When working out the numerical problems, make sure you use a consistent set of units.

1. Using the hydrostatic equation or by another means show that the mass of a vertical column of air of unit cross section that extends from the surface to the "top" of the atmosphere is

The surface pressure p_o is 1000 millibars where 1 millibar is 100 Pascals and a Pascal is a Newton per square meter. The radius of the earth is 6300 kilometers. From this calculate the total mass of the atmosphere.

If the temperature of the atmosphere is uniform at 300 K, calculate its total enthalpy which may be taken as a measure of its total heat content.

By some method, estimate the mass of the world's oceans and make sure you show your technique.

Assuming the temperature of the oceans is uniform at 275K, calculate its total enthalpy and compare that with the previous calculation. What does this comparison tell you?

2. From the hydrostatic equilibrium equation, derive and show the functional form of the change of pressure vs height.

From that expression and assuming an isothermal temperature for the atmosphere of 240K and a surface pressure of 1000 millibars, estimate the levels of the atmosphere where the pressure is 100, 10 and 1 millibar.

3. Calculate the period of oscillation of an air parcel given that dT/dz = -6.5 K/Km and T = 270K. (your answer should be around 10 minutes).

4. The potential density can be expressed as:

where c_p and c_v are specific heats of air at constant pressure and constant volume. Calculate the potential density of air at a pressure of 600 millibars and temperature = 258 K (typical conditions at an altitude of about 15,000 feet).

Calculate the height at which the pressure is 10% of the surface pressure in the case where there is a uniform lapse rate of 10 K/Km and compare that to the case where the atmosphere has a uniform temperature of 300K. Note that Γ is the dry adiabatic lapse rate