Boyle - previous index next Boyles Law and the Law of...

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previous index next Boyle’s Law and the Law of Atmospheres Michael Fowler, UVa 6/14/06 Introduction We’ve discussed the concept of pressure in the previous lecture, introduced units of pressure (Newtons per square meter, or Pascals, and the more familiar pounds per square inch) and noted that a fluid in a container exerts pressure on all the walls, vertical as well as horizontal—if a bit of wall is removed, the fluid will squirt out. Everyone knows that although water (like other liquids) is pretty much incompressible, air is compressible—you can squeeze a small balloon to a noticeably smaller volume with your hands, and you can push in a bicycle pump to some extent even if you block the end so no air escapes. . Boyle was the first person to make a quantitative measurement of how the volume of a fixed amount of air went down as the pressure increased. One might imagine doing the experiment with gas in a cylinder as in the diagram here, putting on different weights and measuring the volume of the gas. Once the piston is at rest, the pressure of the gas multiplied by the area of the piston would just balance the weight of the piston plus the added weight, so the pressure is easy to find. Moveable piston Gas But there is one tricky point here: if the gas is compressed fairly rapidly—such as by adding a substantial weight, so the piston goes down suddenly—the gas heats up. Then, as the heat escapes gradually through the walls of the cylinder, the gas gradually settles into an even smaller volume. Boyle’s idea was to find out how the volume of the gas varied with outside pressure if the temperature of the gas stayed the same . So, if he’d done his experiment with the cylinder pictured above, he would have had to wait quite a time between volume measurements to be sure the gas was back to room temperature. But Boyle didn’t use a piston and cylinder. He did the experiment in 1662. Possibly the gun barrels manufactured at the time would have worked, with a greasy piston (I’m not sure) but he found a very elegant alternative: he trapped the air using mercury in a closed glass tube, and varied the pressure as explained below (in his own words).
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2 He found a simple result : if the pressure was doubled, at constant temperature, the gas shrank to half its previous volume. If the pressure was tripled, it went to one-third the original volume, and so on. That is, for pressure P and volume V , at constant temperature T , PV = constant. This is Boyle’s Law . After reviewing Boyle’s ingenious experiment, we shall see how Boyle’s Law is the key to understanding a central feature of the earth’s atmosphere: just how the density and pressure of air decreases with altitude. Of course, the temperature of the atmosphere also varies with height and
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Boyle - previous index next Boyles Law and the Law of...

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