The Diffusion of Air through Water in the Lapse of Years

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Issue 20, Previous Article Next Article. From the journal: Analyst. Wenming Wu a. The mesosphere contains only about 0. We will examine the factors controlling the vertical profile of atmospheric temperature in chapters 4 and 7. We focus here on explaining the vertical profile of pressure. Consider an elementary slab of atmosphere thickness dz, horizontal area A at altitude z:. Figure Vertical forces acting on an elementary slab of atmosphere. For the slab to be in equilibrium, its weight must balance the pressure-gradient force:.

Substituting 2. We then integrate 2. Equation 2. It is convenient to define a scale height H for the atmosphere:. The barometric law explains the observed exponential dependence of P on z in Figure ; from equation 2.

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The small fluctuations in slope in Figure are caused by variations of temperature with altitude which we neglected in our derivation. The vertical dependence of the air density can be similarly formulated. From 2. A similar equation applies to the air number density na. In calculating the scale height from 2. Dalton's law stipulates that each component of the air mixture must behave as if it were alone in the atmosphere.

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One might then expect different components to have different scale heights determined by their molecular weight. In particular, considering the difference in molecular weight between N2 and O2, one might expect the O2 mixing ratio to decrease with altitude. However, gravitational separation of the air mixture takes place by molecular diffusion, which is considerably slower than turbulent vertical mixing of air for altitudes below km problem 4. Turbulent mixing thus maintains a homogeneous lower atmosphere. Only above km does significant gravitational separation of gases begin to take place, with lighter gases being enriched at higher altitudes.

During the debate over the harmful effects of chlorofluorocarbons CFCs on stratospheric ozone, some not-so-reputable scientists claimed that CFCs could not possibly reach the stratosphere because of their high molecular weights and hence low scale heights.