# Kinetic Theory of Gases

Kinetic theory of gases

D. Bernaulli (1738) forwarded this theory which was developed by Clausius, Maxwell, Boltzmann, Kelvin etc.

The following are the main postulates of kinetic theory of gases:

(i)    Every gas consists of very large number of minute (tiny) particles called molecules. The actual volume of these molecules is negligible as compared to the total volume of the gas.

(ii)    The molecules of a gas are not stationary but are always in a state of rapid random motion in all possible directions with widely differing velocities. They travel in straight lines, but on collision with another molecule or with the sides of the containing vessel, direction of motion is changed.

(iii)    The molecules are spherical and perfectly elastic and therefore exert no appreciable attraction on each other. Hence there is no loss of kinetic energy on collision or mutual friction.

(iv)   The pressure exerted by a gas is due to the bombardment of the moving molecules on the walls of the containing vessel.

(v)    The motion imparted to the molecules by gravity is negligible in comparison to the effect of the continued collisions between them.

(vi)   The kinetic energy of a perfect gas depends on the temperature and not on the nature of the gas.

The above mentioned postulates help us in obtaining the fundamental kinetic gas equation:

$PV = \dfrac{1}{3}mnu^2$

where P = pressure of a gas, volume of a gas, m = mass of a molecule, n =total number of molecules in the given mass of thegas and u mean square velocity of the molecules in $cm s^{-1}$ .

For 1 mole of a gas n =N (Avogadro number) hence the above equation may be written as:

$PV = RT = \dfrac{1}{3}m Nu^2 = \dfrac{1}{3}Mu^2$

(Since mN = M =molecular mass of the gas)

Or $u$= $\sqrt{\dfrac{3PV}{M}}$= $\sqrt{\dfrac{3RT}{M}}$= $\sqrt{3P}{d}$ (since; d = M/V)

$\text{Since, } PV = RT = \dfrac{1}{3} mnu^2 \\ \text{or} \hspace{20mm} \dfrac{1}{2}mnu^2 = \dfrac{3}{2}RT \\ \text{or} \hspace{20mm} K.E. = \dfrac{3}{2} RT$ (For 1 mole of an ideal gas)

(K.E. = kinetic energy of the molecules)

$K . E . = \dfrac{3}{2} \dfrac{R}{N} T$

$K . E . = \dfrac{3}{2} K T$

$k = \dfrac{R}{N}$

Where k = boltz mann constant

or K E. =5 RT (For 1 mole of an ideal gas)

(K E. Kinetic energy of the molecules)

where k = Boltz mann constant

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