LectureT2

LectureT2 - Chapter 2: Ideal Gases In this chapter we want...

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5/10/2004 H133 Spring 2004 1 Chapter 2: Ideal Gases In this chapter we want to begin to explore the relationship between temperature and thermal energy and some of the microscopic properties of an object. We will begin by developing a model for an ideal gas . ± We will define an ideal gas as any gas that behaves like our model. ² This definition does not guarantee that such a gas exists. ² However, it turns out that many gases, especially in the low density limit behave very much like the model we are about to construct, so it is a useful exercise. Ideal Gas: (Assumptions) ± ± ±
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5/10/2004 H133 Spring 2004 2 Ideal Gas ± ± ± Now let’s work with this model to understand what it predicts regarding the connection between temperature and internal energy. ± First, we assume for this model that the pressure that a gas exerts on its container must be from the molecules of the gas hitting the walls of the container and giving the wall a small impulse (momentum transfer) ± Let’s consider the following setup ± The piston can move without friction. However, we are going to apply an external force that is just large enough to keep the piston in place. L Area A m ext F ± Frictionless movement of Piston.
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5/10/2004 H133 Spring 2004 3 Ideal Gas Law Now consider a single gas molecule hitting the piston. ± What is the momentum transfer? ± The collision is elastic (ideal gas assumption) ² ² By conservation of momentum the piston must feel an impulse: Now the molecule can bounce off other walls but its |v x | will not change. So eventually the molecule will bounce off the opposite wall and head back towards the piston. The time between collisions with the piston will be: The average force that this particle exerts on the piston is Pressure is force per unit area: L mv v L v m F F x x x avg x avg 2 , 2 2 collisions between time collision per impulse = = = = V mv AL mv A F P x x avg 2 2 particle one = = =
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5/10/2004 H133 Spring 2004 4 Ideal Gas Law Now how do we extend this idea to the many molecules of gas that are flying around inside of the cylinder? ± Since the molecules do not significantly interact with one another we have to sum up the contributions from all the molecules.
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This note was uploaded on 06/03/2011 for the course H 133 taught by Professor Furnstahl during the Spring '11 term at Ohio State.

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LectureT2 - Chapter 2: Ideal Gases In this chapter we want...

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