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Kinetic Model of an Ideal Gas

The Molecular World. People observe physical phenomenon on a macroscopic (large) scale.Wind blowingBlue skies Rivers flowingObjects falling Temperature, Pressure, Heat transferMolecules/atoms are the building blocks of materials round us. The Microscopic World. Macroscopic phenomenon is dict

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Kinetic Model of an Ideal Gas

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    1. Kinetic Model of an Ideal Gas

    2. The Molecular World People observe physical phenomenon on a macroscopic (large) scale. Wind blowing Blue skies Rivers flowing Objects falling Temperature, Pressure, Heat transfer Molecules/atoms are the building blocks of materials round us

    3. The Microscopic World Macroscopic phenomenon is dictated by processes occurring on a molecular scale. Constructing a molecular model/theory of macroscopic phenomenon is of practical importance.

    4. Our goal: Construct a simple microscopic (molecular) model to understand the bulk properties of an ideal gas (pressure & temperature).

    5. Model Assumptions A container with volume V containing a very large number N of identical molecules, each with mass m. The molecules behave as point particles (their size is negligible compared to the distance between neighbouring molecules.

    6. The molecules are in constant motion and they obey Newtons laws of motion. Each molecule collides occasionally with the wall of the container Collisions are assumed to be perfectly elastic (no momentum loss).

    7. The containers walls are perfectly rigid and infinitely massive and do not move.

    9. Collisions produce force

    10. For N-particle Collisions

    11. For N-particle Collisions Since

    12. For N-particle Collisions

    13. The pressure of the Gas

    14. The pressure of the Gas

    15. The pressure of the Gas With a bit of mathematical magic

    16. Exercise Two gas cylinders are identical. One contains the monatomic gas argon (Ar), and the other contains an equal mass of the monatomic gas krypton (Kr). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio of the average kinetic energy of a krypton atom to average kinetic energy of an argon atom.

    17. Root Mean Speed

    18. Heat Capacity of an Ideal Gas Average kinetic energy of N monatomic particles is given by:

    19. Heat Capacity of an Ideal Gas Assuming no interaction between neighbouring molecules as well as the container, then all internal energy is in the form of translational kinetic energy.

    20. Heat Capacity of an Ideal Gas If heat is transfer to a system with a constant volume, then NO WORK IS DONE!!!. Hence from the 1st law of thermodynamics

    21. Heat Capacity of an Ideal Gas Thus

    22. Heat Capacity of an Ideal Gas For a system at constant pressure:

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