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2015-04-01T13:03:48+05:30

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This is the mean free path as per the Kinetic theory of gases.  In other contexts, the meaning of mean free path has different meanings and applications.

     Suppose we have a lot (N number ) of gas molecules in a given volume V.  Let the molecules all be of the same radius R,  density and nature.  Let them be randomly be moving around in all directions in an equally probable way.  Then the molecules travel, collide with other molecules, bounce back or deviate elastically, and again travel in other directions.  This is the Brownian motion.

     The free path of a particle or molecule is the length of the path (straight line) that it travels between two successive collisions that it encounters.

   The mean free path is the average length of the free paths of all particles in a given volume.

   l = mean free path = 1 / (√2 σ n)  according to Maxwell's distribution.
       n = number of target particles for colliding per unit volume = N / V
       N = number of molecules in a volume V
       σ = effective cross sectional area for collision
          = π (radius of colliding particle + radius of collided molecule)²
           = π d²
       d = diameter of molecule.
 
  p V = K_B N T ,
    as per Ideal Gas law.
         K_B = Boltzmann's constant, T = abs. temperature of the gas

      l = K_B T / (√2 π d² p )

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It is used in optics, acoustics, particle physics and nuclear physics.  Its applications include estimation of diameter of particles, the electrical resistivity of the materials for the movement of electrons.  The definition of mean free path is different for sound waves and for other applications.


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