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Published byAvis Davidson Modified over 9 years ago
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Kinetic Theory of Gases
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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
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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
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Basic Processes Thermal expansion Evaporation –A cooling process Dissolving solids in liquids Reaction rates …
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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
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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
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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)
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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!
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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)
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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)
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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)
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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
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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?
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Reference R. P. Feynman, et al., The Feynman Lectures on Physics, v. I (Addison Wesley, 1970)
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