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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 weve 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, well talk about gases. In particular, well 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 dont interact with eachother, then all the internal energy is is going to be kinetic energy. In a solid, weve 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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- Spring '08