Problems

1. Use the hydrostatic equation to show that the mass of a vertical column of air of unit cross section, extending from the ground to great height, is g, where ps is the surface pressure. Insert numbers to estimate the mass on a column or air of area 1 m2. Use your answer to estimate the total mass of the atmosphere.

2. Using the hydrostatic equation, derive an expression for the pressure at the center of a planet in terms of its surface gravity, radius a, and density p, assuming that the latter does not vary with depth. Insert values appropriate for the Earth and evaluate the central pressure. [Hint: the gravity at radius r is g(r) = Gm(r)/r2, where m(r) is the mass inside a radius r and

G = 6.67 x 10-11 kg-1 m3 s-2 is the gravitational constant. You may assume the density of rock is 2000 kg m-3.]

3. Consider a horizontally uniform atmosphere in hydrostatic balance. The atmosphere is isothermal, with temperature of -10°C. Surface pressure is 1000 mbar.

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