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Mean free path

The development of a theory in physic is always based on certain simplifying assumptions about the system whose behaviour the theory intends to explain. The founders of kinetic theory, R. Clausius (1822-1888) of Germany and J.C. Maxwell (1831-1875) of Scotland conceived a model of a gas. The model, which is an idealization, is called a perfect or ideal gas. The kinetic theory is based on the following fundamental assumptions regarding the model of a gas.
  1. A gas consists of particles called molecules. We consider all molecules of a gas to be identical.
  2. The molecules are in random motion and obey Newton’s laws of motion. The molecules move about in all directions with various speeds. We assume the Newton’s laws of motion are applicable at the microscopic level.
  3. The total number of molecules is large. Any particular molecule will follow a zig-zag path due to collisions with other molecules or with the walls of the container. But, because there are so many particles, we assume that the resulting large number of collisions maintains an overall distribution of molecular velocities.
  4. The volume of the molecules is a negligibly small fraction of the volume occupied by the gas. Even though there are many molecules, they are extremely small and occupy a very small volume.
  5. No appreciable force acts on the molecules during collision. In other words, a molecule travels with a uniform velocity in a straight line between two collisions. The average distance through which a molecule moves freely between two collisions is called the mean free path.
  6. Collisions are elastic and of negligible duration. The law of conservation of momentum should certainly hold when a molecule collides with another molecule or with the walls of the container. We further assume that kinetic energy is also conserved. Because the collision time is negligible compared to the time spend by a molecule between collisions, the kinetic energy which is converted into potential energy during a collision is again (almost instantaneously) available as kinetic energy without any decrease. Collisions are said to be elastic if there is no dissipation of energy in a collision, i.e. the kinetic energy after collision is the same as that before it. These simplifying assumptions help avoid mathematical complication. They define an ideal gas. Strictly speaking, none of these assumption is really true. However, this model, though approximate, satisfactorily explains a large number of experimental facts about gases. We will now use this model to see how far this can explain the experimental facts.

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