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 k B is Boltzmann’s constant Note that

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, (Boyle)

Computer Simulation Allows changing N, W, v Replaces tedious mathematical analysis Explore all relations encoded in the Ideal Gas Law: PV = Nk B T 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 (constant P)

Another Example Increase N with P and T held fixed More particles means more collisions, piston rises Reduced collision rate restores equilibrium In detail: (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: (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)