Consider an element of air in the standard atmosphere at a standard altitude of 1000 m. Assume that you somehow raise this element of air isentropically to a standard altitude of 2000 m, where the element now takes on the standard pressure at 2000 m. Calculate the density of this isentropically raised element of air and compare it with the density of its neighboring elements of air that all have a density equal to the standard density at 2000 m. What does this say about the stability of the atmosphere in this case?
NOTE: The properties of the standard atmosphere are based on statics, i.e., an element of fluid that is stationary, where the pressure change is dictated by the hydrostatic equation, Eq. (3.2). An isentropic process is not relevant to the establishment of the standard atmosphere. Indeed, a purpose of this question is to demonstrate that the changes in atmospheric properties with altitude are quite different from the changes corresponding to an isentropic process.
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