EAS 370: Atmospheric Physics
Assignment 3: Due in class Wednesday November 10 at 10am.
1. A person perspires. How much liquid water (as a percentage of the person’s mass) must
evaporate to lower the temperature of the person by 5.0◦ C.
[For this problem, take the latent heat of vapourization to be Lv = 2.5 × 106 J/(kg) and
take the specific heat of the human body to be that of water, c = 4.2 × 103 J/(kg K).]
2. Air at temperature T = 5.0◦ C has a relative humidity of 85%. Using the approximate
formula for the saturation vapour pressure,
Lv
es (T ) = e0 exp
Rv
1
1
−
T0 T
,
find the partial vapour pressure (in hPa) and the dew point Td (in ◦ C).
Compute T −Td and compare this result with the heuristic formula given in class for T −Td
as it depends upon relative humidity.
[For this problem, take T0 = 273.16 K for which e0 = 6.11 hPa and Lv = 2.50 × 106 J/(kg).
Rv = 461 J/(kg K).]
3. A parcel of moist air has a total pressure of 975 hPa and a temperature of 15.0◦ C. If the
mixing ratio is 1.80 g/kg, what are the water vapour pressure (in hPa) and the virtual
temperature (in ◦ C)?
4. A parcel of moist air at the ground (where p = 1 atm) is at its dew point temperature
of 5.0◦ C. The parcel is carried upward cooling until it loses all of its contained water.
Thereafter it descends adiabatically back to the ground. What is the temperature of this
dry parcel of air (in ◦ C)?
5. Moist air at 1000 hPa has a temperature of 20◦ C and a mixing ratio of 10 g/kg. Using the
attached “skew T - ln p” chart, answer the following questions:
a) What is the lifting condensation level (in hPa)?
b) The parcel is lifted to 700 hPa. What mass of water vapour (in grams) per kilogram
of air has condensed out.
c) The parcel then descends to 900 hPa. Assuming 80% of the condensed water rains
out, what is the resulting temperature of the air (in ◦ C)?
With your solution, include the sketch of the “path” of moist air drawn on the “skew
T -ln p” chart.