Basic concepts for molecular motion

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Basic concepts for molecular motion

• 2004/3/9

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Brownian motion

• 1828, Robert Brown, under microscope
• Tiny grains of pollen suspended in water
  underwent ceaseless random motion
• The same dancing motion occurred when particles
  of finely powdered coal, glass, rocks and various
  minerals suspended in a fluid

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Brownian motion

• 1905, Einstein, predicted
• The motion is the evidence that the fluid is made
  of atoms
• A few years later, Jean Baptiste Perrin
• Made quantitative measurement of the motion
• Random Walk in three dimensions
• Langevin equation

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Brownian motion

• Brownian motion is a basic performance for
  particles (atoms, molecules, and so on)
• Brownian motion is random, Langevin equation can
  describe the motion mathematically
• Brownian motion causes diffussion
• Brownian movement is not the movement of
  molecules ,it is only very clearly reveals the
  existence of chaotic molecular movement

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Velocity distribution function

• Velocity space
• Velocity distribution

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Speed distribution

Is the probability of the fact that any of
molecules of a gas contained in a unit of its
volume has a velocity that is within the interval
near the velocity
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The intermolecular forces

• Are of elctromagnetic origin
• All molecules contain changes
• When two molecules approach, the charges depart
  slightly from their usual positions and hence a
  force results
• Other forces, such as Debye, London forces
• Chemical bonds

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Microscopic models for gas

• Promise
• according to the experiment findings
• the problem we are discussing

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Lennard-Jones Potential

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Full pair potential
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Hard-sphere repulsion
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Microscopic model of ideal gas

• Compared to the mean distance ,the dimension of
  the molecules can be ignored
• The intermolecular forces in them are completely
  absent,the momentum is changed only when
  molecules collide with the walls of the vessel
• The collisions are completely elastic

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Microscopic model of ideal gas

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Pressure for ideal gas

• The pressure exerted by a gas on a wall equals to
  the pressure of a gas

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Pressure for ideal gas

• The mean collision number of molecules with the
  walls of vessel is

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Temperature and internal energy

• Since temperature is determined by the mean
  energy of molecules ,so it stand for the
  intensity of the chaotic motion of gas

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Van de Waals Equation

• The constant b is intend to account somewhat for
  the volume occupied by the gas molecules.
• The constant a is included to correct for the
  intermolecular forces between molecules.

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Collision between molecules

• The mean free path and the mean number of
  collision in a unit time are the main
  characteristic of the process of collisions of
  gas molecules .

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Cross section

• It is depended on the interaction of particle A
  and B.
• If we imagine the collision of molecules as that
  of rigid spheres then we can get the formula of
  cross section

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Free path, collision rate
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Free path distribution among molecules

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Thank You

• Have a good
• Time