Moist Air

* Reading Assignments:
All sections of Chapter 5
6. Transformations of Moist Air
6.1 Description of Moist Air
* The equation of state for vapor:
evv  RvT
the specific gas constant for vapor:
Rv 
the ratio of molar weights of vapor and dry air:
Rd  Rd
v 
 0.622
* Absolute humidity (density):
v 
* Specific humidity:
md  mv
* Mixing ratio:
md 1  q
* Relation between the mixing ratio and vapor pressure:
* What is the value of specific gas constant for moist air (a mixture of
dry air and vapor) ?
R  (1  0.61q ) Rd
* The equation of state for moist air (a mixture of dry air and vapor):
pv  R T  Rd Tv
The virtual temperature:
Tv  (1  0.61q)T
* Specific heats for moist air:
cv  (1  0.97q)cvd
c p  (1  0.87q)c pd
* Saturation Properties:
An indication of how far the system is from saturation
Relative humidity:
RH 
ec rc
Dew point temperature: Td
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  Td
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:
 p0 
 p
 v  Tv 
6.3.2 Saturated moist air
A mixture of dry air and two phases of water (vapor and condensate)
The chemical equilibrium requires
r  rc , e  ec
   ( p, T )
dh  c p dT  ldr
du  cv dT  ldr
ds  c p d ln  
6.4 Thermodynamic behavior accompanying vertical motion
6.4.1 Condensation and the release of latent heat
Saturation mixing ratio:
 l  1 1 
exp    
Rv  T T0 
rc 0
p 
 p 
rc 0  c 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 , rc  r
Above LCL:
r  rc
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
 l rc
 e   exp 
 c pT
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.,
 s
dz 1 
c p dT
Because of the release of latent heat,
s  6.5 K km1
d  9.8 K km1
s  d
On a winter day, the outside air has a temperature of -15oC and
a relative humidity of 70%.
a) If outside air is brought inside and heated to room temperature of
20oC without adding moisture, what is the new relative humidity?
b) If the room volume is 60 m3, 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 m3 of the air is compressed isothermally to a
volume of only 0.2 m3, 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: rc  const (thin solid lines)
Meteorology 341
Homework (6)
1. Problem 5 on page 146
2. Problem 10 on page 148
3. Problem 12 on page 148