Kinetic Theory of Ideal Gases

German scientists R.Classius and J.C. Maxwell had propounded the kinetic theory of gases. According to this model, every gas is made up of very fine particles called molecules. All the molecules of a gas are similar in all properties. We know that $ 1 cm^{3}$ of water at $100^{\circ}C$ temperature and $1$ atmosphere pressure produces $1671 cm$ of water vapour. From this, it is known that the volume actually occupied by the molecules in $1671 cm^{3}$ of water vapour is only $1 cm^{3}$ and the remaining $1670 cm^{3}$ of volume is empty. In other words, we can say that in the gaseous state of matter, there is a lot of free space between the molecules. This fact is true for all gases. The molecules of gases are always moving randomly in all possible directions. During motion, these molecules collide with each other and with the walls of the vessel in which the gas is kept. After each collision, both the direction and speed of motion of these molecules keep changing.

All collisions between molecules and molecules or between molecules and the walls are elastic. This implies that total kinetic energy and momentum are conserved.

Assumptions of Kinetic Theory of Gases

There are the following assumptions of the kinetic theory of gases.

1. The molecules of a gas are very small, rigid, spherical and completely elastic. The volume of the molecules is the volume in which the gas is present, is negligible compared to the volume of the gas.

2. Although the molecules of a gas can move with every possible velocity in every direction, but the number of molecules per unit volume or molecular density remains the same.

3. There is no force of attraction or repulsion between the molecules, as a result of which they do not have potential energy, their entire energy is kinetic energy.

4. When the molecules of a gas come very close to each other, there is a repulsive force between them, due to which their speed and direction of motion change. This phenomenon is called a 'collision' between two molecules. Between two consecutive collisions, the molecules move in a straight line with a constant speed. The distance travelled by the molecule between two consecutive collisions is called the free path and its average is called the mean free path.

5. The mutual collision between the molecules and the collision between the molecule and the wall is perfectly elastic, that is, the kinetic energy of the molecules is conserved.

6 The time of collision between the molecules is negligible compared to the distance travelled freely by the molecule.

7. Since the amount of molecules is negligible and the velocity is high, therefore there is no effect of gravity on the motion of the molecules.

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Concept of Perfect Gas

Concept of Perfect (ideal) Gas:

An imaginary gas whose properties are similar to the properties of a real gas (a gas whose molecules occupy space and interact with each other) at infinitely low pressure. This imaginary gas is called 'perfect gas' or ideal gas'.

According to the definition, the following properties are imagined in a perfect gas :

(1) It strictly obeys Boyle's law, Charles' law, and the law of pressure under all conditions of temperature and pressure.

(2) Its pressure coefficient and volume coefficient are exactly equal to each other.

(2) Its molecules are infinitesimally small.

(3) There is no force of attraction between its molecules. Obviously, a perfect gas cannot be converted into a liquid or solid state, because a force of attraction is necessary between the molecules in the liquid or the solid state.

In practice, the gases that are difficult to liquefy, such as oxygen, nitrogen, hydrogen, and helium can be considered as perfect, although these are also not ideally perfect.

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