30 November 2000 

You should be able to work all of these problems using the knowledge that you have learned this semester. I expect that you will know the equations that are necessary to solve many of these problems without referring to the text. Use the constants in the Appendix in Bohren and Albrecht.

1. Consider a dry air parcel that is at a pressure of 1000 hPa and temperature of 273 K. If we reduce the volume from 2 m³ to 1 m³ isothermally, what is the new pressure?
2. If we had done the compression adiabatically, what would the temperature be?
3. If we had done the compression adiabatically, what would the pressure be?
4. Consider a dry air parcel that is at a pressure of 1000 hPa and temperature of 273 K. Suppose that we compress this air parcel from 2 m² to 1 m³ at constant pressure. What is the new temperature?
5. How much work is done on the air parcel to reduce the volume at constant pressure?
6. What is the mass of dry air in 10 m³ at a pressure of 950 hPa and temperature of 300 K?
7. What is the density of an air parcel at a pressure of 500 hPa and a temperature of 250 K?
8. How does the energy of an air parcel change as it descends from 700 hPa to 900 hPa adiabatically?
9. Consider an air parcel at the surface that is at a pressure of 1000 hPa and a temperature of 280 K and a thickness of 100 m. If the solar heating rate is 800 watts m^-2, what is the isobaric temperature change in one hour?
10. Consider the heating of an air parcel. What is the ratio of the temperature change that occurs at constant pressure to the temperature change that occurs at constant volume.
11. What is the potential temperature of an air parcel that has a pressure of 200 hPa and a temperature of 200 K?
12. What is the temperature of this air parcel as it is brought adiabatically to 500 hPa?
13. What is the density of an air parcel that contains 1% water vapor at a pressure of 1000 hPa and 293 K?
14. Which air parcel is most buoyant at the same pressure (1000 hPa): one with a temperature of 310 K with no water vapor or one with a temperature of 305 K and a water vapor fraction of 0.01? (That means that the water vapor pressure is 1% of the total pressure.)
15. What is the water vapor saturation pressure if the dry air pressure is 850 hPa and the temperature is 280 K?
16. If the relative humidity is 75% and the temperature is 293 K, what is the saturation vapor pressure? What is the vapor pressure?
17. If the dew point temperature is 275 K, what is the saturation vapor pressure?
18. If the relative humidity is 50% and the dew point temperature is 290 K, what is the vapor pressure?
19. If an air parcel with a temperature of 290 K and a relative humidity of 70% is raised from the surface adiabatically, at what altitude is the lifting condensation level?
20. If an air parcel with temperature of 290 K and a dew point temperature of 280 K is raised from the surface adiabatically, at what altitude is the lifting condensation level?
21. If an air parcel has a temperature of 270 K and a relative humidity of 70%, what is the water vapor partial pressure over liquid water? What is the water vapor pressure over ice? Which is greater?
22. If an air parcel has a temperature of 290 K and a relative humidity of 70%, what is the mass of water vapor in 1 m³?
23. Assume that a cloud has a liquid water content (LWC) of 1 g m^-3. How much solar energy is required to convert all the liquid water to water vapor at a constant temperature for a stratus cloud that is 100 m thick?
24. An ice cube (10 cm³) at 0^oC, when completely melted, will lower the temperature of how much water from 90^o C to 10^oC?
25. How much energy is required to evaporate a water puddle that is 1 m² in area and 1 cm deep? Assume no temperature change.
26. If the mixing ratio, w, is 0.01, and the total pressure is 850 hPa, what is the water vapor partial pressure?
27. If the dew point temperature is 20^oC, and the air temperature is 30^oC, what is the relative humidity? What is the water vapor pressure?
28. What is the saturation water vapor mixing ratio, w_s, if the temperature is 280 K and the total pressure is 850 hPa?
29. What is the water vapor mixing ratio, w, if the temperature is 280 K, the total pressure is 850 hPa, and the relative humidity is 65%?
30. Consider an air parcel rising in a cloud. At cloud base, the temperature is 298 K at 900 hPa. The parcel ascends moist adiabatically up in the cloud, reaching a temperature of 283 K at 590 hPa. What is the water vapor mixing ratio at 590 hPa? What fraction of the water is in the liquid at 590 hPa?