Various Measures of Water Vapor Content

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Various Measures of Water Vapor Content

• Virtual temperature
• Dew point temperature
• Wet bulb temperature
• Equivalent temperature
• Isentropic Condensation Temperature

• Vapor pressure
• Vapor density absolute humidity
• Mixing ratio
• Specific humidity
• Relative humidity

• Potential temperature
• Wet-bulb potential temperature
• Equivalent potential temperature

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Consider a mixture of dry air and water vapor.
Let Md mass of dry air Mv mass of water
vapor md molecular weight of dry air mv
molecular weight of water.
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Water Vapor Pressure
Equation of state for water vapor ev rv Rv
T where ev is the partial pressure of water vapor
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Clausius-Clapeyron
Lv latent heat of vaporization
Where es is saturation water vapor pressure which
is held constant during phase change
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Also assume T is constant
Combine this equation with the last one
The combination is a constant for isothermal,
isobaric change of phase.
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Gibbs Function G
G is a state variable and dG is an exact
differential
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This is the original form of the
Clausius-Claeyron Eq. Since density of water
vapor is much lower than liquid water, i.e. a2gtgta1
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Assuming Lv is constant
For T0oC es6.11 mb Lv2500 J/g
Saturation water vapor pressure is
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Water Vapor Variables (Continued)

• Vapor pressure relative pressure of water vapor
  e
• Absolute humidity or vapor density rv
• Mixing ratio
• wMv/Mdrv/rd ee/(p-e) ee/p
• rve/RvT emv/RT
• rd (p-e)/RdT(p-e)md/RT
• Relative humidity
• fw/ws(p,T) e/es
• Specific humidity
• qrv/(rd rv)ee/p

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Virtual Temperature Tv or T
Temperature dry air would have if it had the
same density as a sample of moist air at the
same pressure.
Question should the virtual temperature be
higher or lower than the actual temperature?
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Daltons law P Spi
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Combine P and r to eliminate V
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Since P rRT
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Unsaturated Moist Air
Equation of state Pa RT
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Specific Heats for Moist Air
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Likewise, for constant pressure
So Poissons equation becomes
(10.6w)/(10.9w) gt (1-0.2w) due to rounding
error.
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Methods for Reaching Saturation
Relative humidity

• f increases by
• Increasing w by adding water vapor
• Decreasing ws while keeping w constant
• decrease temperature, etc.
• Many paths have theoretical and/or practical
  significance.

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Dew Point Temperature Td
Temperature to which moist air may be cooled with
pressure and mixing ratio constant in order for
it to just reach saturation with respect to
H2O. The frost point is the saturation
temperature with respect to ice.
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At the dewpoint w ws(Td,P)
At a given temperature
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liquid
e
solid
gas
T
T0
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Wet-Bulb Temperature Tw
Temperature to which air may be cooled by
evaporating water into air at constant pressure.
When water is evaporated, energy is added to the
water. This energy comes at the expense of the
dry air, which is cooled.
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Consider 1. Isobaric process 2. Mixing ratio
increased by evaporating water into air w
gt 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 from it, we must correct for
the mass of the water the air contains
Integrate from T to Tw
w gt ws(Tw,p)
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Measure T, 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
We may now apply the Clausius Clapeyron equation.
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From Isobaric Condensation
The Clausius Clapeyron Equation gives
Solve for Tw
(f ws(T))
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Also note
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Adiabatic Wet Bulb Temperature Twa
Follow pseudo/saturated adiabats from Pe, Tc to
initial pressure. Tw- Twa 0.5o or less.
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Equivalent Temperature Te
Temperature a sample of moist air would obtain if
all the moisture were condensed out at constant
pressure (i.e. latent heat converted to sensible
heat).
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Equivalent Potential Temperature qe
qe is the temperature that a parcel of air would
have if all of its latent heat were converted to
sensible heat in a pseudoadiabatic expansion to
low pressure, followed by a dry adiabatic
compression to 1000 mb.
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Adiabatic Equivalent Temperature Tea
Instead of compressing to 1000 mb, we go instead
to the initial pressure.
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Note
Since T is in the range of 200-300 K and w is
generally lt 20 x 10-3
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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. Tc can be determined by
the intersection of the adiabatic equation
(Poissons) and the Clausius Clapeyron equation.
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Poisson
p
Clausius Claypeyron
T
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Conservative Properties of Air Parcels
Variable dry adiabatic
saturated/pseudo adiabatic
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Homework 2Sep 19

• Problems 2.2, 2.3 in the textbook
• Generate your own tephigram based on the formulae
  introduced.