What is the typical speed of a gas molecule near the surface?
b.what is the scale height of the atmosphere?
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We can derive the scale height H by starting with the equation of hydrostatic equilibrium and using the ideal gas law to eliminate either pressure or density. Thus, although it is done here for pressure, scale height can be derived in terms of either pressure or density.
Note that the mass of a hydrogen atom (mH= 1.67 × 10-27) and Boltzmann's Constant (k = 1.38 × 10-23 J/K) are truly constants. The acceleration of gravity g and temperature T change slightly with elevation, but are treated as constant here. Note that μ is the average mass of an atmospheric particle (in units of a hydrogen atom mass). Thus, one normally does a weighted calculation for the masses of all constituents of the atmosphere.
We then integrate from the surface value of pressure to the elevation of interest, basically adding up the weight of the overlying atmosphere.
We now move pressure to one side of the equation, integrate, and solve an equation relating pressure and elevation.
Note that the mass of a hydrogen atom (mH= 1.67 × 10-27) and Boltzmann's Constant (k = 1.38 × 10-23 J/K) are truly constants. The acceleration of gravity g and temperature T change slightly with elevation, but are treated as constant here. Note that μ is the average mass of an atmospheric particle (in units of a hydrogen atom mass). Thus, one normally does a weighted calculation for the masses of all constituents of the atmosphere.
We then integrate from the surface value of pressure to the elevation of interest, basically adding up the weight of the overlying atmosphere.
We now move pressure to one side of the equation, integrate, and solve an equation relating pressure and elevation.
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