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L25 - "Kinetic Theory of Gases MQ Chapter 27 Prof Gianluigi...

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“Kinetic Theory of Gases” MQ Chapter 27 Prof. GianluigiVeglia

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Let’s recall the definition of an ideal gas: The gas molecules which have mass m and diameter d are in constant motion The molecules are small compared to the distances they travel between collisions The molecules do not interact except when they collide and then the collisions are perfectly elastic.
Physical interpretation of gas pressure In this vessel, the velocity of a molecule of mass m has components: u 1x , u 1y, u 1z . The particle moves along the direction of the vector and collides with the surface of the box. Assuming an elastic collision: The time elapsed between the collision is (the molecule needs to travel a distance 2a) x x x x mu mu mu mu 1 1 1 1 2 ) ( ) ( = = The momentum is conserved x u a t 1 / 2 =

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Applying Newton’s law: Where F is the force that the molecule exerts on the wall. From the force it is possible to calculate the pressure: Where V=abc is the volume of the box. The total pressure is given by The average value of u 2 is F a mu u a mu t mu x x x x = = = 2 1 1 1 1 / 2 2 ) ( V mu abc mu bc F P x x 2 1 2 1 1 = = = = = = = = = N j jx N j x N j j u V m V mu P P 1 2 1 2 1 1 = = N j jx x u N u 1 2 2 1