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lecture26 - Lecture 26 Pressure and Introduction to an...

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Unformatted text preview: Lecture 26: Pressure and Introduction to an Ideal Gas 1 Review from Last Time • Finish heat capacity of lead and aluminum problem 2 Gases So far we’ve just talked about how to treat a solid object that is large. This is a system containing many particles that must be treated statistically. In this case, the interactions between neighboring atoms are modeled as tiny springs. But, we can also have a large system where the atoms are not interacting - where there are no springs. This means the internal energy only consists of kinetic energy (no potential energy). In a very low density gas, we can assume neighboring atoms do not interact. This is called and “ideal gas”. • The Ideal Gas - introduction – For the last two lectures, we’ll talk about gases. In particular, we’ll talk about an “ideal gas”. – A gas has much less structure than a solid. The molecules are essentially free to move around as they wish, and fill up any volume that is given to them. – An “ideal” gas is a gas in which the individual molecules do not interact with eachother. This is, of course, a simplified model, but it works rather well for low density gases. – If the particles don’t interact with eachother, then all the internal energy is is going to be kinetic energy. In a solid, we’ve got potential energy in the interatomic “springs” as well as kinetic energy. – But, if the density is low enough in a gas, there are no internal interactions between particles, and therefore the internal potential energy is zero. So, all the internal energy is kinetic. – Recall that the average kinetic energy is related to the temperature (temperature is essentially a measure of the average kinetic energy). – The Equipartition Theorem says that this energy is divided equally among the different degrees of freedom of the gas. * Degrees of freedom refers to the number of different ways a system can move. * Bridge analogy * A single atom can move in three directions (x,y,z), so it has three degrees of freedom.This is its center of mass motion. * A molecule can also rotate or vibrate. These would correspond to additional degrees of freedom. * The energy in each degree of freedom is 1 2 kT for each particle....
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lecture26 - Lecture 26 Pressure and Introduction to an...

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