Kinetic Theory of Gases

Overview

• Assume atomic picture of gases– Simpler than solids/liquids, as interactions

can be neglected

• Predict behavior– E.g., relations between P and V, P and T…

• Test in lab experiments

Basic Picture

• Gas consists of noninteracting particles

• They move around randomly

• Temperature corresponds to (average) speed of particles– Hotter faster

• Pressure a manifestation of collisions with container walls

Basic Processes

• Thermal expansion

• Evaporation– A cooling process

• Dissolving solids in liquids

• Reaction rates

• …

More on Temperature

• Prediction of kinetic theory:

v is the average speed

T is the temperature (in Kelvins)

m is the mass of a gas particle

kB is Boltzmann’s constant

• Note that

Tkmv B2

3

2

1 2

2vT

More on Pressure

• Canonical example: container wih movable piston

• P is the average force per unit area due to collisions with walls– Average because it fluctuates

• Weight on piston balances this force, in equilibrium– W tells us P of gas

Weight W

Now change something…

• E.g. add weight to the piston (T = const)• Forces out of equilibrium; piston drops• Collision rate increases until forces again

balance• P has increased, V decreased• In fact,

VP 1 (Boyle)

Computer Simulation

• Allows changing N, W, v

• Replaces tedious mathematical analysis

• Explore all relations encoded in the Ideal Gas Law: PV = NkBT

• Most of these relations are qualitatively obvious, some even quantitatively so!

Another Example

• Increase T keeping P fixed– Note: doubling T means increasing v by

• Faster particles means harder collisions and more rapid

• Piston rises, reducing collision rate• Equilibrium is restored• Model gives

TV (constant P)

2

Another Example

• Increase N with P and T held fixed• More particles means more collisions, piston

rises• Reduced collision rate restores equilibrium• In detail:

NV (constant T, P)

A slightly more complicated one…

• Increase T with V and N held constant

• Do it in two steps:– Increase T with P unchanged– Increase W to return V to its original value

• Result: TP (constant V, N)

Verifying the Predictions

• These relations are simple predictions of atomic/kinetic theory

• If they are found to hold in experiments, we gain confidence that the atomic picture is correct!

• Several of them are easily checked in lab exercises

Sample Exercises

• Calculate v for gas at room temperature

• It may take a few seconds for a smell to reach you from across a room, e.g. from a perfume bottle. What does this suggest about the path taken by the perfume particles?

Reference

• R. P. Feynman, et al., The Feynman Lectures on Physics, v. I (Addison Wesley, 1970)