Transcript Slide 1
* Reading Assignments:
All sections of Chapter 5
6. Transformations of Moist Air
6.1 Description of Moist Air
* The equation of state for vapor:
ev v
R v T
where the specific gas constant for vapor:
R v
M d M v R d
1
v R d
the ratio of molar weights of vapor and dry air:
v
M M d v
0 .
622
* Absolute humidity (density):
v
1
v v
* Specific humidity:
q
m d m v
m v
* Mixing ratio:
r
m v m d
q
1
q
q
* Relation between the mixing ratio and vapor pressure:
r
e p d
p
e
e
e p
* What is the value of specific gas constant for moist air (a mixture of dry air and vapor) ?
R
( 1 0 .
61
q
)
R d
* The equation of state for moist air (a mixture of dry air and vapor):
pv
R T
R d T v
The virtual temperature:
T v
( 1 0 .
61
q
)
T
* Specific heats for moist air:
c c p v
( 1 0 .
97
q
)
c vd
( 1 0 .
87
q
)
c pd
* Saturation Properties:
An indication of
how far
the system is from saturation
Relative humidity
:
RH
e e c
r r c Dew point temperature
:
T d
The temperature to which the system must be cooled
isobarically
to achieve saturation If the saturation is with respect to ice, this temperature is called the frost point temperature
T f Dew point spread
:
T
T d
What is the relation between the relative humidity and dew point spread?
6.2 Implications for the Distribution of Water Vapor
Saturation values represent the maximum amount of water vapor that can be supported by air for a given temperature and pressure.
Saturation vapor pressure depends exponentially on temperature.
* Condensation in the atmosphere by isobaric cooling Radiation fog Advection fog * Global distribution of water vapor
6.3 State variables of the two-component system
6.3.1 Unsaturated moist air Three state variables are required to specify the moist air.
Pressure, temperature and moisture (
p
,
T
,
r
) Because there is only trace amount of vapor, the thermodynamic processes for moist air are very much similar to those for dry air.
The virtual potential temperature:
v
T v
p
0
p
6.3.2 Saturated moist air A mixture of dry air and two phases of water (vapor and condensate) The chemical equilibrium requires
r
r c
,
e
e c
therefore (
p
,
T
)
dh
c p dT du
c v dT
ldr
ldr ds
c p d
ln
l T dr
6.4 Thermodynamic behavior accompanying vertical motion
6.4.1 Condensation and the release of latent heat
Saturation mixing ratio: where
r c
0
r c r c
0 exp
l R v p
1
T p
0
e c
0
p
0 1
T
0 is a reference saturation mixing ratio The saturation mixing ratio increases with decreasing pressure, but decreases with decreasing temperature.
Lifting Condensation Level (LCL):
As an air parcel is lifted it can cool until condensation begins at the cloud base or LCL. Below LCL:
r
const
,
r c
r
Above LCL:
r
r c
6.4.2 The Pseudo-adiabatic process
The pseudo-adiabatic process is nearly identical to a reversible saturated adiabatic process, i.e., an isentropic process.
ds
0 * The condensate does not precipitate out.
* The heat transfer with the environment is negligible.
The equivalent potential temperature is defined as
e
exp
l r c c p T
which is constant during the pseudo-adiabatic process.
* 6.4.3 The saturated adiabatic lapse rate
The saturated parcel’s temperature decreases with height is defined as the
saturated adiabatic lapse rate
, i.e.,
dT dz
1
l c p d dr c dT
s
Because of the release of latent heat,
s
d
s
d
6 .
5
K km
1 9 .
8
K km
1
Problem: On a winter day, the outside air has a temperature of -15 o C and a relative humidity of 70%.
a) If outside air is brought inside and heated to room temperature of 20 o C without adding moisture, what is the new relative humidity?
b) If the room volume is 60 m 3 , what mass of water must be added to the air by a humidifier to raise the relative humidity to 40%?
Meteorology 341 Homework (5)
1. Problem 3 on page 146 2. Problem 4 on page 146 3. Problem 6 on page 147 4. A sample of air has a temperature of 20oC, a relative humidity of 80%, and a pressure of 900 hPa.
a) Find its vapor pressure; b) Find its dewpoint temperature; c) Find its mixing ratio; d) Find the saturation mixing ratio; e) If 1 m 3 of the air is compressed isothermally to a volume of only 0.2 m 3 , find the mass of water that must condensate out in order to eliminate any supersaturation.
6.5 The Pseudo-Adiabatic Chart
The
pseudo-adiabatic chart
is one of many different thermodynamic charts, and is used to describe the
adiabatic
process in the atmosphere. * Adiabats:
const
(dark solid lines) For the dry and unsaturated conditions, temperature changes with height at the rate of
d
* Pseudo-adiabats:
e
const
(dashed lines) For the saturated conditions, temperature varies with height at the rate of
s
* Isopleths of saturation mixing ratio:
r c
const
(thin solid lines)
1. Problem 5 on page 146 2. Problem 10 on page 148 3. Problem 12 on page 148
Meteorology 341 Homework (6)