Kinetic Theory of Gas

Molecular nature of matter and Behaviour of Gases

  • A gas consisting of large number of identical, tiny spherical, neutral and elastic particles called molecules.
  • In a gas molecules none in all possible directions with all possible speeds.
  • The pressure of gas is due to elastic collisions of the gas molecular with the walls of the container.
  • The time of contact of moving molecules with the walls of container is negligible as compared to the intervals between two successive collisions on the same walls of container.
  • Between two collisions a molecule moves in a straight path with a uniform velocity.
  • The collisions are perfectly elastic and there are no forces of attraction or repulsion between them.
  • For a gas molecules in container
    Impulse = change in momentum of the molecule

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1. Behaviour of Gases: Gases at low pressure and high temperature follow a relation,
pV = kT

2. The perfect gas equation is given by pV = nRT
where, n is number of moles and R = NA kB is universal constant and T is absolute temperature in kelvin.

3. In terms of density, perfect gas equation is p = \frac{\rho RT}{M_{0}}

4. Boyle's Law: It states that for a given mass of a gas at constant temperature, the volume of that mass of gas is inversely proportional to its pressure.
i.e., V \propto \frac{1}{p}
⇒ p1V1 = p2V2 = p3V3 ..... = constant

5. Charles' Law: It states that for a given mass of an ideal gas at constant pressure, volume (V) of a gas is directly proportional to its absolute temperature T.
i.e, V ∝ T
\tt \Rightarrow \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} = \frac{V_{3}}{T_{3}}..... = constant

6. Dalton's Law of Partial pressure: It states that the total pressure of a mixture of non-interacting ideal gases is the sum of partial pressures exerted by individual gases in the mixture.
i.e., p = p1 + p2 + p3 + ......