Kinetic theory of gases – Assumptions

The kinetic theory of the gases is a simple, historically significant classical model of the thermodynamic behaviour of gases that established many fundamental thermodynamic concepts. A gas is described by the model as a large number of identical submicroscopic particles (atoms or molecules) that are all in constant, rapid, random motion. Their size is assumed to be much smaller than the average particle distance. Random elastic collisions occur between the particles and with the enclosing walls of the container. The basic version of the model describes the ideal gas and takes into account no other particle interactions. The kinetic theory of gases explains macroscopic properties of gases like volume, pressure, and temperature, as well as transport properties like viscosity, thermal conductivity, and mass diffusivity. The model also takes into account related phenomena like Brownian motion. Historically, the kinetic theory of gases was the first explicit application of statistical mechanics ideas. The behaviour of gases is studied by taking into account either the small scale action of individual molecules or the large scale action of the gas as a whole. The large-scale action of the gas can be easily studied and measured; however, a theoretical model is required to study the action of the gas molecules. The kinetic theory of gases is the name given to this theoretical model. Let us look at the kinetic theory of gases and the assumptions that go into it in this article.

Overview

Kinetic theory of gases is a theory that is based on a simplified molecular or particle description of a gas and can derive many gross properties of the gas from this. It is a theory derived from the fact that particles in a gas move freely and rapidly along straight lines but frequently collide, resulting in changes in velocity and direction. The impacts of these particles on the walls of a container are also interpreted as causing pressure. The greater the density of a gas, the more collisions between molecules and the surface there will be, and the greater the pressure exerted.

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 elapsed between collisions between particles and the container’s wall is negligible in comparison to the time 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.
• The transfer of kinetic energy between molecules is known as heat. These theories confine the properties of gases to a specific range of mathematical treatment.
• The distance between all of the molecules is greater than the size of the molecules. The molecules in a kinetic gas sample all follow the laws of motion.
• If a kinetic gas sample is left for a long enough period of time, it will eventually reach a steady state. As a result, the density and distribution of molecules are independent of position, distance, and time.

Thus, particle motion dynamics can be treated classically, and the equations of motion are time-reversible. As a simplifying assumption, the particles are usually 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. Many of the model’s predictions are the same whether or not particle collisions are included, so they are frequently ignored as a simplifying assumption in derivations. These assumptions are relaxed in more recent developments, which are based on the Boltzmann equation. These can accurately explain the features of dense gases because they incorporate the volume of the particles as well as contributions from intermolecular and intramolecular interactions, quantized molecular rotations, quantum rotational-vibrational symmetry effects, and electronic excitation.

Postulates of Kinetic Theory of Gases

The following are the postulates of gas kinetic theory:

• The space-volume-to-molecule ratio is insignificant.
• At normal temperature and pressure, there is no force of attraction between the molecules.
• When the temperature and pressure decrease, the force of attraction between the molecules increases.
• The molecules are separated by a large space, resulting in continuous motion.
• The free movement of molecules causes a perfectly elastic collision.
• Because of their random movement, the molecules have kinetic energy. The average kinetic energy of these molecules, however, varies with temperature.
• Molecules exert pressure on the container’s walls.

Components of the kinetic theory of gas

The three main components of the gas kinetic theory are as follows:

• There is no gain or loss of energy when molecules collide.
• The space occupied by gas molecules in a container is insignificant.
• These molecules always move in a straight line.

FAQ’s

What exactly is a gas kinetic theory?

Kinetic theory explains the behaviour of gases by assuming that the gas is made up of rapidly moving atoms or molecules. This is possible because in gas, interatomic forces between molecules are ignored.

What is the significance of gas kinetic theory?

The macroscopic properties of gases, such as volume, pressure, and temperature, are explained by the kinetic theory of gases.

Q. What are the three primary components of gas kinetic theory?

Ans: The three main components of gas kinetic theory are as follows:
1) There is no gain or loss of energy when molecules collide.
2) The amount of space occupied by gas molecules in a container is negligible.
3) These molecules always move in a straight line.

Q. What assumptions does the kinetic theory of gases make?

Ans: 1) All gases are composed of molecules that move in random directions all the time.
2) All collisions between molecules, as well as collisions between molecules and walls, are considered elastic.
3) All molecules in a given gas sample follow Newton’s laws of motion.