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class08lecnotes - Class 8 Monday Reading 17.1 18.1 18.2...

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Class 8, Monday, January 25, 2010 Reading: 17.1, 18.1., 18.2, 18.3 The Ideal Gas Approximation We talked about molecules in gases as being able to move freely to large distances in a given interval of time. The energy per particle for gases is large enough so that the molecules can overcome the attractive forces associated with their molecular bonds. By contrast, in liquids the energy per particle is too small to allow the particle to move a significant distance in a small given interval of time, but large enough to allow it to move a length of the order of its own diameter. Gas-molecules can change their initial neighbors and given enough time a molecule can get quite far. For solids, the energy per particle is too small in order for the particle to overcome the attractive molecular bond forces. The molecules vibrate and spin, but can't leave their potential well associated with these attractive forces (egg-carton analogy). In reality, molecules are not only subject to these attractive forces, but also to the repulsive electrostatic forces associated with the negative charge of the electron clouds that surround their nucleus. In a thought experiment we monitor the potential energy of a system of 2 atoms, one fixed (A), and the other (B) moved toward A from a very large distance. At first the potential energy of the system would be pretty much zero until the atoms get close enough to each other to feel their attractive molecular bond forces. At large distance the atoms don't know anything about each other's existence. Once brought closely enough, th~L~ome increasingly bound (the potential energy of the system decreases, becomes Ynegative). This goes on until a minimum critical distance is reached (just slightly larger than the size of an atom). At this point the repulsive electrostatic forces take over, and the potential energy U goes back up quickly. The atoms become less bound. For liquids and solids the atoms are about as close as this minimum distance (r min ). Forcing them closer together would cause them to repel each other. In gases, however, the constituent atoms and molecules are much more distant than this minimum critical distance . .... ~._ B u I I rol rMlan.. o r f!
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Over the course of the coming week of class, we will not be concerned about attractive or repulsive forces between molecules. We make the simple approximation that the molecules behave like hard spheres: they can approach each other to the touching point and then bounce off again. This idealized situation is a good approximation for gases but does not work for liquids or solids. This ideal gas approximation works well for gases at low densities (that is the volume of all particles, if crowded up, should be small compared to the volume of the container in which the gas rests). The gas temperature needs to be much larger than the condensation temperature for any given pressure.
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class08lecnotes - Class 8 Monday Reading 17.1 18.1 18.2...

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