It is well-known that the temperature of the atmosphere varies with altitude. In the troposphere, which extends to an altitude of 11 km, for example, the variation of temperature can be approximated by T = T0 - bz, where T0 is the temperature at sea level, which can be taken to be 288.15 K, and B = 0.0065 K/m. The gravitational acceleration also changes with altitude as g (z) = g0 / (1 + z/6,370,320)2 where g0 = 9.807 m/s2 and z is the elevation from sea level in m. Obtain a relation for the variation of pressure in the troposphere
(a) By ignoring and
(b) By considering the variation of g with altitude.