6 Thermo 3 - Kinetic theory of the ideal gas Kinetic energy...

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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.
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L reaction F Collisions of the gas molecules with a wall. . As a result of a collision the momentum changes by x x mv p p 2 2 = = Δ Force due to one molecule as a function of time
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Collisions of the gas molecules with a wall (cont.) Newton’s second law for an instantaneous force: dt dp dt dv m ma F x x x x = = = Now Δ t is a long time interval – the time between two consecutive collisions with the wall. For the average force on the wall it becomes: t mv t p a m F x x x x Δ = Δ Δ = = 2 reaction F change of momentum in a collision time between collisions Δ t
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Now Δ t is – the time between two consecutive collisions with the wall. t mv a m F x x x Δ = = 2 L x v L t / 2 = Δ L mv v L mv t mv F x x x x x 2 / 2 2 2 = = Δ = Δ t
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Kinetic theory of the ideal gas. L v mN F x 2 = L v v v m F Nx x x ) ... ( 2 2 2 2 1 + + + = N v v v v Nx x x x ) ... ( 2 2 2 2 1 2 + + + = Let’s try to account for all molecules of the gas:
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Kinetic theory of the ideal gas. L v Nm F x 2 = Pressure on the wall with surface area A : V v m N LA v m N A F P x x 2 2 = = = Velocity of a molecule: ) , , ( z y x v v v v r 2 2 2 2 z y x v v v v + + = The average velocity – average of a sum is equal to the sum of averagesE 2 2 2 2 z y x v v v v + + = All the directions of motion (x, y, z)
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6 Thermo 3 - Kinetic theory of the ideal gas Kinetic energy...

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