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2) If this is true, how can this best be squared with the 2nd law of
thermodynamics? If the top and bottom of the column were held at a the
same temperature, there would be a continuous flow of energy from top to
bottom, even though they are the same temperature. Even if the top were
slightly cooler than the bottom, there would be a downward flow. This
would violate a standard statement of the 2nd law, since we have
spontaneous heat from cool to warm.
I've been trying to think of a good way to explain that this is not
indeed a violation.
I suspect the best explanation will have to involve
the more fundamental statement of the 2nd law -- that entropy tends to a
maximum. The adiabatic lapse rate leads to an isentropic gas and a
constant potential temperature.