The atmospheric pressure (force per unit area) on a surface at an altitude z is due to t...

The atmospheric pressure (force per unit area) on a surface at an altitude z is due to the weight of the column of air situated above the surface. Therefore, the difference in air pressure p between the top and bottom of a cylindrical volume element of height _z and cross-section area A equals the weight of the air enclosed (density p times volume times gravity g), per unit area:

Let

(a) Derive the equation

(b) If the temperature also varies with altitude T= T(z) , derive the solution

(c) Suppose an engineer measures the barometric pressure at the top of a building to be 99,000 Pa (pascals), and 101,000 Pa at the base (z = z₀). If the absolute temperature varies as determine the height of the building. Take R =8.31 N-m mol-K, M = 0.029 kg mol, and g = 9.8 m sec². (An amusing story concerning this problem can be found at http://www.snopes.com/college/exam/ barometer.asp)