Post on 13-Dec-2015
Copyright © 2013 R. R. Dickerson 11
Professor Russell Dickerson Room 2413, Computer & Space Sciences Building Phone(301) 405-5364russ@atmos.umd.edu web site www.meto.umd.edu/~russ
AOSC 620PHYSICS AND CHEMISTRY
OF THE ATMOSPHERE, ILecture 5A, Moist Air
Copyright © 2013 R. R. Dickerson & Z.Q. Li
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Dew Point Temperature Td
Temperature to which moist air may be cooled with pressure and mixing ratio held constant to just reach saturation with respect to H2O.
The “frost point” is the saturation temperature with respect to ice.
Copyright © 2013 R. R. Dickerson & Z.Q. Li
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At the dewpoint w = ws(Td, P)
)(
)(
ds
ds
TeP
Tew
As in Henry’s Law, at a given temperature
dv
vsds
v
vss
TTR
LTeTe
TTR
LTeTe
11exp)()(
11exp)()(
00
00
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0000
111
11exp
)(
)(TTfor
TTR
L
TTR
L
Te
Te
v
v
v
v
s
s
e
T
gassolid
liquid
T0
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Phase Diagram of Water
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Wet-Bulb Temperature Tw
Temperature to which air may be cooled by evaporating water into it at constant pressure. When water is evaporated into air, energy is added to the water. This energy comes at the expense of the dry dry air,air, which is cooled.
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Consider
1. Isobaric process2. Mixing ratio increased by evaporating water into air: w => ws(Tw,p)
The heat necessary to evaporate dw grams of water per kilogram of dry air is:
dq = Lvdw
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To find the heat lost to dry air alone due to evaporation of water, we must correct for the mass of the water that the dry air now contains:
dwc
L
w
dw
c
LdT
dTcw
dwLqdor
dwLqdw
p
v
pm
v
pmv
v
1
1
')1(
Integrate from T to Tw
w => ws(Tw,p)
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p
v
ws
w
wsp
vw
c
L
ww
TTor
wwc
LTT
T
T
)(
)( )()(
Useful for isobaric condensation.Measure using a Sling Pychrometer or aspirated wet and dry bulbs:We measure T and Tw. Since ws is a known function of Tw and p, you can determine w from ws and the above equation.
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Alternatively, if w and T are known, one can calculate the wet bulb temperature Tw.
Example:
pew
pew wTwTs
/)()(
We may now apply the Clausius Clapeyron equation.
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Copyright © 2013 R. R. Dickerson & Z.Q. Li
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From Isobaric Condensation:
wwc
LTT wTs
p
vw )()(
The Clausius Clapeyron Equation gives:
wv
svss TTR
wLww TTT
w
11)()()(
Solve for Tw:
(f = w/ws(T))
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2
)1(
TfR
wL
L
c
wTT
v
v
v
pw
f
f
After extensive algebra:
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Also note:
TTT
TT
ww
wd
dw
s wT
or
then
; since )(
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Equivalent Temperature Te
Temperature a sample of moist air would reach if all the moisture were condensed out at constant pressure (i.e., latent heat converted to sensible heat).
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p
ve
vep
T
T
p
w
v
pv
p
c
wLTT
wLTTc
dTcdwL
dTcdwLqd
dpdTcqd
e
)(
problem. for this but
:Law1st
0
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Isentropic Condensation Temperature Tc
Tc is the temperature at which saturation is reached when moist air is cooled adiabatically with w held constant. See R&Y Figure 2.3 or W&H Figure 3.10.
Tc can be determined by the intersection of the adiabatic equation (Poisson’s) and the Clausius Clapeyron equation and found on a SkewT.
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p
SkewT
Dry adiabatConstant H2O mixing ratio
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For completeness
Absolute humidity, v, density of water vapor.
Specific humidity, q, g H2O /kg air
(not dry air). Same as [H2O].
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Conservative Properties of Air Parcels
C NC
e C C
w C C
Td NC NC
Tw NC NC
w C NC
T* NC NC
Te NC NC
Tc C NC
f NC C
q C C
Variable dry adiabatic saturated/pseudo adiabatic