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Collisions of the gas molecules with a wall..

Collisions of the gas molecules with a wall. L. As a result of a collision the momentum changes by. Force due to one molecule as a function of time. Collisions of the gas molecules with a wall (cont.). Newton’s second law for an instantaneous force:. change of momentum in a collision.

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Collisions of the gas molecules with a wall..

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  1. Collisions of the gas molecules with a wall.. L As a result of a collision the momentum changes by Force due to one molecule as a function of time

  2. Collisions of the gas molecules with a wall (cont.) Newton’s second law for an instantaneous force: change of momentum in a collision For the average force on the wall it becomes: time between collisions Now Dt is a long time interval – the time between two consecutive collisions with the wall. Dt

  3. L Dt Now Dtis – the time between two consecutive collisions with the wall.

  4. Kinetic theory of the ideal gas. one molecule Collective effect of N molecules moving with different velocities:

  5. Kinetic theory of the ideal gas. L Pressure on the wall with surface area A: Velocity of a molecule: The average velocity – average of a sum is equal to the sum of averages… All the directions of motion (x, y, z) are equally probable!

  6. L Pressure on the wall with surface area A: The average kinetic energy of a molecule The ideal gas law (experimental fact!) Therefore:

  7. Physical meaning of the absolute temperature a measure of the average kinetic energy of a molecule. The average speed of a molecule – thermal speed:

  8. Number of molecules having speeds in an interval of width Dv around v. It is proportional to Dv, the total number of molecules, N, and to the height of the distribution curve.

  9. Kinetic theory of the ideal gas Kinetic energy is the only form of molecular energy that is important and it is preserved in the collision events.

  10. Collisions do not change the situation as long they are elastic… Colliding particles exchange momenta and velocities. Collision with a wall – the velocity components along the wall stay the same.

  11. The ideal gas law What happens if we reduce T to zero. Is volume of the gas, V, going to become zero? Not necessarily, since it maybe the pressure, P, which becomes zero at T= 0. Wait! We can set P 0. Then what? By the ideal gas law we would have V = 0, which cannot be true. We can correct for it by a term equal to the total volume of the gas molecules, when totally compressed (condensed) nb. Now at T = 0 and P 0 we have V = nb.

  12. When and why does the ideal gas law stop working? • The molecules occupy a significant fraction of the volume. • Collisions are more frequent. • There is less volume available for molecular motion. • 2. There are long range attractive – Van der Waals forces between the molecules, which become more important as the density grows. Real gas – Van der Waals equation. Introduces corrections to the ideal gas law to take into account some of these effects. Attractive force between couples of molecules. Goes as (n/V)2square of the concentration. Less volume available for motion, because of nmoles of the gas.

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