The Kinetic Theory of Gases

The earth is bathed in an atmosphere of gases that interact intimately with the Earth's biosphere.  The  biogeochemical cycles that replenish the Earth's supply of carbon, nitrogen and oxygen, gases that are necessary for life on earth, all rely on the interactions between activities on the surface of the earth and the envelope of gases the separates the earth's atmosphere from vacant space.  Then it is clear that a good understanding of atmospheric science should include a basic understanding of gas behavior.

The forces that attract gas molecules to one another are significantly weaker than similar forces between liquid and solid phase materials.  Gas molecules move around more or less independantly of one another traveling in straight lines until a collision occurs between molecules,container walls or small airborne particles. The Kinetic Molecular Theory very successfully describes the behavior of gases and allows detailed predicitions of gas characteristics under a full range of atmospheric conditions.  The kinetic-molecular theory is itself mathematical, But it can be summarized qualitatively. The theory is is based on three general principals:
 
  • Size of Gas Particles


  • The volume of an individual gas molecule is vanishingly small when compared with the space between molecules.  As a result, the model considers individual gas molecules to be points of mass and a sample of gas to be nearly empty space.

 
  • Motion of Gas Molecule


  • Gas molecules are in constant, random, straight-line motion until they collide with one another, airborne particles, or surface.  Between collisions the molecules do not influence each other.  When they do collide the collisions are elastic which means that the two particles in the collision exchange energy but that the total kinetic energy of the two molecules remains constant.

 
  • Particle Speed, Temperature and Energy


  • The molecules in a sample of gas have a range of speeds (u), with the most probable speed near the average speed for the whole sample of gas. As the temperature of a gas increases, so does the average particle speed. The increase in speeds occurs because the average kinetic energy of the molecules, that is the energy associated with the motion of the gas particles,  is proportional to the absolute temperature. This means that at a given temperature all gases have the same average kinetic energy.  The figure at right shows this information graphically for gas samples at two different temperatures. The x-axis shows the number of gas particles with a velocity (u). The average velocity at the higher temperature is greater but the number of particles at the highest average velocity is smaller.

With these basic ideas in mind it is a small step to understand and predict the relationship between pressure (P), volume (V), and the temperature of a gas (T).


Quick Quiz: Which of the following statements about gas molecules is incorrect?

Gas molecules are in constant motion.
Gas molecules can be diverted from a straight line path if a temperature increase occurs.
Gas molecules do not affect each other unless they collide.
When a collision occurs between gas molecules the total kinetic energy of the two molecules before the collison occurred is preserved.


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