3.1.2 Variation of Pressure with Elevation With the variation of temperature in the troposphere as found above, it is now rather straightforward to find the variation in pressure with (geopotential) elevation. Once again, beginning with the expression for a small change in pressure, dp = -pg dz and assuming air to be an ideal gas: dp gp RT dz The Standard Atmosphere Elev (m) T (K) p (kPa) 0 288.2 101.33 In = go To + Az In 500 284.9 95.46 And finally, XR 1,000 281.7 89.88 2,000 275.7 79.50 5,000 255.7 54.05 go 8,850 230.7 31.50 XR p(z) = = Po 1+ (3.2) 11,000 216.8 22.70 To See Appendix E for more details. Exercise 3.1 (ii) (a) Verify Eq. 3.2. Note the use of go, rendering z to be goepotential height. (b) Using the values of Earth's radius and gravity at sea-level derive a simple equation for geopotential height as a function of geometric altitude. (c) Estimate the atmospheric pressures at 410, 1609, 2250, and 3640 meters.