Kinetic theory of gases & Assumptions of  Kinetic theory of gases

Learn about : Kinetic theory of gases & Assumptions of  Kinetic theory of gases ♦

A gas is a collection of large number of molecules, which are in rapid continuous motion (rapid). The gas molecules have a size of the order of 2 × 10–10 m. Ordinarily, the distance between gas molecules is of the order of 2 × 10–9 m i.e. about 10 times as large as their size. Therefore, the molecules of gas can be considered as to be moving freely with respect to each other. However, during motion when they come close to each other, they suffer a change in their velocities due to inter-molecular forces between them. Such changes may be understood as collisions at molecular level.

In 19th century scientists Claussius , Rudolph and James Clark Maxwell developed the kinetic theory of gases in order to explain the behaviour of gases . This theory explains a gas as a collection of tiny, hard spheres that interact with each other and with the surface of the gas’s container. These spheres represent molecules in the gas and behave according to the law of motion developed by Newton in the 17th century. The kinetic theory is widely accepted explanation of the theory of gas behaviour. It describes how interactions between molecules influence gas characteristics such as temperature and pressure. It also explains why gases follow Boyle’s law.

According to kinetic theory, the pressure of a gas is caused by collisions between gas molecules and the container walls. The temperature of a gas is directly related to the average speed of the gas molecules. In a gas at constant temperature, the speed of the molecules will remain constant. If a scientist reduces the volume of the container, the molecules will have less distance to travel before they hit a container wall more often, resulting in a higher pressure. If the volume is increased, the molecules will heat the container wall less often, hence reducing pressure.

Empirical laws like (Boyle’s law, Charles law, Gay-Lussac law) have been developed that correlate macroscapic variables. For gas, the macroscapic variables include pressure(P), Volume(V) and  Temperature T. But with the advert of the atomic theory of matter, the above mentioned empirical laws acquired a microscopic bases. The volume of a gas reflects simply the position distribution of its constituent molecules.

Thus volume V → Represents the available amount of space in which a molecule can move.

Pressure , P → It can be measured with gauges placed on the container walls, registers the change of momentum experienced by molecules as they collide with, and subsequently rebound from the walls.

Temperature T → is proportional to the average kinetic energy of the molecules. The reduction of   these macroscopic variables to such mechanical variables as position, velocity, momentum and kinetic energy      of molecules, which can be correlated through Newton’s laws of mechanics should yield all gas laws.

The Physics that relates the properties of gases to classical mechanics is called Kinetic theory of Gases.

It predicts many other properties of gases

–    Statistical distribution of molecular velocity

–    Transport properties like thermal conductivity, the coefficient of diffusion, viscosity

The theory is based on following assumptions as regards to motion of molecules and nature of gases.

  Assumptions :

(1)  All gases consists of molecules. The molecules of a gas are all alike and differ from those of other    gases. That is a gas will have same group of atoms.

(2)  The molecules of a gas are very small in size as compared to distance between then.

(3)  The molecules of a gas behave as perfect elastic spheres

(4)  The molecules are always in random motion and obey Newton’s law of motion. They have velocities    in all direction ranging from zero to infinity.

(5)  During their random motion, they collide against one another and the walls of the containing vessel .  The collisions of the molecules with one another and with the walls of vessel are perfectly elastic i.e. conserve momentum and (we assume) kinetic energy.

(6)  The collisions are almost instantaneous is time during which a collision takes place is negligible as compared to the time taken by the molecule to cover the free path.* [*Between two collisions, a molecule moves along a straight line and the distance covered between two successive collisions is called the free path.

(7)  No appreciable forces act on the molecules except during a collision. To the extent that this is true a molecule moves with uniform velocity between collisions. Because we have assumed the molecules  to be small, the average distance between the molecules is large compared to the size of a molecules. Hence, we assume that the range of molecular forces is comparable to the molecular size.