Heat and Thermodynamics

Kinetic Theory of Gases

The properties of gases can be explained on the basis of the kinetic model of gases.

According to this model, a gas is a collection of a large number of molecules which are identical and are in a state of continuous rapid motion.

Claussius and Maxwell developed the kinetic theory of gases in order to explain gas laws in terms of the motion of the gas molecules. The theory is based on the following assumptions.

  1. The number of molecules in the gas is large and the average separation between them is large compared with their dimensions.
  2. The molecules obey Newton's law of motion, but as a whole they move randomly.
  3. The molecules interact only by short range forces during elastic collisions.
  4. All the collisions between molecules among themselves or between molecules and the walls are elastic.
  5. The gas under consideration is a pure substance, that is, all molecules are indentical.
  6. The duration of a collision is negligible compared to the time spent by the molecules between collisions.
  7. The molecules exert no force on each other or on the walls of the container except during collision.

On the basis of kinetic theory of gases, the pressure exerted by an ideal gas on the walls of a container is given by

P =

where is the density of the gas and is mean squre velocity of the molecules of the gas.

The root mean square velocity of the molecules of the gas. =

If there be N number of molecules, each having mass m, in a V volume of gas, then from (i)

P =

or, PV = = , PV = .

where kinetic energy =

Temperature of a gas, T = .

Temperature of gas is a direct measure of average translational molecular kinetic energy.

The square root is called the root-mean square (rms) of the molecules.

= =

Where M is the molar mass in kilogram per mole.

The average speed of molecules = =

The most probable speed, = = .

.

Maxwell, on purely statistical considerations, showed that the distribution of molecular speeds in a gas takes place according to a difinite law. This is a known as Maxiwell's law of distribution of molecular speeds.

Maxwell's law of speed distribution in a gas at temperature T is =

= , b =

Where N is the total number of molecules and n (v) stands for the number of molecules between speed + . The versus v plot is the Maxwell's speed distribution.


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