Physics 137 - Introduction to the Atmosphere and Weather                                                                            Homework Key - Assignment #4
Revised Winter 2007

4-QT3. Explain how and why each of the following will change as a parcel of air with an unchanging amount of water vapor rises, expands, and cools: (a) absolute humidity; (b) relative humidity; (c) actual vapor pressure; (d) saturation vapor pressure.

    (a) The total amount of water vapor in the parcel will remain constant but the volume of the parcel increases hence the absolute humidity (= mass of water vapor per unit volume) decreases.
    (b) Because of cooling the relative humidity increases.
    (c) The expansion results from a reduction in total air pressure and, since the actual vapor pressure remains a fixed fraction of that total pressure, the actual vapor pressure decreases.
    (d) Because of cooling the saturation vapor content of the air and therefore the saturation vapor pressure decreases.

4-QT6. On a clear, calm morning, water condenses on the ground in a thick layer of dew. As the water slowly evaporates into the air, you measure a slow increase in dew point. Explain why.

    Because of the evaporation of the dew the water vapor content of the air increases. Thus the dew point increases.

4-QT8.   Suppose the dew point of cold outside air is the same as the dew point of warm air indoors. If the door is opened, and cold air replaces some of the warm inside air, would the new relative humidity indoors be (a) lower than before, (b) higher than before, or (c) the same as before?  Explain your answer.

    The dew point of the inside air would be unaffected by the mixing. However the inside temperature would drop and, as a consequence of that temperature change, (b), the inside relative humidity would increase.

4-PE1.   On a bitter cold, snowy morning, the air temperature and dew point of the outside air are -7°C. If this air is brought indoors and warmed to 21°C, with no change in vapor content, what is the relative humidity of the air inside the home?  (Hint: See Table 1, p. 98.)

    From Table 1, if the air temperature is -7°C, the saturation vapor pressure is es=3.7 mb, and, if the dew point is also -7°C, then the actual vapor pressure equals the saturation vapor pressure, or e =3.7 mb. However at the indoor temperature of 21°C the saturation vapor pressure is es=25.0 mb. Hence the indoor relative humidity is RH = e/es = 3.7 mb/25.0 mb = 15%..

4-PE2.   (a) With the aid of Fig. 4.13b,  p. 94, determine the average summer dew points in St. Louis, MO; New Orleans, LA; and Los Angeles, CA. (b) If the high temperature on a particular summer day in all three cities is 32°C (90°F), then calculate the afternoon relative humidity at each of the three cities. (Hint: Either Fig. 4.10, p. 91, or Table 1, p. 98, will be helpful.)

    (a) Using Fig. 4.13b to infer summer dew points (temperatures at which the actual vapor pressures equal the saturation vapor pressures) yields: St. Louis:  Tdew= 18.3°C (65°F); New Orleans:  Tdew= 23.8°C (75°F); Los Angeles:  Tdew= 10.8°C (51°F).
    (b) Since RH=e/es and since the saturation vapor pressure at 32°C is es=48.1 mb, we get for each of the three cities, using Table 1 to infer the actual vapor pressure e from the inferred dew point:  St. Louis: RH = 21.7 mb/48.1 mb = 45%; New Orleans: RH = 27.6 mb/48.1 mb = 57%; Los Angeles: RH = 14.4 mb/48.1 mb = 30%.

4-PE4.   If the air temperature is 35°C and the dew point is 21°C, determine the relative humidity using (a) Table 1, p. 98; (b) Fig. 4.10, p. 91, and (c) Tables D.1 and D.2 in Appendix D.

    (a) Entering a temperature of 35°C in Table 1 yields a saturation vapor pressure of es=56.2 mb. Entering the dew point temperature of 21°C yields the actual vapor pressure, e = 25.0 mb. Hence the relative humidity is RH = e/es = 25.0 mb/56.2 mb = 44.5%.
    (b) Entering a temperature of 35°C in Figure 4.10 yields a saturation vapor pressure of es=56 mb. Entering the dew point temperature of 21°C yields the actual vapor pressure, e=25 mb. Hence the relative humidity is RH = e/es= 25 mb/56 mb= 45%.
    (c) Entering a (dry-bulb) temperature of 35°C and a dew point temperature of 21°C in Table D.1 yields a wet-bulb depression of 10.0°C. Entering a (dry-bulb) temperature of 35°C and a wet-bulb depression of 10.0°C in Table D.2 yields a relative humidity of RH = 44%. Within the accuracy of rounding errors, all three methods yield the same result.