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If we assume that the atmosphere is in thermal equilibrium and at a uniform temperature, then we expect the density of a given kind of molecule to decrease as we go up, due to the increase of the gravitational PE and the Boltzmann factor.
A. Sometimes we write the Boltzmann factor as  and sometimes we write it as  . In this case, our energy factor is going to be the gravitational PE as a function of height, h. Which should we use and why?
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 PhET simulation
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B. For convenience, we would like to write our Boltzmann factor as the following in order to see what the height scale is:
where h0 is a height scale that is a function of our parameters and constants, and h is the variable representing the height above the ground. Find an expression for h0. What does h0 mean physically?
C. Find h0 for oxygen.
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