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Kinetic Theory Of Gases



10. Mean free Path


  • On the basis of kinetic theory of gases, it is assumed that the molecules of a gas are continously collilding against each other.
  • Molecules move in straight line with constant speeds between two successive collisions.
  • Thus path of a single molecule is a series of zig-zag paths of different lengths as shown in fig -.

    Mean free Path
  • These paths of different lengths are called free paths of the molecule

  • Mean Free Path is the averege distance traversed by molecule between two successive collisions.
  • If s is the Total path travelled in Ncoll coilisions, then mean free path
         λ= s/Ncoll
    Expression for mean free path :
  • Consider a gas containing n molecules per unit volume.
  • We assume that only one molecule which is under consideration is in motion while all others are at rest.
  • If σ is the diameter of each molecule then the moving molecule will collide with all these molecules where centers lie within a distance from its centre as shown in fig

    <Mean free Path -2

  • If v is the velocity of the moving molecule then in one second it will collide with all moleculeswith in a distance σ between the centres.
  • In one second it sweeps a volume πσ2v where any other molecule will collide with it.
  • If n is the total number of molecules per unit volume, then nπσ2v is number of collisions a molecule suffers in one second.
  • If v is the distance traversed by molecule in one second then mean free path is given by
         λ = total distance traversed in one second /no. of collision suffered by the molecules
          =v/πσ2vn
          =1/πσ2n

  • This expression was derived with the assumption that all the molecules are at rest except the one which is colliding with the others.
  • However this assumption does not represent actual state of affiar.
  • More exact statement can be derived considering that all molecules are moving with all possible velocities in all possible directions.
  • More exact relation found using distribution law of molecular speeds is
         λ=1/(√2)πσ2n
    its derivation is beyond our scope.





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