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class10lecnotes - Class 10, Friday, January 29, 2010...

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Class 10, Friday, January 29, 2010 Reading: 17.1 (The Kinetic Theory of Gases) The Connection between the Macroscopic and the Microscopic World Brownian Motion In the past few weeks we focused mainly on the behavior of matter from a macroscopic standpoint. Sometimes, we illuminated what might be going on a small scale, and invoked a multitude of particles zipping around or vibrating in place in a crystalline lattice. We grew up with the knowledge of the existence of this microscopic world, and we accept it, even though few of us have actually seen it. Indeed, how do we know that that the atoms of a gas are in constant motion? In 1827, the Scottish botanist Robert Brown discovered while he was looking through a microscope at tiny pollen particles suspended in a liquid that these particles were jiggling around. He suspected and later proved that what he saw was not the random motion of some small organisms, but particles of dirt, pushed around by something in the water. f~.,,;WfL (He delivered the proof by analyzing a water bubble that had been trapped in a piece of quartz for millions of years, and thus must have been completely devoid of any living organisms. In this liq~d.h~ ~w the same jiggling of small dirt particles). This jiggling motion' clearly .wJi~Jthe existence of even smaller, and thus at Brown's time, not observable, particles, constituents of the liquids studied. Robert Brown Albert Einstein Indeed, many years later, it was understood that this phenomenon was a direct consequence of molecular motion. The suspended dirt particles move in a random fashion as a result of the underlying molecules of the fluid moving randomly about, colliding with the dirt particles and imparting them some of their own momentum. The effect of these collisions is less obvious for a larger mass of the suspended particles. Example 1. Calculating the particle speed: We assume particles 2 JAm in diameter and In: f.:.;~~.f with an average density of 2900 kglm 3 What is their speed at room temperature? Here we _I.~ ./o-Jf1L need to use a formula that we will discuss somewhat later. - . ~ !YI1 {/ t._ 1 k r __ ~ ht ~C- lAAL'/7 ctl'"//tdt. Utf'-U<LtJ ~ 2 - 2 /tv bJur'A 10. I
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~ ~:: I. ?Jlo -!1~ = ~ _ ".!. 3No- n -k. 2ff!JjC c= ~!WM/.s) ) zr ~ I I. 2 . lo-!¥ k.J . This is not a small speed, but because the particle constantly changes its direction of motion, it doesn't get too far in a given interval of time. If we decreased the particle's mass and also its size, the net effect of the collisions of the surrounding molecules on it would be more dramatic. If we could see the particle, it would still move around in a random fashion, but the change from one position to the next would be more clearly visible. The jiggle turned into what is called a random-walk. In a paper published in 1905, Albert Einstein answered the question about how far away a random-walking particle can get in a given interval of time. In the next section we want to assess this distance. Random Walk
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class10lecnotes - Class 10, Friday, January 29, 2010...

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