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Assumptions of Kinetic Theory of Gases

Kinetic theory of gases relates the macroscopic properties of gases (such as pressure, temperature, etc.) to the microscopic properties of the gas molecules (such as speed, momentum, kinetic energy of molecule, etc.). It is based on following assumptions:
  • The molecules of a gas are identical, spherical, rigid, and perfectly elastic point masses.
  • Their size is negligible in comparison to intermolecular distance (10–9 m).
  • Molecules of a gas keep on moving randomly in all possible directions with all possible velocities.
  • The gas molecules keep on colliding among themselves as well as with the walls of containing vessel. These collisions are perfectly elastic (i.e., the total energy before collision = total energy after the collision).
  • The distance covered by the molecules between two successive collisions is known as free path and mean of all free paths is known as mean free path.
  • The time spent in a collision between two molecules is negligible in comparison to time between two successive collisions.
  • The number of collisions per unit volume in a gas remains constant.
  • No attractive or repulsive force acts between gas molecules.
  • Molecules constantly collide with the walls of container due to which their momentum changes. The change in momentum is transferred to the walls of the container. Consequently pressure is exerted by gas molecules on the walls of container.
  • The density of gas is constant at all points of the container.
Pressure of an ideal gas 57835.png


Important Points
  • 59695.png or 59691.png [as 59687.png]
    • If volume and temperature of a gas are constant, P ∝ mN, i.e., pressure ∝mass of gas), i.e., if mass of gas is increased, the number of molecules and hence, the number of collision per second increases, i.e., pressure will increase.
    • If mass and temperature of a gas are constant, P ∝ (1/V), i.e., if volume decreases, number of collisions per second will increase due to lesser effective distance between the walls, resulting in greater pressure.
    • If mass and volume of gas are constant, 59682.png, i.e., if temperature increases, the mean square speed of gas molecules will increase and as gas molecules are moving faster, they will collide with the walls more often with greater momentum resulting in greater pressure.
  • 59678.png59674.png
    [as M = mN = Total mass of the gas]
    ∴ 59670.png59664.png
  • Relation between pressure and kinetic energy,
    Kinetic energy 59660.png
    ∴ Kinetic energy per unit volume,
    58155.png  (1)
    and we know 58149.png  (2)
    From (i) and (ii), we get 58143.png
    i.e., the pressure exerted by an ideal gas is numerically equal to two-thirds of the mean kinetic energy of translation per unit volume of the gas.

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