# kinetic theory of gases

## About kinetic theory of gases

All gaseous laws (e.g., Boyle’s law, Charles’ law etc.) are concise statements of experimental facts observed in the laboratory by the scientists. Conducting careful experiments is an important aspect of scientific method and it tells us how the particular system is behaving under different conditions. However, once the experimental facts are established, a scientist is curious to know why the system is behaving in that way. A theory is constructed to answer this question. A theory is a model (i.e., a mental picture) that enables us to better understand our observations. The theory that attempts to elucidate the behaviour of gases is known as kinetic molecular theory.

In order to derive the theoretical aspect of the various gas laws based on simple experimental facts, Maxwell proposed the following postulates under the heading of kinetic theory of gases.

### Postulates of kinetic theory of gases

A gas consists of a large number of very small spherical tiny particles, which may be identified as  molecules. The molecules of a given gas are completely identical in size, shape and mass.

The volume occupied by the molecules is negligible in comparison to the total volume occupied by the gas (i.e. volume of the container).

The molecules are in rapid motion which is completely random. During their motion, they collide with one other and with the sides of the vessel. The pressure of the gas is due to the collisions of molecules with the sides of the vessel.

The molecules are perfectly elastic, i.e. there occurs no loss of energy when they collide with one another and with the sides of the vessel.

The laws of classical mechanics, in particular Newton’s second law of motion, are applicable to the molecules in motion.

There is no force of attraction or repulsion amongst the molecules, i.e. they are moving independent of one another.

At any instant, a given molecule can have kinetic energy ranging from a small value to a very large value, but the average kinetic energy remains constant for a given temperature, i.e. the average kinetic energy is proportional to the absolute temperature of the gas.

### Velocity Distribution of Gas molecules

Speed of a gas molecule changes continuously due to the intermolecular collisions and their collisions with the wall of container. Thus, speed of an individual molecule is not constant. Also, the observable properties of gas such as volume, pressure and temperature are constant with time. It is expected to be applicable to the distribution of molecular speed and we consider a statistical average of the speed of whole of the collection of gas molecules to remain constant with time. That is the  fraction of the total molecules having speed between any definite ranges must be constant, even though the speeds of the individual molecules may be changing as a result of molecular collisions. Distribution of molecular speed over a possible range was first investigated by Maxwell using the theory of probability. Results were expressed as the Maxwell law for distribution of molecular speed as    