# Kinetic Theory - PowerPoint PPT Presentation

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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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Kinetic Theory

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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.

• The particles are moving in random dirctions with speeds independent of direction

• Collisions between particles and with the walls are perfectly elastic.

### 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

• 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

• 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

• The expression from a particle level relates the average kinetic energy.

• This almost matches the ideal gas law.

V

P

N

### 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.

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

### 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

• 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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