energy. In this article, we shall understand what kinetic theory of an ideal gas is.

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Basics of Kinetic Theory

It says that the molecules of gas are in random motion and are continuously colliding with each other and with the walls of the container. All the collisions involved are elastic in nature due to which the total kinetic energy and the total momentum both are conserved. No energy is lost or gained from collisions.

Ideal Gas Equation

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The ideal gas equation is as follows

PV = nRT

the ideal gas law relates the pressure, temperature, volume, and number of moles of ideal gas. Here R is a constant known as the universal gas constant.

Browse more Topics under Kinetic Theory

• Behaviour of Gases
• Specific Heat Capacity and Mean Free Path
• Law of Equipartition of Energy
• Behaviour of Gases

Assumptions

1. The gas consists of a large number of molecules, which are in random motion and obey Newton’s laws of motion.
2. The volume of the molecules is negligibly small compared to the volume occupied by the gas.
3. No forces act on the molecules except during elastic collisions of negligible duration.

At the ordinary temperature and pressure, the molecular size is very very small as compared to the intermolecular distance. In case of gas, the molecules are very far from each other. So when the molecules are far apart and the size of the molecules is very small when compared to the distance between them. Therefore the interactions between the molecules are negligible.

In case there is no interaction between the molecules than there will be no force acting on the molecule. This is because it is not interacting with anything.  Newton’s first law states that an object at rest will be at rest and an object will be in motion unless an external force acts upon it.

So in this case, if the molecule is not interacting with any other molecule then there is nothing that can stop it. But sometimes when these molecules come close they experience an intermolecular force. So this basically something we call as a collision.

Solved Question For You

Question: The number of collisions of molecules of an ideal gas with the walls of the container is increasing per unit time. Which of the following quantities must also be increasing?

I.pressure
II. temperature
III. the number of moles of gas.

1. I only
2. I and II only
3. II  only
4. II and III only

Solution: B. If there are more collisions between the molecules and the walls of the container, there must be more pressure against the wall. If there are more collisions than the molecules must have high average kinetic energy. Since kinetic energy is proportional to temperature, the temperature is also increasing.

Question: When the volume of a gas is decreased at constant temperature the pressure increases because of the molecules

1. strike unit area of the walls of the container more often
2. strike unit area of the walls of the container with higher speed
3. move with more kinetic energy
4. strike unit area of the walls of the container with less speed

Solution: A. The kinetic theory of the molecules depends on the temperature and since here the temperature remains constant, the pressure cannot increase due to the other options mentioned. So option A is correct as more pressure is generated here and hence pressure increases.