Copyright © 2013 R. R. Dickerson11 Professor Russell Dickerson Room 2413, Computer & Space Sciences...

Copyright © 2013 R. R. Dickerson 11

Professor Russell Dickerson Room 2413, Computer & Space Sciences Building Phone(301) [email protected] 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

2

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.


3

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


4

0000

111

11exp

)(

)(TTfor

TTR

L

TTR

L

Te

Te

v

v

v

v

s

s

e

T

gassolid

liquid

T0


5

Phase Diagram of Water


6


7

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.


8

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


9

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)


10

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.


11

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.


12


13

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))


14

2

)1(

TfR

wL

L

c

wTT

v

v

v

pw

f

f

After extensive algebra:


15

Also note:

TTT

TT

ww

wd

dw

s wT

or

then

; since )(


16

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).


17

p

ve

vep

T

T

p

w

v

pv

p

c

wLTT

wLTTc

dTcdwL

dTcdwLqd

dpdTcqd

e

)(

problem. for this but

:Law1st

0


18

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.


19

p

SkewT

Dry adiabatConstant H2O mixing ratio


20

For completeness

Absolute humidity, v, density of water vapor.

Specific humidity, q, g H2O /kg air

(not dry air). Same as [H2O].


21

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

Copyright © 2013 R. R. Dickerson11 Professor Russell Dickerson Room 2413, Computer & Space Sciences...

Documents

Transcript of Copyright © 2013 R. R. Dickerson11 Professor Russell Dickerson Room 2413, Computer & Space Sciences...