Model the temperature profile T(z) of the Earth’s atmosphere as a function of height z. Ignore winds, clouds and the many effects due to the presence of moisture in the air and treat the air as an ideal gas. Assume that the Earth’s atmosphere reaches an equilibrium mostly by matter transfer. Suppose that when an air mass moves up or down, it does so adiabatically because the air thermal conductivity is small.A container with equal heights of oil and water, with water filling the spout to its end.A spherical floater used as tub stopper.

a) Show that,where c^*_p is the specific heat at constant pressure per unit mass.

b) Deduce from the temperature profile T (z), the pressure profile p (z) and the mass density profile m(z) of the Earth atmosphere,where c is defined in equation (5.60).

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h h Oil Water a