Question

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Boltzmann atmosphere Consider a very tall 103 m tube filled with N2 molecules, each of which has mass 4.65 x 1026 kg. Recall that the acceleration of gravity is 9.8 m/s2 We will be considering the ratio of pressure r between the top (103 m) and halfway up the tube (500 m); that is, pressure(hop) pressure(2middle) 1) If the temperature is 250 K, what is r? 0.876 0.936 01 0.987 0.993 Submit Your submissions: B Submitted: Monday, April 8 at 11:44 AM Feedback: Correct! 2) Suppose we increase the temperature in the tube. r will Increase Decrease Stay the same Submit

Answer 1

The N_2 molecules follow bolts man distribution . so the population of N_2 molecules at different energy levels at temperature T is given by A N_e = N E negative E/K T In this of is nothing but the potential energy at different height E = m g h Now pressure is force per unit area integral this case force is the gravitational force due to mass of N^2 molecule let
For the second part if you are increasing the temperature KT will increase, effectively decrease the exponential term. The exponential term is negative So r will increase with increasing the temperature