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I'm doing a school project on cosmic rays (using data from the HiSPARC database), and we need to be able to calculate the average temperature of the atmosphere above specific cities on a specific date to input into the Ideal Gas Equation (PV=nRT). We are trying to find an estimate for the number of molecules between the detectors and space, which is where the proton emitted breaks down into the parts which are detected, so that we can create a mathematical model which can calculate an estimate for the number of cosmic rays detected by a detector in a day. I've looked around, but nowhere tells me a way to do it, including other questions on this site. We've decided to do one effect at a time, so there may be more questions like this in the future. Can anyone help me?

Good news - thanks to those that gave answers I have values for the number of molecules. This question is answered! (Watch me for others soon: possibly clouds and such)

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    $\begingroup$ Did you have specific height/altitude in mind? The trouble with the Earth's atmosphere is that is not uniform. There are 4 layers, each with their own temperature & density characteristics. In the troposphere, temperature decreases with altitude, whereas in the stratosphere it increases with altitude. $\endgroup$ – Fred Nov 3 '17 at 11:18
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    $\begingroup$ Indeed, as Fred said, this may be a complicated problem. Not only does T vary, but so do P. Plus, what type of average would you do (height averaged, mass weighted, pressure weighted, etc). Likewise, there are issues with what you call the top of the atmosphere. $\endgroup$ – JeopardyTempest Nov 3 '17 at 12:15
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    $\begingroup$ Wonder if just maybe a better starting point would be that atmospheric pressure is force/area. And the force is the weight of the molecules above. You'd still have trouble due to the fact gas compositions vary by height. So you couldn't just turn the mass determined into the number of molecules. And although a majority of mass in the atmosphere is in the troposphere, where it is quite homogeneous (EXCEPT FOR WATER VAPOR!), I'd think the stratified layers of lighter gases very high in the atmosphere may still contribute greatly to molecule count. Oye. $\endgroup$ – JeopardyTempest Nov 3 '17 at 12:21
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    $\begingroup$ Probably not helpful, but the term of art you should google for is "parcel of air" (no quotes). $\endgroup$ – user967 Nov 5 '17 at 12:18
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    $\begingroup$ Look up lapse rate. While it varies with circulation and watervapor, it gives a rough calculation for how temperature drops above sea level and that can be used for temperature above cities. en.wikipedia.org/wiki/Lapse_rate The lapse rate ends at the tropopause where the atmosphere basically settles, and begins to warm, lighter air stays on top, heavier stays on the bottom. That sounds like a fun project. lots of math. You can also calculate mass above by air pressure, they are closely related. 14.4 psi means a square inch column of air weights 14.4 lbs. $\endgroup$ – userLTK Nov 7 '17 at 6:54

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