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Basic concepts for molecular motion

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Basic concepts for molecular motion 2004/3/9 Brownian motion 1828, Robert Brown, under microscope Tiny grains of pollen suspended in water underwent ceaseless random ... – PowerPoint PPT presentation

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Title: Basic concepts for molecular motion


1
Basic concepts for molecular motion
  • 2004/3/9

2
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

3
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

4
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

5
Velocity distribution function
  • Velocity space
  • Velocity distribution

6
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
7
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

8
Microscopic models for gas
  • Promise
  • according to the experiment findings
  • the problem we are discussing

9
Lennard-Jones Potential

10
Full pair potential
11
Hard-sphere repulsion
12
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

13
Microscopic model of ideal gas

14
Pressure for ideal gas
  • The pressure exerted by a gas on a wall equals to
    the pressure of a gas

15
Pressure for ideal gas
  • The mean collision number of molecules with the
    walls of vessel is

16
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

17
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.

18
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 .

19
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

20
Free path, collision rate
21
Free path distribution among molecules

22
Thank You
  • Have a good
  • Time
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