KINETIC THEORY OF GASES
Ludwig Boltzmann --- Father of Kinetic Theory
WORK = Area Under PV Curve
 

ANIMATIONS of the Kinetic Theory of Gases:

1. The Ideal Gas Model
2. Brownian Motion
3. Kinetic Theory Simulation
4. Motion of Gas Molecules in a Cylinder
 
  
    SELF TEST for Gas Properties
Kinetic Molecular Theory Premises
  1. Gas particles are in constant, random motion.
  2. They collide with each other and with the walls of the container.
  3. On the average, the collisions that occur are elastic.
  4. Except for collisions, the gas particles do not interact with each other.
  5. The pressure that a gas exerts is caused by the collisions of its molecules with the walls of the container.
  6. The force applied on the walls of the container by the gas particles is equal but opposite to the force applied on the gas particles by the wall.
The kinetic energy of the gas molecules is directly proportional to the temperature of the gas!

 

Special Processes of an Ideal Gas
 
ISOBARIC
Pressure is constant
ISOCHORIC or ISOVOLUMETRIC
Volume is constant
ISOTHERMAL
Temperature is constant
Visualize the Properties of the IDEAL GAS LAW
How Does This All Connect?
  1. The average force exerted on the kinetic gas molecules by the wall is given by Average force x (time between succesive collisions)= (Final momentum - Initial momentum)
  2. The time for a gas molecule to travel from one end of the box of length L to hit the wall =(L/v). That means that F x (L/v) =[+mv - (-mv)] or Fx L = 2mv2.
  3. Since Newton's Third Law states that the force applied by the wall to the molecules is equal but opposite to the force applied by the molecules to the wall then the average Force applied on the one wall shown above by ONE molecule = + 2mv2/L.
  4. For N molecules in the 6 sided box, an average of N/6 are coming toward the box to hit.
  5. So Total Force x L = [2mv2] x N/6 =N mv2 /(3) .
  6. But Force x L = P x A x L since P= F/A
  7. That means that P x A X L = P x V (Volume equals base area x height)
  8. So P x V= N mv2 /(3)
  9. And Since PV = n RT (from the Universal Gas Law then nRT = N mv2 /(3)
  10. Recall that N = n x NA (Avagadro's Number)
  11. Going to step 9 and substituting, n RT = n x NA mv2/(3)
  12. Using algebra, mv2=3 [R/NA ] T
  13. If we multiply both sides by 1/2 then [mv2]/2=3/2 [R/NA ] T
  14. This becomes KE average = 3/2 kT where k = [R/NA ]
  15. k = 1.38 x 10-23 J/K