In class we derived the rate at which temperature decreases with altitude in the

Question

In class we derived the rate at which temperature decreases with altitude in the troposphere (the layer of the atmosphere closest to the earth’s surface)

result: dT/dy= - (9.7) k/km "dry adiabatic lapse rate" . To do so, we assumed that the acceleration of gravity is constant near the earth’s surface. This is actually quite a good approximation, but for variety, let’s take into account the inverse-square dependence for the acceleration of gravity, i.e. g(r)=gs(R2e/r2).where gsis the acceleration of gravity near the earth’s surface, r is the distance from the center of the earth, and Reis the radius of the earth. Using this expression for the acceleration of gravity, find an equation giving the temperature as a function of the height above the earth’s surface, assuming that the temperature at the earth’s surface is T0.

Explanation / Answer

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