Kinetic Theory of Gases

Introduction 

The kinetic theory of gases is a simple, classical model of the thermodynamic behaviour of gases. It is historically significant as it has established many fundamental thermodynamic concepts. A gas is characterised as a huge number of identical submicroscopic particles (atoms or molecules) moving at a steady, quick, and random rate, as determined by the model. Between the particles and the container’s enclosing walls, random elastic collisions occur. The basic version of the model describes the ideal gas and takes into account no other particle interactions. It explains pressure, temperature, and volume, the macroscopic features and thermal conductivity, viscosity transport, and the transport properties like mass diffusivity. The model also takes into account related phenomena like Brownian motion. It also includes the Kinetic Theory of Gases Postulates.

Kinetic Theory Definition

This involves two physics theories based on the fact that a substance’s minute particles are in rapid motion:

• A theory that states that when heat is added to a substance, the temperature rises in proportion to an increase in either the average kinetic energy or the average potential energy of the particles of separation (as in fusion) of the particles or both, also known as the kinetic theory of heat.

• A theory in which gas particles move in straight lines with high average velocity, constantly collides with one another, changing their individual velocities and directions. The kinetic theory of gases states that pressure is created by colliding against the container’s walls.

What is the Kinetic Theory of Gases?

In the nineteenth century, the British scientist James Clerk Maxwell and the Austrian physicist Ludwig Boltzmann pioneered the theory, which became one of the most important concepts in modern science. The kinetic theory of gases connects macroscopic properties of gases like pressure and temperature to microscopic properties of gas molecules like speed and kinetic energy.

Kinetic Theory of Ideal Gases

The atoms in an ideal gas do not exert forces on each other but instead clash with the container’s walls. Based on experiments, ideal gas law relates the pressure, temperature, volume, and the number of moles of an ideal gas:

PV = nRT,

In which R is a constant also known as the universal gas constant.

Comments:

1. Make sure that all quantities are expressed in the same unit system!
2. The temperature, T, must be expressed in absolute degrees Kelvin.
3. n denotes the number of moles of the gas, which is defined as

n = mass of sample/Molecular mass of gas

The assumption in Kinetic Theory of Gases 

The following assumptions are made when applying kinetic theory to ideal gases:

• The gas is made up of very small particles. Because of their small size, the sum of the volume of the individual gas molecules is negligible in comparison to the volume of the gas container. This is equivalent to saying that the average distance between gas particles is large in comparison to their size and that the time delayed between particle impacts with the container’s wall is insignificant when compared to the duration between successive collisions

• Because the number of particles is so large, a statistical approach to the problem is well justified. This assumption is also known as the thermodynamic limit.

• The rapidly moving particles are constantly colliding with one another and with the container’s walls. Because all of these collisions are perfectly elastic, the molecules are perfect hard spheres.

• Except in collisions, interactions between molecules are negligible. They don’t apply any extra forces to one another.

Thus, particle motion dynamics can be treated classically, and the equations of motion are time-reversible.

The particles are typically assumed to have the same mass; however, the theory can be generalised to mass distribution, with each mass type contributing to the gas properties independently of one another, in accordance with Dalton’s Law of partial pressures. Particle collisions are typically neglected in derivations to simplify things because many of the model’s predictions are the same whether these collisions are included or not. These assumptions are relaxed in more recent developments, which are based on the Boltzmann equation. Because they include contributions from intermolecular and intramolecular interactions, quantized molecular rotations, and the volume of the particles, quantum rotational-vibrational symmetry effects, and electronic excitation, these may accurately explain the characteristics of dense gases.

 Kinetic Theory of Gases Postulates

The following are the characteristics of kinetic theory of gases postulates:

1. A gas’s molecules are small and remain far apart. The majority of a gas’s volume is empty space.

1. Gas molecules are constantly moving at random. There are just as many molecules moving in one direction as there are in the other.

1. Molecules can collide with the container’s walls and with one another as well. The pressure of the gas is determined by collisions with the walls.

1. When molecules collide, they lose no kinetic energy; thus, the collisions are said to be perfectly elastic. Unless there is some outside interference with the molecules, the total kinetic energy of all of them remains constant.

1. Except during the collision process, the molecules have no attractive or repulsive forces on one another. Between the collisions, they move in straight lines.

Conclusion

The kinetic theory of gases tries to explain a gas’s microscopic features in terms of its molecules’ mobility. A molecule is the smallest unit with the same chemical properties as the substance, and the gas is thought to be made up of a huge number of similar, discrete particles called molecules. The pressure is exerted by the gas’s continuous collision with any surface; the higher the density of a gas, the more frequent the number of collisions between molecules and the surface, and the greater the pressure exerted. Between the 1860s and the 1880s, Maxwell, Boltzmann, and Clausius created elements of kinetic theory. There are kinetic theories for gases, solids, and liquids. The kinetic theory of gases is vital for understanding how the diffusion mechanism captures particles.