Kinetic theory of gases

(1) The Kinetic theory was developed by the Bernoulli, Joule, Clausius, Maxwell and the Boltzmann etc and it represents dynamic particle or microscopic model for the different gases since it throws light on behavior of the particles (such as atoms and molecules) which constitute the gases and cannot be seen. Properties of the gases which we studied former are part of the macroscopic model.

         (2) Postulates

         (i)  Every gas comprises of a large number of the small particles called as molecules moving with the very high velocities in all the possible directions.

         (ii) The volume of an individual molecule is negligible as compared to total volume of the gas.

         (iii) The gaseous molecules are perfectly elastic so that there is no net loss of the kinetic energy due to their collisions.

         (iv) The effect of the gravity on the motion of molecules is negligible.

         (v) The gaseous molecules are considered as the point masses because they do not have potential energy. So attractive and repulsive forces between the gas molecules are negligible.

         (vi) The pressure of the gas is due to continuous bombardment on the walls of the containing vessel.

         (vii) At constant temperature average kinetic energy of all the gases is same.

         (viii) The average kinetic energy of the gas molecules is directly proportional to absolute temperature.

         (3) Kinetic gas equation : On the basis of the above stasted postulates, the following gas equation can be derived,

         here, P = pressure exerted by the gas

         V = volume of the gas

         m = average mass of each molecule

         n = number of molecules

         u = root mean square (RMS) velocity of the gas.

         (4) Calculation of kinetic energy

            We know that,

         K.E. of one molecule 

         K.E. of n molecules     

         n = 1, Then K.E. of 1 mole gas        

This equation shows that K.E. of translation of a gas depends only on the absolute temperature. This is usually known as the Maxwell generalization. Therefore the average kinetic energy   T.

         If T=0K (that is -273.15 degree C then, average Kinetic energy= 0. Thus, absolute zero (0K) is the temperature at which molecular motion ceases.

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