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Kinetic Theory. Microscopic Analysis. The behavior of a gas should be described by the molecules. The gas consists of a large number of identical particles of mass m . The particles have negligible size and no internal structure.

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Presentation Transcript
microscopic analysis
Microscopic Analysis
  • The behavior of a gas should be described by the molecules.
  • The gas consists of a large number of identical particles of mass m.
  • The particles have negligible size and no internal structure.
  • The particles are moving in random dirctions with speeds independent of direction
  • Collisions between particles and with the walls are perfectly elastic.
collision force
Collision Force
  • Follow a collision with a wall perpendicular to x.
  • Particle has mass m and a velocity vx.
    • Strike the wall: Dt = 2L/vx.
    • Impulse: Dp = 2mvx.
  • The force from one particle:

L

Fx

v

m

pressure force
Pressure Force
  • The pressure on the wall comes from all the particles.
  • The volume is V = AL.
  • Find the value for N particles.

L

A

three dimensions
Three Dimensions
  • The pressure come from all three dimensions, and is equal in all three.
  • Relate the pressure to the average speed.

V

P

N

theory match
Theory Match
  • The expression from a particle level relates the average kinetic energy.
  • This almost matches the ideal gas law.

V

P

N

temperature as energy
Temperature as Energy
  • For the particle-level theory to match the experimental law we equate them.
  • This is kinetic theory.
  • Temperature measures the average kinetic energy.
average energy
What is the average energy of an air molecule at room temperature (293 K)?

What is average speed for a nitrogen molecule (28 g/mol)?

Energy directly relates to temperature.

(3/2)kT = 6.07 x 10-21 J.

To get the speed requires the mass.

m = (0.028 kg/mol) / (6.022 x 1023 /mol) = 4.65x10-26 kg

Average Energy
distribution of speeds
Distribution of Speeds
  • Kinetic theory used the average speed.
  • Actual atoms fall into a range of speeds.
  • The Maxwell-Boltzmann distribution describes the probability of a molecule having a particular speed.
real gases
Real Gases
  • The assumptions for kinetic theory are approximately true.
    • Non-zero molecular size
    • Non-zero force between molucules
  • For the Van der Waals force in air, the effect is about 1% difference from an ideal gas.

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