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Kinetic Theory

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Kinetic Theory

- 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.

- 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

- The pressure on the wall comes from all the particles.
- The volume is V = AL.
- Find the value for N particles.

L

A

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

V

P

N

- The expression from a particle level relates the average kinetic energy.
- This almost matches the ideal gas law.

V

P

N

- For the particle-level theory to match the experimental law we equate them.
- This is kinetic theory.
- Temperature measures the average kinetic 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

- 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.

- 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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