MolecularCollisions

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previous index next Molecular Collisions Michael Fowler 7/21/08 Difficulties Getting the Kinetic Theory Moving Oddly, the first published calculation of the average speed of a molecule in the kinetic theory of gases appeared in the Railway Magazine , of all places, in 1836. Why there? Well, the calculation was by John Herapath—he owned the magazine. He was definitely not part of the scientific establishment: a previous paper of his on the kinetic theory had been rejected by the Royal Society. But the calculation of molecular speed was in fact correct. Another outsider, John James Waterston, submitted an excellent paper on the kinetic theory to the Royal Society in 1846, to have it rejected as “nonsense”. This was evidently still the age of the caloric theory, at least in the Royal Society. In 1848, Joule (who had worked with Herapath, and was also something of an outsider) presented a paper at a meeting of British Association where he announced that of the speed of hydrogen molecules at 60F was about 1 mile per second, close to correct. Again, though, this did not excite wide interest… Finally, in 1857, a pillar of the scientific establishment—Clausius—wrote a paper on the kinetic theory, repeating once more the calculation of average molecular speed (around 460 meters per second for room temperature oxygen molecules). He mentioned the earlier work by Joule, and some more recent similar calculations by Krönig. Suddenly people sat up and took notice! If a highly respected German professor was willing to entertain the possibility that the air molecules in front of our faces were mostly traveling faster than the speed of sound, perhaps there was something to it… How Fast Are Smelly Molecules? But there were obvious objections to this vision of fast molecules zipping by. As a Dutch meteorologist, C. H. D. Buys-Ballot, wrote: [if the molecules are traveling so fast] how does it then happen that tobacco-smoke, in rooms, remains so long extended in immoveable layers?” (Nostalgia trip for smokers!) He also wondered why, if someone opens a bottle of something really smelly, like ammonia, you don’t smell it across the room in a split second, if the molecules are moving so fast. And, why do gases take ages to intermingle? These were very good questions, and forced Clausius to think about the theory a bit more deeply. Buys-Ballot had a point: at that speed, the smelly NH 3 ’s really would fill a whole room in moments. So what was stopping them? The speed of the molecules follows directly from measuring the pressure and density—you don’t need to know the size of molecules. If the kinetic theory is right at all, this speed has to be correct. Assuming, then, the speed is more or less correct, the molecules are evidently not going in straight lines for long. They must be bouncing
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2 off the other molecules. Still, the standard kinetic theory pressure calculation assumed each molecule to be bouncing from wall to wall inside the box, collisions with the other molecules had always been ignored, because the molecules were so tiny. Evidently, though, they weren’t.
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This note was uploaded on 12/07/2011 for the course PHYSICS 152 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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MolecularCollisions - previous index next Molecular...

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