Suppose the vertical temperature gradient takes on a constant value dT/dz=? (whe

Question

Suppose the vertical temperature gradient takes on a constant value dT/dz=? (where ? is constant throughout the troposphere). The values of the temperature and pressure at the ground (z=0) are T_0 and P_0, respectively. How does the pressure vary with height in the troposphere? Leave your answer in terms of the P_0, T_0, ?, and of course z. Consider the atmosphere to be dry. Note: there's enough information given where you can derive a formula for T(z). It will be convenient to do that first. In the course of obtaining the solution for p(z) you may need to review the rules and properties of ln.

Explanation / Answer

use linear parts, integrate from bottom to top...

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