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Group A—Continued Group B—Continued
3. The density of air at sea level and a temperature of 20°C is about 3 . Using the same air density as the group A exercise, what would be the
3
2
1.2 kg/m . What would be the atmospheric pressure at sea level, atmospheric pressure, in N/m , at an altitude of 12 km if the density
2
in N/m , if the density of air were constant rather than of air were constant rather than decreasing with altitude? (Assume
decreasing with altitude? (Assume constant temperature of 20°C a constant temperature of 20°C and an air column height of 20 km.)
and an air column height of 32 km.)
4. If the density of air were constant with altitude, what would be 4. If the density of air were constant with altitude, what would be the
2
the height of the atmosphere necessary to exert a force of 10 N/m uniform density of the atmosphere necessary to exert a force of
2
3
at sea level? (Assume a constant air density of 1.2 kg/m .) 10 N/m at sea level? (Assume the height of the air column is 32 km.)
5. Meteorologists use the units of millibar and hectopascals (hPa) 5. The air pressure at an altitude of 5.6 km is 7.4 lb/sq in. Using
−3
for expressing atmospheric pressure. One millibar equals 10 bar the conversion factor inside the front cover of the textbook,
and 1 hPa equals 1 millibar. The air pressure at sea level is what is the atmospheric pressure at this altitude in millibars? In
14.7 lb/sq in. Using the conversion factor inside the front cover hectopascals?
of the textbook, what is the atmospheric pressure at sea level in
millibars? In hectopascals?
6. If the atmospheric pressure at 5.6 km is 507 millibars, what is the 6. If the atmospheric pressure in the eye of a hurricane is 9.2 millibars,
barometric pressure measured in inches of mercury? (The what is the barometric pressure measured in inches of mercury?
atmospheric pressure at sea level is 1,013 millibar.) (Normal atmospheric pressure at sea level is 1,013 millibars.)
3
3
7. A helium balloon has a volume of 1.0 m at an altitude of 12 km 7. A helium balloon at sea level had a volume of 1.50 m when it
2
where the atmospheric pressure is 2.5 N/cm . What is the volume was filled. The barometric pressure at sea level was 1,013 hPa.
3
of the helium balloon at sea level? (Use the simplified pressure- What was the volume of the balloon, in m , when it reached an
volume relationship P 1 V 1 = P 2 V 2 , and assume the balloon itself altitude where the pressure was 560 hPa? (Assume the balloon
has no effect on the gas.) itself has no effect on the gas.)
3
3
8. A helium balloon has a volume of 250.0 cm at sea level where the 8. A helium balloon had a volume of 1.50 m when it was filled at
3
pressure is 1,013 hPa. The balloon will burst at a volume of 450.0 cm . an altitude where the atmospheric pressure was 775 hPa. What
What is the atmospheric pressure at the altitude where the was the atmospheric pressure of the balloon, in hPa, at the
3
balloon bursts? (Use the simplified pressure-volume relationship altitude where the volume was 1.20 m ? (Assume the balloon
P 1 V 1 = P 2 V 2 , and assume the balloon itself has no effect on the gas.) itself has no effect on the gas.)
9. The peak wavelength of radiant energy from the Sun can be 9. Using Wien’s displacement law, what is the peak wavelength of
determined from a relationship called Wien’s displacement law. Earth? (Assume a surface temperature of 300 K.)
According to Wien’s displacement law, the peak wavelength in
−3
meters is equal to a constant of 2.897 × 10 K∙m divided by the
temperature in Kelvins. What is the peak wavelength of the Sun?
(Assume a surface temperature of 6,000 K.)
10. Using the value for radiation reflected by clouds in Figure 22.6, 10. Sum the values for radiation scattered by air and reflected by
what is the albedo of the clouds? (Assume the incoming solar clouds and the surface in Figure 22.6. Based on this sum, what is
2
3
radiation is 1.37 × 10 W/m .) the albedo of Earth? (Assume the incoming solar radiation is
2
3
1.37 × 10 W/m .)
11. If the temperature at sea level in Hawaii is 25°C, what is the 11. If the temperature on the edge of the Grand Canyon is 35°C,
temperature at the summit of Mauna Loa based on the average lapse what is the temperature at the bottom of the canyon based on the
rate? (Assume the summit elevation of Mauna Loa is 4,169 m.) average lapse rate? (Assume the bottom of the canyon is 1,350 m
lower in elevation than the rim.)
2
2
2
2
12. If the insolation of the Sun shining on asphalt is 7.3 × 10 W/m , 12. If the insolation of the Sun shining on concrete is 7.3 × 10 W/m ,
2
2
what is the change in temperature of a 1.5 m by 5.0 cm thick what is the change in temperature of a 1.5 m by 5.0 cm thick
layer of asphalt in 1 hr? (Assume the albedo of the asphalt is 0.12, layer of concrete in 1 hr? (Assume the albedo of the concrete is
the specific heat of asphalt is 0.22 cal/gC°, and the density of 0.55, the specific heat of concrete is 0.16 cal/gC°, and the density
3
3
asphalt is 2.3 g/cm .) of concrete is 2.4 g/cm .)
2
2
2
2
13. If the insolation of the Sun shining on white sand is 8.7 × 10 W/m , 13. If the insolation of the Sun shining on seawater is 8.7 × 10 W/m ,
2
2
what is the change in temperature of a 2.0 m by 10.0 cm thick what is the change in temperature of a 2.0 m by 10.0 cm thick
layer of sand in 1 hr? (Assume the albedo of the sand is 0.4, layer of seawater at the surface in 1 hr? (Assume the albedo of the
the specific heat of sand is 0.2 cal/gC°, and the density of sand seawater is 0.4, the specific heat of seawater is 0.92 cal/gC°, and
3
3
is 1.6 g/cm .) the density of seawater is 1.03 g/cm .)
14. In the morning, a stick measuring 0.75 m casts a 0.75 m shadow. 14. In the evening, a stick measuring 0.75 m casts a 2.3 m shadow. At
At noon the same stick casts a 0.01 m shadow. What is the noon the same stick cast a 0.30 m shadow. What is the insolation
insolation in each case? (Assume the maximum insolation on a in each case? (Assume the maximum insolation on a clear day is
3
3
2
2
clear day is 1.0 × 10 W/m .) 1.0 × 10 W/m .)
3
3
15. If the absolute humidity of air at 0°C is 4 g/m , what is the 15. If outside air with an absolute humidity of 4 g/m moves inside a
relative humidity? home and is heated to a temperature of 20°C, what is the relative
humidity after the air has been heated?
564 CHAPTER 22 The Atmosphere of Earth 22-24