Mixing and Convection Chapt 4 page 44'

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Mixing and ConvectionChapt 4 page 44.
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Case 1 no condensation
Specific humidity
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Heat lost by warm sample heat gained by cold
sample
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Case 2 condensation and mixing
Question can condensation occur during the
mixing of two unsaturated samples (isobaric
mixing)?
Yes, when you see your breath!
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e
es(T)
e2
e1
T1
T2
T
Isobaric mixing in this case will result in
condensation because es lt ef
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Clausius-Clapeyron
e
es(T)
e2
e1
T1
T2
T
es gt ef so isobaric mixing in this case does NOT
result in condensation.
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How does one determine if condensation will occur?

• 1. Determine T e that would result if NO
  condensation were to occur.
• 2. Compare e with es(T)
• if e lt es(T) - no condensation
• if e gt es(T) - condensation will occur

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If Condensation occurs, what is the final e T?

• e must be less than that calculated assuming no
  condensation because vapor will be removed.
• T must be greater because latent heat has been
  released.

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e
es(T)
(e2 ,T2)
(e1 ,T1)
T
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Latent Heat released during condensation
dq -Lvdw
Isobaric Process dq cpdT
Since w ee/p - Lvdw Lv ede/p cpdT
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To Determine the Final e T
Find the intersection of the isobaric
condensation equation with the Clausius-Clapeyron
equation using eT as initial conditions. The
isobaric condensation equation must be integrated
to arrive at an algebraic form
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The simplified form of the Clausius-Clapeyron equa
tion can be combined with the isobaric condensatio
n equation to find the final values of e and T.
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Since we can not find xo analytically, how
do we proceed?
Expand f and g in a Taylors series f(x)
f(x) f(x)(x- x) g(x) g(x)
g(x)(x- x) Neglect higher order terms and
solve for x.
Isnt this what we did for the CC equation?
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Adiabatic Mixing

• Parcels from different pressure levels are mixed
  after being brought together adiabatically.
• The final state of the combined parcel can be
  calculated as shown previously.
• When a column of air is thoroughly mixed, the
  specific humidity becomes constant throughout.

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Specific Humidity of a Mixed Parcel
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Convective Condensation Level
CCL Pressure and temperature at
which condensation occurs in/at top of a well
mixed layer. It can be found by the
intersection of the dry adiabat for the layer
with the mixing ratio isopleth for the layer.
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Lifting Condensation Level
LCL level at which condensation will occur if
a parcel is lifted from the surface in a
dry adiabatic process with constant w until
just saturated.
Note LCL CCL if the layer is well mixed.
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Homework 4Due Oct. 3

• Problems 4.1, 4.3, 4.5, 4.6