1. (a) Calculate the vapor pressure of water, the relative humidity, and the water vapor mixing ratio (both volume and mass) of an air parcel at sea level that has a temperature of 28 ^oC and a dewpoint temperature of 15 ^oC.

(b) If the air in part (a) rises adiabatically to an altitude where the pressure is 800 mb, what are the water vapor mixing ratio, the water vapor pressure, the relative humidity, and the dewpoint?

2. In a Chinook wind storm Boulder experiences strong westerly winds, and the air often has descended from the continental divide. There are often orographic clouds caused by flow of air forced upward by the mountains to the west of Boulder. Use a thermodynamic diagram and the information below to investigate the air flowing from Grand Junction (in western Colorado) to Boulder.

(a) Grand Junction, P = 850 mb, T = 11.5^oC, RH = 70%. Use the diagram to find the water vapor mixing ratio, the dewpoint, and the potential temperature of this air at the start of its journey over the mountains.

(b) As the westerly flow forces the air parcel up over the mountains, find the pressure level and temperature at which the parcel becomes saturated. What is this level called?

(c) Find the temperature, the water vapor mixing ratio, the potential temperature, and the equivalent potential temperature when the air reaches the continental divide at 600 mb. How much water vapor has condensed (g/kg)?

(d) Check the validity of your graphical results by calculating the equivalent potential temperature for the initial parcel at 850 mb and the parcel at 600 mb. Remember, for unsaturated parcels use the temperature and saturation mixing ratio at the LCL. Why are the two q_e values at Grand Junction and at the continental divide equal?

(e) The air parcel continues its trajectory down to Boulder at 850 mb. Assume all the condensed water precipitated out on the west slope of the mountains, so that the parcel is unsaturated as it flows down to Boulder. (Actually some portion of the cloud would evaporate on the way down.) Use the diagram to find the air temperature and the relative humidity in Boulder. How much warmer is the air in Boulder than in Grand Junction? Why is it warmer, even though it started and ended at the same pressure?

3. (5710 question) The saturation vapor pressure with respect to an ice surface is lower than with respect to a water surface. This fact is very important for cloud microphysics.

(a) Use the Clausius-Clapeyron equation to derive an expression for the difference in saturation vapor pressures e_s-e_si as a function of temperature. You may assume that the latent heats of vaporization and sublimation and the heat capacities are constant.

(b) Find an expression for the temperature of maximum difference in saturation vapor pressures. Calculate this temperature.

(c) What is the percent saturation with respect to ice at this temperature, or 100(e_s/e_si)?