* Reading Assignments:

All sections of Chapter 5

6. Transformations of Moist Air

6.1 Description of Moist Air

* The equation of state for vapor:

TRev vv

where

dv

dv

dv RRM

MR

1

622.0d

vv M

M

the specific gas constant for vapor:

the ratio of molar weights of vapor and dry air:

* Absolute humidity (density):

* Specific humidity:

* Mixing ratio:

* Relation between the mixing ratio and vapor pressure:

vv v

1

vd

v

mm

mq

p

e

ep

e

p

er

d

qq

q

m

mr

d

v

1

* What is the value of specific gas constant for moist air (a mixture of dry air and vapor) ?

* The equation of state for moist air (a mixture of dry air and vapor):

* Specific heats for moist air:

dRqR )61.01(

vdTRTRpv

The virtual temperature: TqTv )61.01(

pdp

vdv

cqc

cqc

)87.01(

)97.01(

* Saturation Properties:

Relative humidity:

Dew point temperature:

Dew point spread:

An indication of how far the system is from saturation

cc r

r

e

eRH

The temperature to which the system must becooled isobarically to achieve saturation

dT

dTT

fTIf the saturation is with respect to ice, this temperatureis called the frost point temperature

What is the relation between the relative humidity and dew point spread?

6.2 Implications for the Distribution of Water Vapor

* Condensation in the atmosphere by isobaric cooling

Radiation fog

Advection fog

* Global distribution of water vapor

Saturation values represent the maximum amount of water vapor thatcan be supported by air for a given temperature and pressure.

Saturation vapor pressure depends exponentially on temperature.

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

Because there is only trace amount of vapor, the thermodynamic processes for moist air are very much similar to those for dry air.

p

pTvv

0

The virtual potential temperature:

),,( rTp

6.3.2 Saturated moist air

A mixture of dry air and two phases of water (vapor and condensate)

cc eerr ,

),( Tp

The chemical equilibrium requires

therefore

drT

ldcds

ldrdTcdu

ldrdTcdh

p

v

p

ln

6.4 Thermodynamic behavior accompanying vertical motion

6.4.1 Condensation and the release of latent heat

Saturation mixing ratio:

0

0

0

11exp

pp

TTRl

r

r v

c

c

where0

00 p

er cc

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: rrconstr c ,

Above LCL: crr

6.4.2 The Pseudo-adiabatic process

The pseudo-adiabatic process is nearly identical to a reversiblesaturated adiabatic process, i.e., an isentropic process.

* The condensate does not precipitate out.

* The heat transfer with the environment is negligible.

0ds

Tc

rl

p

ce exp

The equivalent potential temperature is defined as

which is constant during the pseudo-adiabatic process.

* 6.4.3 The saturated adiabatic lapse rate

The saturated parcel’s temperature decreases with height isdefined as the saturated adiabatic lapse rate, i.e.,

sc

p

d

dTdr

cldz

dT

1

Because of the release of latent heat, ds

1

1

8.9

5.6

kmK

kmK

d

s

Problem:

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 1462. Problem 4 on page 1463. Problem 6 on page 1474. 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 thermodynamiccharts, and is used to describe the adiabatic process in the atmosphere.

* Adiabats: const (dark solid lines)

* Pseudo-adiabats: conste (dashed lines)

* Isopleths of saturation mixing ratio: constrc (thin solid lines)

For the dry and unsaturated conditions, temperature changes with height at the rate of d

For the saturated conditions, temperature varies with height at the rate of s

Meteorology 341 Homework (6)

1. Problem 5 on page 1462. Problem 10 on page 1483. Problem 12 on page 148