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# class09lecnotes - Class 9 Wednesday Reading 18.1,18.2...

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Class 9, Wednesday, January 27, 2010 Reading: 18.1,18.2 Midterm Review: Wed, Feb. 3, 7pm, Thimann 3 Before we return to the thoughts on work from the end of last class, let's look at two interesting applications of the ideal gas law. 1) The exponential atmosphere A._ fr.fo e- H The above formula was derived under the assumption that the temperature is constant with height, which is, of course, not true. Yet we can use this simple model to understand how the pressure of a column of air does not obey the same relationship with height as the pressure of a column of water. The formula shows that our atmospheric pressure decreases with altitude following an exponential law. The quantity H in the above formula is called scale-height Indeed, it has the dimensions of distance. What is its meaning? You can find out by investigating what happens to the pressure as you set h=H. At an altitude H, the pressure P has decreased by a factor of e=2.718 with respect to the atmospheric pressure at altitude zero (on the ground), . it. f=. _ fo . . e.-/ it-=}/ =-) f¢. Po e. - hi ==> (1= ~ e ~ ~ ~ fA'u CiAL kV-t~J". rn ~ NI(! r /h1- m :.: d.L/rF] /zj = /Jf~ T~ 2?tJk - Hz "/0 2 .1 c:~. f' /,J -t1'4J m:~tj ~ 1I11:.,ltuJL )I - If; II 1/1Iv l W u#t/YJ T ;j 6tt~ 7 M'J ~.~~ )- ? {JUff(. . Y'e:r/C4 M" Itt (ttLjU rYl d ;I;ttA J h~ ..

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2) Concerning our experiment with the reversed bottle of water into a container filled to the brim with water (end of Class 2 and beginning of Class 3). We calculated that the water column that could be balanced by the atmospheric pressure is about 10m. Since all bottles that we experimented with are less than 10m tall, we were wondering why the water in the bottle doesn't rise when we create a vacuum at the top, when the bottle was filled to the brim and we turned it upside down. In particular, it was surprising that when the bottle was only partially filled with water (in this case the air enclosed after setting it upside down was at atmospheric pressure), it didn't spill. In fact, it turns out that it does
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class09lecnotes - Class 9 Wednesday Reading 18.1,18.2...

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