# Kinetic Molecular Theory of Gases

A Model of Gases as Moving Particles

The kinetic theory of gases is a scientific model that explains the physical behavior of a gas as the motion of the molecular particles that compose the gas. In this model, the submicroscopic particles (atoms or molecules) that make up the gas are continually moving around in random motion, constantly colliding not only with each other but also with the sides of any container that the gas is within. It is this motion that results in physical properties of the gas such as heat and pressure.

The kinetic theory of gases is also called just the kinetic theory, or the kinetic model, or the kinetic-molecular model. It can also in many ways be applied to fluids as well as gas. (The example of Brownian motion, discussed below, applies the kinetic theory to fluids.)

## History of the Kinetic Theory

The Greek philosopher Lucretius was a proponent of an early form of atomism, though this was largely discarded for several centuries in favor of a physical model of gases built upon the non-atomic work of Aristotle. Without a theory of matter as tiny particles, the kinetic theory did not get developed within this Aristotlean framework.

The work of Daniel Bernoulli presented the kinetic theory to a European audience, with his 1738 publication of Hydrodynamica. At the time, even principles like the conservation of energy had not been established, and so a lot of his approaches were not widely adopted. Over the next century, the kinetic theory became more widely adopted among scientists, as part of a growing trend toward scientists adopting the modern view of matter as composed of atoms.

One of the lynchpins in experimentally confirming the kinetic theory, and atomism is general, was related to Brownian motion. This is the motion of a tiny particle suspended in a liquid, which under a microscope appears to randomly jerk about. In an acclaimed 1905 paper, Albert Einstein explained Brownian motion in terms of random collisions with the particles that composed the liquid. This paper was the result of Einstein's doctoral thesis work, where he created a diffusion formula by applying statistical methods to the problem. A similar result was independently performed by the Polish physicist Marian Smoluchowski, who published his work in 1906. Together, these applications of kinetic theory went a long way to support the idea that liquids and gases (and, likely, also solids) are composed of tiny particles.

## Assumptions of the Kinetic Molecular Theory

The kinetic theory involves a number of assumptions that focus on being able to talk about an ideal gas.

• Molecules are treated as point particles. Specifically, one implication of this is that their size is extremely small in comparison to the average distance between particles.
• The number of molecules (N) is very large, to the extent that tracking individual particle behaviors is not possible. Instead, statistical methods are applied to analyze the behavior of the system as a whole.
• Each molecule is treated as identical to any other molecule. They are interchangeable in terms of their various properties. This again helps support the idea that individual particles don't need to be kept track of, and that the statistical methods of the theory are sufficient to arrive at conclusions and predictions.
• Molecules are in constant, random motion. They obey Newton's laws of motion.
• Collisions between the particles, and between the particles and walls of a container for the gas, are perfectly elastic collisions.
• Walls of containers of gases are treated as perfectly rigid, do not move, and are infinitely massive (in comparison to the particles).

The result of these assumptions is that you have a gas within a container that moves around randomly within the container. When particles of the gas collide with the side of the container, they bounce off the side of the container in a perfectly elastic collision, which means that if they strike at a 30-degree angle, they'll bounce off at a 30-degree angle. The component of their velocity perpendicular to the side of the container changes direction but retains the same magnitude.

## The Ideal Gas Law

The kinetic theory of gases is significant, in that the set of assumptions above lead us to derive the ideal gas law, or ideal gas equation, that relates the pressure (p), volume (V), and temperature (T), in terms of the Boltzmann constant (k) and the number of molecules (N). The resulting ideal gas equation is:

pV = NkT
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